From 32b0dbc364af3b468be50e18797acf9352f2ff94 Mon Sep 17 00:00:00 2001 From: Jessie Yu Date: Mon, 4 Mar 2024 15:44:38 -0500 Subject: [PATCH] Fast forward experimental-0.2 (#1464) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit * Migrate fake backends from `qiskit.providers.fake_provider` (#1140) * Migrate fake provider * fix lint * Only migrate backends and fake_provider file to minimize duplication * Add reno * Update snippet to use runtime service --------- Co-authored-by: Kevin Tian * Fix BYOB job results bytes typing issue (#1220) * try/except raw result truncation * catch typeError * revert try/except, use response.text * update unit test * Fix fake backends integration test (#1225) * Clean up/fix integration test * Update test case * Fix black * Added deprecation warning when using qiskitrc file (#1219) * Added deprecation warning when using qiskitrc file * Fixed bug whereby deprecation warnings cause failure for all 'qiskit*' modules. Changed warning to deprecation warning. * Release note * Small grammer fix * black --------- Co-authored-by: Kevin Tian * Update session.from_id() (#1163) * update session.from_id() * add deprecation warning * add reno * Prepare release 0.15.0 (#1226) * Update main branch 0.16.0 (#1227) * Revert `Session.from_id 0.15.0` changes (#1229) * Revert "Update session.from_id() (#1163)" This reverts commit 8fa0472e15ea36341acd6de67efa54a9815354e8. * add reno * Prepare release 0.15.1 (#1230) * Update main branch to 0.16.0 again (#1232) * Remove all code related to custom programs (#1192) * initial removal * cleanup more files * move result_decoder * fix lint * update unit tests * update integration tests * more docs changes * release note * fix path --------- Co-authored-by: Jessie Yu * Make sessions thread safe (#1196) * Make sessions thread safe. The lock prevents other threads from sending new jobs to the service only if the session hasnot been setup yet. I.e.: when sending the first "session starter job", or root job. After this happens, the code is left unlocked to allow threads to access the service concurrently. Error handling is needed to ensure the lock is always released. * Allow multiple sessions to execute simultaneously * Make session test more deterministic --------- Co-authored-by: Kevin Tian Co-authored-by: Jessie Yu * Instance & channel_strategy validation (#1233) * compare cloud instance with channel strategy * fix unit tests * error wording --------- Co-authored-by: Jessie Yu * Prepare release 0.16.1 (#1239) * release notes * fix release * update to 0.17 (#1240) * Stop referring to qiskit.org in API docs (#1242) * Add job.properties() method (#1252) * Add job.properties() method * add reno * Remove non-API docs and translations (#1256) This is the same as https://github.com/Qiskit/qiskit/pull/11352. Now that qiskit.org/ecosystem/ibm-runtime redirects to docs.quantum.ibm.com, we can simplify the docs. See the PR description in https://github.com/Qiskit/qiskit/pull/11352 for details on the motivation for each change. The only difference from Qiskit is that we still keep the tutorials around because learning.quantum.ibm.com uses them. I used a script with `ripgrep` to confirm that none of the images were in use. * Raise error if backend retrieved not in current instance (#1249) * Error if backend not in instance * add reno * update reno * docs build * fix docs again * docs formatting :/ * add integration test * Update test/integration/test_backend.py Co-authored-by: merav-aharoni * Update test/integration/test_backend.py Co-authored-by: merav-aharoni --------- Co-authored-by: merav-aharoni * Fix backend_converter `faulty_qubit` name error (#1257) * fix backend_converter * add reno * Update Tutorial section names (#1241) * The transpilation tutorial has been updated to use the new runtime transpilation passes, and Batch * Fix style checker * Updated names * Updated section names for transpiled tutorial * Updated grover * Fixed consistency * Final updates --------- Co-authored-by: Kevin Tian * make test_backend_wrong_instance IQP only (#1258) * Add pointer to qiskit/documentation issues (#1260) * add pointer to qiskit/documentation issues * Update .github/ISSUE_TEMPLATE/config.yml Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> * Update CONTRIBUTING.md Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> --------- Co-authored-by: Kevin Tian Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> * Update `test_backend_wrong_instance` (#1259) * wip debug wrong instance test * enable integration test * use backend names instead of obj * Don't block for the first job in a session (#1170) * don't block if backend not selected * add reno * add test * Add `activated_at` field to session.details() (#1266) * add activated_at to session.details() * add reno * Revert "Don't block for the first job in a session (#1170)" (#1267) * Revert "Don't block for the first job in a session (#1170)" This reverts commit f2e24e49829360af4381cb0ffc46f62e343054fa. * keep test * Prepare release 0.17.0 (#1268) * update main branch 0.17.1 (#1269) * Remove test_session_no_backend (#1272) * Added RuntimeJob.queue_info() method (#1210) * Added support for RuntimeJob.queueinfo * Moved methods for consistency with main * Changed backend_status to job.status * lint * update test --------- Co-authored-by: Kevin Tian * Replace programs with primitives in api docs (#1281) * programs -> primitives * address comment * Deprecate service.runtime (#1278) * Deprecate service.runtime * add reno * Removed support for qiskitrc file (#1121) * Removed support for qiskitrc file * lint --------- Co-authored-by: Kevin Tian * Add max_time parameter to IBMBackend.open_session() (#1274) * Added max_time to IBMBackend.open_session. * Release note * Changed format of test * Migrate fake backend base classes (#1270) Co-authored-by: Kevin Tian * Add Q-CTRL integration tests (#1173) * add initial qctrl test file * add test & decorator * add tests from Mirko * Added assertness for preciseness of results * remove print statements * move into e2e folder * setup ci * Update q-ctrl-tests.yml * add account test * add more account tests * Update test/qctrl/test_qctrl.py Co-authored-by: Rathish Cholarajan * address comments * update date to 2023 * Update test/qctrl/test_qctrl.py Co-authored-by: Blake Johnson * Update test/qctrl/test_qctrl.py Co-authored-by: Blake Johnson --------- Co-authored-by: merav-aharoni Co-authored-by: Rathish Cholarajan Co-authored-by: Blake Johnson * update grover tutorial equation (#1293) * Add dynamic circuits backend filter (#1291) * Add dynamic circuits backend filter * add reno * switch docs from mathjax to katex (#1301) Updates the sphinx documentation build to use KaTeX instead of MathJax because the final docs build uses KaTeX. The same change was made in Qiskit in https://github.com/Qiskit/qiskit/pull/11435. * Remove qiskit.org links (#1302) * Update session_id docstring (#1304) * Update provider and qiskit versions (#1305) * Exclude params on job retrieval by default (#1308) * exclude params on job retrieval by default * add reno * add test * Reactive the viewcode extension for docs (#1312) We got source links working in API docs on docs.quantum.ibm.com! See https://github.com/Qiskit/documentation/pull/620. To do this, we need to active `sphinx.ext.viewcode`. Note that we still plan to improve this implementation in the future to have more precise links by using `sphinx.ext.linkcode`, tracked by https://github.com/Qiskit/documentation/issues/517. This PR is to unblock the first iteration of this source links mechanism. * Add config files to manifest (#1319) * Fix pip environment resolution (#1329) Calling `pip install` multiple times can (deeply unfortunately) allow an environment to become out-of-sync; `pip` doesn't "remember" the constraints of previous installation commands. One of the largest effects here is that doing `pip install -e .` _followed_ by `pip install git+@main` installs `qiskit-terra` from the initial installation (via `qiskit==0.45.2`), then installs `qiskit==1.0.0.dev0` from Git, which is an incompatible environment. Doing the whole environment resolution in a single `pip install` command fixes this, as the `qiskit` dependency is correctly resolved to be _only_ the `1.0.0.dev0` version. Co-authored-by: Kevin Tian * Use IBM-Provider-vendored pub/sub mechanism (#1328) This is being removed from Qiskit 1.0, and the IBM Provider is (until deprecated) taking over brokering the IBM-Runtime-internal events. Co-authored-by: Kevin Tian * Add transpiler tests (#1323) * Add transpiler tests * remove qiskittestcase * Prepare release 0.18.0 (#1335) * Update main branch 0.18.1 (#1336) * Turn off qiskit.org docs deploy (#1340) * Remove `qiskit.test` (#1292) * replace qiskit.test.ReferenceCircuits * replace BaseQiskitTest * Update qiskit_ibm_runtime/qiskit_runtime_service.py Co-authored-by: Jessie Yu * Update qiskit_ibm_runtime/sampler.py Co-authored-by: Jessie Yu * Update qiskit_ibm_runtime/session.py Co-authored-by: Jessie Yu * Update test/utils.py Co-authored-by: Jessie Yu --------- Co-authored-by: Jessie Yu * Add missing API Refs to docs (#1343) ### Summary The documentation from the `transpile` and `fake_provider` modules does not appear in the rendered docs in qiskit.org/documentation or docs.quantum-computing.ibm.com. ### Details and comments Fixes [Qiskit Docs Issue #238](https://github.com/Qiskit/documentation/issues/238) Replaces PR #1330. Transpiler Doc files added: - qiskit_ibm_runtime.transpiler.passes.html - qiskit_ibm_provider.transpiler.passes.basis.html - qiskit_ibm_provider.transpiler.passes.scheduling.ALAPScheduleAnalysis.html - qiskit_ibm_provider.transpiler.passes.scheduling.ASAPScheduleAnalysis.html - qiskit_ibm_provider.transpiler.passes.scheduling.BlockBasePadder.html - qiskit_ibm_provider.transpiler.passes.scheduling.DynamicCircuitInstructionDurations.html - qiskit_ibm_provider.transpiler.passes.scheduling.html - qiskit_ibm_provider.transpiler.passes.scheduling.PadDelay.html - qiskit_ibm_provider.transpiler.passes.scheduling.PadDynamicalDecoupling.html
Fake Provider Docs added: - qiskit_ibm_runtime.fake_provider.FakeAlmaden.html - qiskit_ibm_runtime.fake_provider.FakeAlmadenV2.html - qiskit_ibm_runtime.fake_provider.FakeArmonk.html - qiskit_ibm_runtime.fake_provider.FakeArmonkV2.html - qiskit_ibm_runtime.fake_provider.FakeAthens.html - qiskit_ibm_runtime.fake_provider.FakeAthensV2.html - qiskit_ibm_runtime.fake_provider.FakeAuckland.html - qiskit_ibm_runtime.fake_provider.FakeBelem.html - qiskit_ibm_runtime.fake_provider.FakeBelemV2.html - qiskit_ibm_runtime.fake_provider.FakeBoeblingen.html - qiskit_ibm_runtime.fake_provider.FakeBoeblingenV2.html - qiskit_ibm_runtime.fake_provider.FakeBogota.html - qiskit_ibm_runtime.fake_provider.FakeBogotaV2.html - qiskit_ibm_runtime.fake_provider.FakeBrooklyn.html - qiskit_ibm_runtime.fake_provider.FakeBrooklynV2.html - qiskit_ibm_runtime.fake_provider.FakeBurlington.html - qiskit_ibm_runtime.fake_provider.FakeBurlingtonV2.html - qiskit_ibm_runtime.fake_provider.FakeCairo.html - qiskit_ibm_runtime.fake_provider.FakeCairoV2.html - qiskit_ibm_runtime.fake_provider.FakeCambridge.html - qiskit_ibm_runtime.fake_provider.FakeCambridgeV2.html - qiskit_ibm_runtime.fake_provider.FakeCasablanca.html - qiskit_ibm_runtime.fake_provider.FakeCasablancaV2.html - qiskit_ibm_runtime.fake_provider.FakeEssex.html - qiskit_ibm_runtime.fake_provider.FakeEssexV2.html - qiskit_ibm_runtime.fake_provider.FakeGeneva.html - qiskit_ibm_runtime.fake_provider.FakeGuadalupe.html - qiskit_ibm_runtime.fake_provider.FakeGuadalupeV2.html - qiskit_ibm_runtime.fake_provider.FakeHanoi.html - qiskit_ibm_runtime.fake_provider.FakeHanoiV2.html - qiskit_ibm_runtime.fake_provider.FakeJakarta.html - qiskit_ibm_runtime.fake_provider.FakeJakartaV2.html - qiskit_ibm_runtime.fake_provider.FakeJohannesburg.html - qiskit_ibm_runtime.fake_provider.FakeJohannesburgV2.html - qiskit_ibm_runtime.fake_provider.FakeKolkata.html - qiskit_ibm_runtime.fake_provider.FakeKolkataV2.html - qiskit_ibm_runtime.fake_provider.FakeLagos.html - qiskit_ibm_runtime.fake_provider.FakeLagosV2.html - qiskit_ibm_runtime.fake_provider.FakeLima.html - qiskit_ibm_runtime.fake_provider.FakeLimaV2.html - qiskit_ibm_runtime.fake_provider.FakeLondon.html - qiskit_ibm_runtime.fake_provider.FakeLondonV2.html - qiskit_ibm_runtime.fake_provider.FakeManhattan.html - qiskit_ibm_runtime.fake_provider.FakeManhattanV2.html - qiskit_ibm_runtime.fake_provider.FakeManila.html - qiskit_ibm_runtime.fake_provider.FakeManilaV2.html - qiskit_ibm_runtime.fake_provider.FakeMelbourne.html - qiskit_ibm_runtime.fake_provider.FakeMelbourneV2.html - qiskit_ibm_runtime.fake_provider.FakeMontreal.html - qiskit_ibm_runtime.fake_provider.FakeMontrealV2.html - qiskit_ibm_runtime.fake_provider.FakeMumbai.html - qiskit_ibm_runtime.fake_provider.FakeMumbaiV2.html - qiskit_ibm_runtime.fake_provider.FakeNairobi.html - qiskit_ibm_runtime.fake_provider.FakeNairobiV2.html - qiskit_ibm_runtime.fake_provider.FakeOslo.html - qiskit_ibm_runtime.fake_provider.FakeOurense.html - qiskit_ibm_runtime.fake_provider.FakeOurenseV2.html - qiskit_ibm_runtime.fake_provider.FakeParis.html - qiskit_ibm_runtime.fake_provider.FakeParisV2.html - qiskit_ibm_runtime.fake_provider.FakePerth.html - qiskit_ibm_runtime.fake_provider.FakePoughkeepsie.html - qiskit_ibm_runtime.fake_provider.FakePoughkeepsieV2.html - qiskit_ibm_runtime.fake_provider.FakePrague.html - qiskit_ibm_runtime.fake_provider.FakeProviderForBackendV2.html - qiskit_ibm_runtime.fake_provider.FakeProvider.html - qiskit_ibm_runtime.fake_provider.FakeQuito.html - qiskit_ibm_runtime.fake_provider.FakeQuitoV2.html - qiskit_ibm_runtime.fake_provider.FakeRochester.html - qiskit_ibm_runtime.fake_provider.FakeRochesterV2.html - qiskit_ibm_runtime.fake_provider.FakeRome.html - qiskit_ibm_runtime.fake_provider.FakeRomeV2.html - qiskit_ibm_runtime.fake_provider.FakeRueschlikon.html - qiskit_ibm_runtime.fake_provider.FakeSantiago.html - qiskit_ibm_runtime.fake_provider.FakeSantiagoV2.html - qiskit_ibm_runtime.fake_provider.FakeSherbrooke.html - qiskit_ibm_runtime.fake_provider.FakeSingapore.html - qiskit_ibm_runtime.fake_provider.FakeSingaporeV2.html - qiskit_ibm_runtime.fake_provider.FakeSydney.html - qiskit_ibm_runtime.fake_provider.FakeSydneyV2.html - qiskit_ibm_runtime.fake_provider.FakeTenerife.html - qiskit_ibm_runtime.fake_provider.FakeTokyo.html - qiskit_ibm_runtime.fake_provider.FakeToronto.html - qiskit_ibm_runtime.fake_provider.FakeTorontoV2.html - qiskit_ibm_runtime.fake_provider.FakeValencia.html - qiskit_ibm_runtime.fake_provider.FakeValenciaV2.html - qiskit_ibm_runtime.fake_provider.FakeVigo.html - qiskit_ibm_runtime.fake_provider.FakeVigoV2.html - qiskit_ibm_runtime.fake_provider.FakeWashington.html - qiskit_ibm_runtime.fake_provider.FakeWashingtonV2.html - qiskit_ibm_runtime.fake_provider.FakeYorktown.html - qiskit_ibm_runtime.fake_provider.FakeYorktownV2.html
Co-authored-by: Rebecca Dimock <66339736+beckykd@users.noreply.github.com> * Set use_symengine on qpy generation if symengine is installed (#1355) This commit sets the use_symengine flag during qpy export used during job payload generation if symengine is installed. For qiskit <1.0 symengine is a hard dependency on platforms that have support for it (x86_64, aarch64, and ppc64le linux and macOS) and an optional requirement on other qiskit supported platforms, and when available it greatly improves the runtime performance of symbolic expressions in Qiskit. By default QPY opts for the more compatible sympy representation of an unbound ParameterExpression as it's maximally compatible, and means that no matter the environment the payload will be loaded from it will be able to parse the payload. In QPY version 10 a new flag was added to the payload definition that enables users to use a native binary symengine representation of a symbolic expression that is significantly faster to generate and parse, but it still defaults to sympy as using this flag limits the compatibility of the payload. However, for runtime job submission we know that the service always has symengine available so we should be using this flag for job submission if the local environment has symengine installed as it will greatly speed up the serialization of unbound ParameterExpression objects. In Qiskit 1.0, symengine is promoted to a hard requriment for all environments and use_symengine=True is the default in Qiskit's qpy module. But, setting it like this is still a good idea as it will always be safe to do this, it's just in qiskit 1.0 symengine will always be installed. * Fix for unit tests (#1356) * Run all unit tests * Import fake providers * Format * Fake providers not used in this branch * Unused import --------- Co-authored-by: Kevin Tian * Update flaky integration tests (#1359) * Fix bad Sphinx API doc Provider naming (#1360) This resulted in the imports being called `qiskit_ibm_provider` rather than `qiskit_ibm_runtime`. Co-authored-by: Frank Harkins * Merge qiskit-ibm-provider into qiskit-ibm-runtime (#1285) * initial commit * more replacements * more replacements * add auth/api * add reno * add qpy module back * address comments * fix docs build * Update invalid token test (#1367) * Copy pub/sub code into qiskit-ibm-runtime (#1349) * Copy pub/sub code into qiskit-ibm-runtime * fix docs build * Remove mthree from requirements-dev (#1370) * Handle Qiskit 1.0 removals (#1363) * Handle Qiskit 1.0 removals * Remove removed qiskit modules * add both qiskit synthesis imports * fix docs build * fix lint errors from 1.0.0RC1 * update basicaer import * Update qiskit_ibm_runtime/fake_provider/fake_backend.py Co-authored-by: Elena Peña Tapia <57907331+ElePT@users.noreply.github.com> * address comments * Update imports & docstrings --------- Co-authored-by: Elena Peña Tapia <57907331+ElePT@users.noreply.github.com> * Copy over provider session & remove qiskit-ibm-provider (#1368) * Move provider's session & remove qiskit-ibm-provider * fix black * Handle qpy serialization across versions and delete vendored fork (#1377) * Handle qpy serialization across versions and delete vendored fork For the next qiskit-ibm-runtime release it is desired to have it support both Qiskit 0.45.x/0.46.x and Qiskit 1.0.0. To do this with QPY it means we need to emit a fixed qpy version of 10 as that's currently the maximum version the server side can parse. The easiest way to manage this across versions is actually to rely on Qiskit's qpy module again. Starting in Qiskit 1.0.0 the qiskit.qpy.dump() function a new kwarg, version exists to specify the version of qpy emitted. We can use this to control the rollout of QPY format versions as the server side is updated. For right now this is fixed to version 10 which is the same as the QPY format version emitted by 0.45.x and 0.46.0. Because the versions are the same we can just use qiskit's qpy module moving forward as either we're on qiskit 0.45.x/0.46.x and will emit version 10 (as there is no option) or we're on >=1.0.0 and we explicitly set the qpy version to one that's compatible with the server side. The qpy internals usage to serialize parameters and parameter expressions are left in place (although expanded on to include #1355 for parameter expressions) as an alternative needs to be considered for this. It is not a good idea to rely on qpy internals and explicitly private functions to do partial serialization. This commit also deletes the vendored fork as it's never been included in a released version of qiskit-ibm-runtime and nothing is using it anymore. Related to: #1375 * Fix lint * Fix lint again * Run integration tests against Qiskit main (#1376) * Fix qiskit main integratino tests cron job (#1379) * Prepare release 0.19.0 (#1380) * Prepare release 0.19 * add reno stating compatibility * Update main branch version 0.19.1 (#1382) * Porting qiskit-ibm-provider/787: Fix `DynamicCircuitInstructionDurations.from_backend` for both `Backend versions` (#1383) * porting qiskit-ibm-provider/pull/787 * porting qiskit-ibm-provider/pull/787 * black * oops * monkey patch https://github.com/Qiskit/qiskit/pull/11727 * black lynt * mypy --------- Co-authored-by: Kevin Tian * Cast use_symengine input to a bool (#1385) * Cast use_symengine input to a bool This commit works around a bug in Qiskit 0.45.x, 0.46.0, and 1.0.0rc1 with the `use_symengine` flag on `qpy.dump()`. The dump function has a bug when it receives a truthy value instead of a bool literal that it will generate a corrupt qpy because of a mismatch between how the encoding was processed (the encoding is incorrectly set to sympy in the file header but uses symengine encoding in the actual body of the circuit. This is being fixed in Qiskit/qiskit#11730 for 1.0.0, and will be backported to 0.46.1. But to ensure compatibility with 0.45.x, 0.46.0, and 1.0.0rc1 while waiting for those releases we can workaround this by just casting the value to a boolean. * Fix mypy failures * Mypy fixes again * Prepare release 0.19.1 (#1386) * Update main branch version 0.19.2 (#1388) * Use barrier labels to define intervals for DD (#1358) * Add transpiler tests * Named barrier to select dd intervals * reno * consistent pad arguments in PadDelay * Decouple single_pulse option * fix docsting * Add test * Fix for PadDelay * format * line too long --------- Co-authored-by: kevin-tian * Remove remaining qiskit.org links (#1397) * Remove remaining qiskit.org links * Update qiskit_ibm_runtime/provider_session.py Co-authored-by: Kevin Tian --------- Co-authored-by: Kevin Tian * Support Python 3.12 (#1347) * Support Python 3.12 * update requirments * update requirements * Add deprecation policy (#1405) * add deprecation file * update guide * fix wording Co-authored-by: Kevin Tian --------- Co-authored-by: Kevin Tian * Fix scheduling in control flow with instructions of non-uniform durations (#1378) * Map indices for durations in inner block * Add test * Reno * Fix docs * Missing docstring --------- Co-authored-by: Kevin Tian * Add deprecation warning for abstract circuits (#1404) * Add abstract circuit warning * add reno * use correct Sequence import * unit tests * Fix docs build with Qiskit 1.0 (#1411) * fix docs build * Replace qiskit.tools * Use POST /sessions endpoint (#1372) * wip use post sessions * address comments * fix mypy & lint * use private method * Add reno * attempt fix unit tests * unit tests * add logic to work with IQP * remove todo * Update releasenotes/notes/session-modes-5c22b68620f8d690.yaml Co-authored-by: Jessie Yu * Update docstrings, passing mode into payload * Update unit tests * address comments * Pass max_time to /sessions * unit tests * integration test --------- Co-authored-by: Jessie Yu * Use POST /sessions in backend.run sessions (#1415) * Use POST /sessions in backend.run sessions * Add reno * update tests * add test_run_after_cancel back * remove max_time arg from Session * Add max_time * Prepare release 0.20.0 (#1418) * Update main branch version 0.20.1 (#1419) * Update ISA validation (#1414) * check coupling map * restore stack level * mypy * remove layout check * check width * allow pulse gates * add release note * Fix bug with retrieving fake backends (#1402) * bug fix w retrieving fake backend * Move test * Update sessions mode release note (#1430) * Add warning if no backend provided on cloud channel (#1425) * add warning if no backend provided * add test and reno * Update msg & add to base_primitive * Update reno * Update releasenotes/notes/require-cloud-backend-38a74144347c735d.yaml Co-authored-by: Jessie Yu --------- Co-authored-by: Jessie Yu * Fix missing releases notes before Runtime 0.9 (#1434) Even though we had the release note files, Reno was not including them. * Use sphinx.ext.linkcode for more precise source code links (#1431) * added .idea to .gitignore for Pycharm * switched sphinx-ext-viewcode for sphinx-ext-linkcode * remove leftover code from Azure Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> * Update tox.ini * remove leftover code from Azure part 2 Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> * change dashes to underscores Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> * switch from qiskit to qiskit_ibm_runtime Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> * remove leftover code from Azure part 3 Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> * final updates to determine_github_branch method Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> * cha Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> * added colon * Fix issue with inherited methods --------- Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> Co-authored-by: Kevin Tian * Update deprecated actions in workflows (#1439) ### Summary In recent PRs including my PR https://github.com/Qiskit/qiskit-ibm-runtime/pull/1431, the CI has been throwing several errors due to old versions of actions that are using node12 or node16 instead of node20. I updated the actions to use the latest versions which should eliminate the CI warnings. * Fix deprecated `upload-artifact` GitHub action (#1441) * Fix bad tox.ini passenv setting (#1445) See https://github.com/Qiskit/qiskit-ibm-provider/pull/825 for context. * Handle control flow instructions in Target generation (#1443) * Handle control flow instructions in Target generation This commit updates the convert_to_target() function that is used to convert the API response objects used to describe a backend and generate a Qiskit Target object from that to properly handle control flow instructions. The supported control flow instructions are listed in the `supported_instructions` field of the configuration payload. [1] This commit updates the logic to look for the presence of known control flow instruction names in that field and add them as appropriate to the target as global variadic instructions to indicate to Qiskit's transpiler and other Target object users that the backend supports the instructions. [1] https://github.com/Qiskit/ibm-quantum-schemas/blob/0231221082ec722cc31db09c0b41a25f441ac338/schemas/backend_configuration_schema.json#L165-L170 * Add release note --------- Co-authored-by: Jessie Yu * Update backend() type hint to BackendV2 (#1442) Co-authored-by: Jessie Yu * Updates to tutorials for 1.0 + ISA changes (#1408) * A majority of these tutorials are already 1.0 ready, but were re-run to double-check Additional changes include fixes for the ISA changes in #794 * fix black/lint * docs build * fix docs build again * docs build --------- Co-authored-by: Kevin Tian * Migrate from `pkg_resources` to `importlib.metadata` (#1449) PR #1347 added `setuptools` to `requirements-dev.txt` in an effort to make `qiskit-ibm-runtime` work with Python 3.12. However, `qiskit_ibm_runtime/api/session.py` actually imports `pkg_resources`, which is provided by setuptools, so really setuptools should have been added to [`REQUIREMENTS`](https://github.com/Qiskit/qiskit-ibm-runtime/blob/e152d122782959a04ebf2330f776d4c4e309ad14/setup.py#L21) in `setup.py` so that it is installed automatically for any downstream users of Qiskit Runtime, too. Better yet, however, is to drop this explicit dependency on setuptools, since [`pkg_resources` is deprecated](https://setuptools.pypa.io/en/latest/pkg_resources.html) in favor of `importlib`. Hence, this PR migrates from `pkg_resources` to `importlib.metadata` (there are a few more words about this [here](https://github.com/googleapis/python-api-core/issues/27#issuecomment-676563754)). My investigation into this was prompted by us trying to add Python 3.12 support to the circuit-knitting-toolbox (https://github.com/Qiskit-Extensions/circuit-knitting-toolbox/pull/429), and seeing CI errors prompted by `qiskit-ibm-runtime`'s importing of `pkg_resources`. Co-authored-by: Kevin Tian * Add fake backends for newer IBM backends (#1440) * Add fake backends for newer IBM backends This commit adds news fake backend classes for the following newer IBM backends: Algiers, Brisbane, Cusco, Kawasaki, Kyoto, Osaka, Peekskill, Quebec, and Torino. This was done using a modified version of the qiskit script to update backends [1] (to use qiskit-ibm-runtime instead of qiskit-ibmq-provider). There is a standalone script adding this functionality for this repo in #1263. [1] https://github.com/Qiskit/qiskit/blob/stable/0.46/tools/update_fake_backends.py Fixes #1421 * Remove unused import * Add new backends to FakeProviderForBackendV2 too * Don't forget FakeKyiv in docs or provider class --------- Co-authored-by: Kevin Tian * Run q-ctrl tests nightly (#1452) * Raise if abstract circuits are used (#1437) * support dynamic circuits * raise for abstract circuits * lint * fix test * remove hard coded instructions * check target is not none * lint * fix test * check for error not warning * bypass simulator * fix merge issues * delete extra line --------- Co-authored-by: Elena Peña Tapia <57907331+ElePT@users.noreply.github.com> Co-authored-by: Kevin Tian Co-authored-by: merav-aharoni Co-authored-by: Salvador de la Puente González Co-authored-by: Eric Arellano <14852634+Eric-Arellano@users.noreply.github.com> Co-authored-by: Sanket Panda Co-authored-by: abbycross Co-authored-by: Kevin Tian Co-authored-by: Rathish Cholarajan Co-authored-by: Blake Johnson Co-authored-by: Kevin J. Sung Co-authored-by: Jake Lishman Co-authored-by: Kaelyn Ferris <43348706+kaelynj@users.noreply.github.com> Co-authored-by: Rebecca Dimock <66339736+beckykd@users.noreply.github.com> Co-authored-by: Matthew Treinish Co-authored-by: Diego Ristè <10402430+dieris@users.noreply.github.com> Co-authored-by: Frank Harkins Co-authored-by: Luciano Bello Co-authored-by: melechlapson Co-authored-by: melechlapson Co-authored-by: Sanket Panda Co-authored-by: Jim Garrison --- .github/workflows/ci.yml | 24 +- .github/workflows/deploy.yml | 6 +- .github/workflows/docs.yml | 6 +- .github/workflows/e2e-tests.yml | 4 +- .../integration-tests-qiskit-main.yml | 4 +- .github/workflows/integration-tests.yml | 4 +- .github/workflows/q-ctrl-tests.yml | 6 +- .github/workflows/unit-tests-terra-main.yml | 4 +- .gitignore | 3 + docs/conf.py | 76 ++- docs/index.rst | 10 +- docs/release_notes.rst | 1 + docs/tutorials.rst | 10 +- .../chsh_inequality/chsh_with_estimator.ipynb | 515 ++++++++++++++ docs/tutorials/chsh_with_estimator.ipynb | 478 ------------- docs/tutorials/grover_with_sampler.ipynb | 391 ----------- .../grover_with_sampler.ipynb | 411 +++++++++++ docs/tutorials/learning-api.conf.yaml | 15 + docs/tutorials/qaoa_with_primitives.ipynb | 598 ---------------- .../qaoa_with_primitives.ipynb | 617 +++++++++++++++++ .../user-transpiled-circuits.ipynb | 377 ++++++++++ docs/tutorials/user-transpiled-circuits.ipynb | 372 ---------- .../vqe_with_estimator.ipynb | 637 +++++++++++++++++ docs/tutorials/vqe_with_estimator.ipynb | 644 ------------------ qiskit_ibm_runtime/api/session.py | 4 +- qiskit_ibm_runtime/base_primitive.py | 15 +- qiskit_ibm_runtime/fake_provider/__init__.py | 10 + .../fake_provider/backends/__init__.py | 10 + .../backends/algiers/__init__.py | 15 + .../backends/algiers/conf_algiers.json | 1 + .../backends/algiers/defs_algiers.json | 1 + .../backends/algiers/fake_algiers.py | 28 + .../backends/algiers/props_algiers.json | 1 + .../backends/brisbane/__init__.py | 17 + .../backends/brisbane/conf_brisbane.json | 1 + .../backends/brisbane/defs_brisbane.json | 1 + .../backends/brisbane/fake_brisbane.py | 28 + .../backends/brisbane/props_brisbane.json | 1 + .../fake_provider/backends/cusco/__init__.py | 17 + .../backends/cusco/conf_cusco.json | 1 + .../backends/cusco/defs_cusco.json | 1 + .../backends/cusco/fake_cusco.py | 28 + .../backends/cusco/props_cusco.json | 1 + .../backends/kawasaki/__init__.py | 17 + .../backends/kawasaki/conf_kawasaki.json | 1 + .../backends/kawasaki/defs_kawasaki.json | 1 + .../backends/kawasaki/fake_kawasaki.py | 28 + .../backends/kawasaki/props_kawasaki.json | 1 + .../fake_provider/backends/kyiv/__init__.py | 17 + .../backends/kyiv/conf_kyiv.json | 1 + .../backends/kyiv/defs_kyiv.json | 1 + .../fake_provider/backends/kyiv/fake_kyiv.py | 28 + .../backends/kyiv/props_kyiv.json | 1 + .../fake_provider/backends/kyoto/__init__.py | 17 + .../backends/kyoto/conf_kyoto.json | 1 + .../backends/kyoto/defs_kyoto.json | 1 + .../backends/kyoto/fake_kyoto.py | 28 + .../backends/kyoto/props_kyoto.json | 1 + .../fake_provider/backends/osaka/__init__.py | 17 + .../backends/osaka/conf_osaka.json | 1 + .../backends/osaka/defs_osaka.json | 1 + .../backends/osaka/fake_osaka.py | 28 + .../backends/osaka/props_osaka.json | 1 + .../backends/peekskill/__init__.py | 15 + .../backends/peekskill/conf_peekskill.json | 1 + .../backends/peekskill/defs_peekskill.json | 1 + .../backends/peekskill/fake_peekskill.py | 28 + .../backends/peekskill/props_peekskill.json | 1 + .../fake_provider/backends/quebec/__init__.py | 17 + .../backends/quebec/conf_quebec.json | 1 + .../backends/quebec/defs_quebec.json | 1 + .../backends/quebec/fake_quebec.py | 28 + .../backends/quebec/props_quebec.json | 1 + .../fake_provider/backends/torino/__init__.py | 17 + .../backends/torino/conf_torino.json | 1 + .../backends/torino/defs_torino.json | 1 + .../backends/torino/fake_torino.py | 28 + .../backends/torino/props_torino.json | 1 + .../fake_provider/fake_provider.py | 10 + qiskit_ibm_runtime/qiskit_runtime_service.py | 2 +- qiskit_ibm_runtime/sampler.py | 16 +- qiskit_ibm_runtime/session.py | 12 +- qiskit_ibm_runtime/utils/backend_converter.py | 10 + qiskit_ibm_runtime/utils/json.py | 4 +- qiskit_ibm_runtime/utils/utils.py | 29 +- .../0.20/session-modes-5c22b68620f8d690.yaml | 13 +- .../fix-control-flow-d5a61dd5647acb42.yaml | 6 + ...isa-circuit-required-ed361bd65cef5ed8.yaml | 10 + ...equire-cloud-backend-38a74144347c735d.yaml | 10 + test/unit/test_backend.py | 25 +- test/unit/test_ibm_primitives.py | 90 ++- test/unit/test_sampler.py | 8 +- test/unit/test_session.py | 7 + test/utils.py | 27 +- tox.ini | 3 + 95 files changed, 3411 insertions(+), 2599 deletions(-) create mode 100644 docs/tutorials/chsh_inequality/chsh_with_estimator.ipynb delete mode 100644 docs/tutorials/chsh_with_estimator.ipynb delete mode 100644 docs/tutorials/grover_with_sampler.ipynb create mode 100644 docs/tutorials/grovers_algorithm/grover_with_sampler.ipynb create mode 100644 docs/tutorials/learning-api.conf.yaml delete mode 100644 docs/tutorials/qaoa_with_primitives.ipynb create mode 100644 docs/tutorials/quantum_approximate_optimization_algorithm/qaoa_with_primitives.ipynb create mode 100644 docs/tutorials/submitting_transpiled_circuits/user-transpiled-circuits.ipynb delete mode 100644 docs/tutorials/user-transpiled-circuits.ipynb create mode 100644 docs/tutorials/variational_quantum_eigensolver/vqe_with_estimator.ipynb delete mode 100644 docs/tutorials/vqe_with_estimator.ipynb create mode 100644 qiskit_ibm_runtime/fake_provider/backends/algiers/__init__.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/algiers/conf_algiers.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/algiers/defs_algiers.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/algiers/fake_algiers.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/algiers/props_algiers.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/brisbane/__init__.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/brisbane/conf_brisbane.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/brisbane/defs_brisbane.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/brisbane/fake_brisbane.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/brisbane/props_brisbane.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/cusco/__init__.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/cusco/conf_cusco.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/cusco/defs_cusco.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/cusco/fake_cusco.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/cusco/props_cusco.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kawasaki/__init__.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kawasaki/conf_kawasaki.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kawasaki/defs_kawasaki.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kawasaki/fake_kawasaki.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kawasaki/props_kawasaki.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kyiv/__init__.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kyiv/conf_kyiv.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kyiv/defs_kyiv.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kyiv/fake_kyiv.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kyiv/props_kyiv.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kyoto/__init__.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kyoto/conf_kyoto.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kyoto/defs_kyoto.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kyoto/fake_kyoto.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/kyoto/props_kyoto.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/osaka/__init__.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/osaka/conf_osaka.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/osaka/defs_osaka.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/osaka/fake_osaka.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/osaka/props_osaka.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/peekskill/__init__.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/peekskill/conf_peekskill.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/peekskill/defs_peekskill.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/peekskill/fake_peekskill.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/peekskill/props_peekskill.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/quebec/__init__.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/quebec/conf_quebec.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/quebec/defs_quebec.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/quebec/fake_quebec.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/quebec/props_quebec.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/torino/__init__.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/torino/conf_torino.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/torino/defs_torino.json create mode 100644 qiskit_ibm_runtime/fake_provider/backends/torino/fake_torino.py create mode 100644 qiskit_ibm_runtime/fake_provider/backends/torino/props_torino.json create mode 100644 releasenotes/notes/fix-control-flow-d5a61dd5647acb42.yaml create mode 100644 releasenotes/notes/isa-circuit-required-ed361bd65cef5ed8.yaml create mode 100644 releasenotes/notes/require-cloud-backend-38a74144347c735d.yaml diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 112103463..7ad8f0ddc 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -23,11 +23,11 @@ jobs: name: Run code quality checks runs-on: ubuntu-latest steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Set up Python 3.9 - uses: actions/setup-python@v2 + uses: actions/setup-python@v5 with: python-version: 3.9 - name: Install dependencies @@ -45,11 +45,11 @@ jobs: name: Build documentation runs-on: ubuntu-latest steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Set up Python 3.9 - uses: actions/setup-python@v2 + uses: actions/setup-python@v5 with: python-version: 3.9 - name: Install dependencies @@ -69,7 +69,7 @@ jobs: - name: Build documentation run: tox -edocs - name: Upload documentation - uses: actions/upload-artifact@v2 + uses: actions/upload-artifact@v4 with: name: html_docs path: docs/_build/html @@ -88,11 +88,11 @@ jobs: STREAM_LOG: True QISKIT_IN_PARALLEL: True steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Set up Python ${{ matrix.python-version }} - uses: actions/setup-python@v2 + uses: actions/setup-python@v5 with: python-version: ${{ matrix.python-version }} - name: Install dependencies @@ -102,12 +102,12 @@ jobs: - name: Run unit tests run: make unit-test-coverage - name: Report coverage to coveralls.io - uses: coverallsapp/github-action@1.1.3 + uses: coverallsapp/github-action@v2 with: github-token: ${{ secrets.GITHUB_TOKEN }} flag-name: unit-tests_python${{ matrix.python-version }}-${{ matrix.os }} parallel: true - path-to-lcov: coverage.lcov + file: coverage.lcov integration-tests: if: github.event_name == 'push' && github.repository_owner == 'Qiskit' # only kick-off resource intensive integration tests if unit tests and all basic checks succeeded @@ -130,11 +130,11 @@ jobs: STREAM_LOG: True QISKIT_IN_PARALLEL: True steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Set up Python ${{ matrix.python-version }} - uses: actions/setup-python@v2 + uses: actions/setup-python@v5 with: python-version: ${{ matrix.python-version }} - name: Install dependencies @@ -150,7 +150,7 @@ jobs: runs-on: ubuntu-latest steps: - name: Notify coveralls.io that all parallel tests have finished - uses: coverallsapp/github-action@1.1.3 + uses: coverallsapp/github-action@v2 with: github-token: ${{ secrets.GITHUB_TOKEN }} parallel-finished: true diff --git a/.github/workflows/deploy.yml b/.github/workflows/deploy.yml index f79b2ba33..48ddca4bb 100644 --- a/.github/workflows/deploy.yml +++ b/.github/workflows/deploy.yml @@ -27,15 +27,15 @@ jobs: matrix: python-version: [3.9] steps: - - uses: actions/checkout@v2 - - uses: actions/setup-python@v2 + - uses: actions/checkout@v4 + - uses: actions/setup-python@v5 with: python-version: ${{ matrix.python-version }} - name: Install deps run: pip install -U pip setuptools build - name: Build sdist run: python3 -m build - - uses: actions/upload-artifact@v3 + - uses: actions/upload-artifact@v4 with: path: ./dist/* - name: Deploy to Pypi diff --git a/.github/workflows/docs.yml b/.github/workflows/docs.yml index 45971290d..065c00804 100644 --- a/.github/workflows/docs.yml +++ b/.github/workflows/docs.yml @@ -10,11 +10,11 @@ jobs: deploy: runs-on: ubuntu-latest steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Set up Python - uses: actions/setup-python@v2 + uses: actions/setup-python@v5 with: python-version: '3.9.12' - name: Install dependencies @@ -25,7 +25,7 @@ jobs: - name: Build docs run: tox -e docs - name: Upload artifact - uses: actions/upload-artifact@v2 + uses: actions/upload-artifact@v4 with: name: html_docs path: docs/_build/html diff --git a/.github/workflows/e2e-tests.yml b/.github/workflows/e2e-tests.yml index 0738bccc7..9bbfdd266 100644 --- a/.github/workflows/e2e-tests.yml +++ b/.github/workflows/e2e-tests.yml @@ -37,11 +37,11 @@ jobs: STREAM_LOG: True QISKIT_IN_PARALLEL: True steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Set up Python ${{ matrix.python-version }} - uses: actions/setup-python@v2 + uses: actions/setup-python@v5 with: python-version: ${{ matrix.python-version }} - name: Install dependencies diff --git a/.github/workflows/integration-tests-qiskit-main.yml b/.github/workflows/integration-tests-qiskit-main.yml index 2aee5c0ec..b49e5db3d 100644 --- a/.github/workflows/integration-tests-qiskit-main.yml +++ b/.github/workflows/integration-tests-qiskit-main.yml @@ -37,11 +37,11 @@ jobs: STREAM_LOG: True QISKIT_IN_PARALLEL: True steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Set up Python ${{ matrix.python-version }} - uses: actions/setup-python@v2 + uses: actions/setup-python@v5 with: python-version: ${{ matrix.python-version }} - name: Install dependencies diff --git a/.github/workflows/integration-tests.yml b/.github/workflows/integration-tests.yml index f6b4b4c01..9e8cafb90 100644 --- a/.github/workflows/integration-tests.yml +++ b/.github/workflows/integration-tests.yml @@ -37,11 +37,11 @@ jobs: STREAM_LOG: True QISKIT_IN_PARALLEL: True steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Set up Python ${{ matrix.python-version }} - uses: actions/setup-python@v2 + uses: actions/setup-python@v5 with: python-version: ${{ matrix.python-version }} - name: Install dependencies diff --git a/.github/workflows/q-ctrl-tests.yml b/.github/workflows/q-ctrl-tests.yml index 971195584..c138e9289 100644 --- a/.github/workflows/q-ctrl-tests.yml +++ b/.github/workflows/q-ctrl-tests.yml @@ -12,6 +12,8 @@ name: Q-CTRL Tests on: + schedule: + - cron: '0 1 * * *' push: tags: - "*" @@ -37,11 +39,11 @@ jobs: STREAM_LOG: True QISKIT_IN_PARALLEL: True steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Set up Python ${{ matrix.python-version }} - uses: actions/setup-python@v2 + uses: actions/setup-python@v5 with: python-version: ${{ matrix.python-version }} - name: Install dependencies diff --git a/.github/workflows/unit-tests-terra-main.yml b/.github/workflows/unit-tests-terra-main.yml index 70e0b0933..87fae3642 100644 --- a/.github/workflows/unit-tests-terra-main.yml +++ b/.github/workflows/unit-tests-terra-main.yml @@ -25,11 +25,11 @@ jobs: STREAM_LOG: True QISKIT_IN_PARALLEL: True steps: - - uses: actions/checkout@v2 + - uses: actions/checkout@v4 with: fetch-depth: 0 - name: Set up Python 3.9 - uses: actions/setup-python@v2 + uses: actions/setup-python@v5 with: python-version: 3.9 - name: Install dependencies diff --git a/.gitignore b/.gitignore index a4393ae2a..3eae17842 100644 --- a/.gitignore +++ b/.gitignore @@ -107,3 +107,6 @@ Qconfig.py .DS_Store /docs/stubs/ + +# Pycharm +.idea diff --git a/docs/conf.py b/docs/conf.py index 621a3a38d..08a28ec2e 100644 --- a/docs/conf.py +++ b/docs/conf.py @@ -11,7 +11,9 @@ # that they have been altered from the originals. # -- Path setup -------------------------------------------------------------- +import inspect import os +import re import sys sys.path.insert(0, os.path.abspath('.')) @@ -34,7 +36,7 @@ 'sphinx.ext.autodoc', 'sphinx.ext.autosummary', # This is used by qiskit/documentation to generate links to github.com. - "sphinx.ext.viewcode", + "sphinx.ext.linkcode", 'jupyter_sphinx', 'sphinx_autodoc_typehints', 'reno.sphinxext', @@ -117,3 +119,75 @@ html_last_updated_fmt = '%Y/%m/%d' html_sourcelink_suffix = '' autoclass_content = 'both' + + +# ---------------------------------------------------------------------------------- +# Source code links +# ---------------------------------------------------------------------------------- + +def determine_github_branch() -> str: + """Determine the GitHub branch name to use for source code links. + + We need to decide whether to use `stable/` vs. `main` for dev builds. + Refer to https://docs.github.com/en/actions/learn-github-actions/variables + for how we determine this with GitHub Actions. + """ + # If CI env vars not set, default to `main`. This is relevant for local builds. + if "GITHUB_REF_NAME" not in os.environ: + return "main" + + # PR workflows set the branch they're merging into. + if base_ref := os.environ.get("GITHUB_BASE_REF"): + return base_ref + + ref_name = os.environ["GITHUB_REF_NAME"] + + # Check if the ref_name is a tag like `1.0.0` or `1.0.0rc1`. If so, we need + # to transform it to a Git branch like `stable/1.0`. + version_without_patch = re.match(r"(\d+\.\d+)", ref_name) + return ( + f"stable/{version_without_patch.group()}" + if version_without_patch + else ref_name + ) + + +GITHUB_BRANCH = determine_github_branch() + + +def linkcode_resolve(domain, info): + if domain != "py": + return None + + module_name = info["module"] + module = sys.modules.get(module_name) + if module is None or "qiskit_ibm_runtime" not in module_name: + return None + + obj = module + for part in info["fullname"].split("."): + try: + obj = getattr(obj, part) + except AttributeError: + return None + is_valid_code_object = ( + inspect.isclass(obj) or inspect.ismethod(obj) or inspect.isfunction(obj) + ) + if not is_valid_code_object: + return None + try: + full_file_name = inspect.getsourcefile(obj) + except TypeError: + return None + if full_file_name is None or "/qiskit_ibm_runtime/" not in full_file_name: + return None + file_name = full_file_name.split("/qiskit_ibm_runtime/")[-1] + + try: + source, lineno = inspect.getsourcelines(obj) + except (OSError, TypeError): + linespec = "" + else: + ending_lineno = lineno + len(source) - 1 + linespec = f"#L{lineno}-L{ending_lineno}" + return f"https://github.com/Qiskit/qiskit-ibm-runtime/tree/{GITHUB_BRANCH}/qiskit_ibm_runtime/{file_name}{linespec}" diff --git a/docs/index.rst b/docs/index.rst index 1511a3162..95643f6cc 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -28,11 +28,11 @@ Next steps Get started with Estimator Get started with Sampler Get started with error suppression and error mitigation - CHSH with Estimator - VQE with Estimator - Grover with Sampler - QAOA with Primitives - Submit user-transpiled circuits using primitives + CHSH with Estimator + VQE with Estimator + Grover with Sampler + QAOA with Primitives + Submit user-transpiled circuits using primitives All tutorials diff --git a/docs/release_notes.rst b/docs/release_notes.rst index ec77acc34..a54f126c3 100644 --- a/docs/release_notes.rst +++ b/docs/release_notes.rst @@ -1 +1,2 @@ .. release-notes:: Release Notes + :earliest-version: 0.1.0rc1 diff --git a/docs/tutorials.rst b/docs/tutorials.rst index 1a7fed645..36f4dd7bc 100644 --- a/docs/tutorials.rst +++ b/docs/tutorials.rst @@ -11,8 +11,8 @@ Estimator tutorials/how-to-getting-started-with-estimator tutorials/Error-Suppression-and-Error-Mitigation - tutorials/chsh_with_estimator - tutorials/vqe_with_estimator + tutorials/chsh_inequality/chsh_with_estimator + tutorials/variational_quantum_eigensolver/vqe_with_estimator Sampler ================================= @@ -20,9 +20,9 @@ Sampler .. nbgallery:: tutorials/how-to-getting-started-with-sampler - tutorials/grover_with_sampler - tutorials/user-transpiled-circuits - tutorials/qaoa_with_primitives + tutorials/grovers_algorithm/grover_with_sampler + tutorials/submitting_transpiled_circuits/user-transpiled-circuits + tutorials/quantum_approximate_optimization_algorithm/qaoa_with_primitives .. Hiding - Indices and tables diff --git a/docs/tutorials/chsh_inequality/chsh_with_estimator.ipynb b/docs/tutorials/chsh_inequality/chsh_with_estimator.ipynb new file mode 100644 index 000000000..af02e2f66 --- /dev/null +++ b/docs/tutorials/chsh_inequality/chsh_with_estimator.ipynb @@ -0,0 +1,515 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "98fa28f0", + "metadata": {}, + "source": [ + "## Background" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In this tutorial, you will run an experiment on a quantum computer to demonstrate the violation of the CHSH inequality with the Estimator primitive. \n", + "\n", + "The CHSH inequality, named after the authors Clauser, Horne, Shimony, and Holt, is used to experimentally prove Bell's theorem (1969). This theorem asserts that local hidden variable theories cannot account for some consequences of entanglement in quantum mechanics. The violation of the CHSH inequality is used to show that quantum mechanics is incompatible with local hidden-variable theories. This is an important experiment for understanding the foundation of quantum mechanics. \n", + "\n", + "The 2022 Nobel Prize for Physics was awarded to Alain Aspect, John Clauser and Anton Zeilinger in part for their pioneering work in quantum information science, and in particular, for their experiments with entangled photons demonstrating violation of Bell’s inequalities." + ] + }, + { + "cell_type": "markdown", + "id": "36669708", + "metadata": {}, + "source": [ + "For this experiment, we will create an entangled pair on which we measure each qubit on two different bases. We will label the bases for the first qubit $A$ and $a$ and the bases for the second qubit $B$ and $b$. This allows us to compute the CHSH quantity $S_1$:\n", + "\n", + "$$\n", + "S_1 = A(B-b) + a(B+b).\n", + "$$\n", + "\n", + "Each observable is either $+1$ or $-1$. Clearly, one of the terms $B\\pm b$ must be $0$, and the other must be $\\pm 2$. Therefore, $S_1 = \\pm 2$. The average value of $S_1$ must satisfy the inequality:\n", + "\n", + "$$\n", + "|\\langle S_1 \\rangle|\\leq 2.\n", + "$$\n", + "\n", + "Expanding $S_1$ in terms of $A$, $a$, $B$, and $b$ results in:\n", + "\n", + "$$\n", + "|\\langle S_1 \\rangle| = |\\langle AB \\rangle - \\langle Ab \\rangle + \\langle aB \\rangle + \\langle ab \\rangle| \\leq 2\n", + "$$\n", + "\n", + "You can define another CHSH quantity $S_2$:\n", + "\n", + "$$\n", + "S_2 = A(B+b) - a(B-b),\n", + "$$\n", + "\n", + "This leads to another inequality:\n", + "\n", + "$$\n", + "|\\langle S_2 \\rangle| = |\\langle AB \\rangle + \\langle Ab \\rangle - \\langle aB \\rangle + \\langle ab \\rangle| \\leq 2\n", + "$$\n", + "\n", + "If quantum mechanics can be described by local hidden variable theories, the previous inequalities must hold true. However, as is demonstrated in this notebook, these inequalities can be violated in a quantum computer. Therefore, quantum mechanics is not compatible with local hidden variable theories." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you want to learn more theory, explore [Entanglement in Action](https://learning.quantum-computing.ibm.com/course/basics-of-quantum-information/entanglement-in-action#the-chsh-game) with John Watrous.\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "d4cec8d8", + "metadata": {}, + "source": [ + "You will create an entangled pair between two qubits in a quantum computer by creating the Bell state $|\\Phi^+\\rangle = \\frac{|00\\rangle + |11\\rangle}{\\sqrt{2}}$. Using the Estimator primitive, you can directly obtain the expectation values needed ($\\langle AB \\rangle, \\langle Ab \\rangle, \\langle aB \\rangle$, and $\\langle ab \\rangle$) to calculate the expectation values of the two CHSH quantities $\\langle S_1\\rangle$ and $\\langle S_2\\rangle$. Before the introduction of the Estimator primitive, you would have to construct the expectation values from the measurement outcomes.\n", + "\n", + "You will measure the second qubit in the $Z$ and $X$ bases. The first qubit will be measured also in orthogonal bases, but with an angle with respect to the second qubit, which we are going to sweep between $0$ and $2\\pi$. As you will see, the Estimator primitive makes running parameterized circuits very easy. Rather than creating a series of CHSH circuits, you only need to create *one* CHSH circuit with a parameter specifying the measurement angle and a series of phase values for the parameter.\n", + "\n", + "Finally, you will analyze the results and plot them against the measurement angle. You will see that for certain range of measurement angles, the expectation values of CHSH quantities $|\\langle S_1\\rangle| > 2$ or $|\\langle S_2\\rangle| > 2$, which demonstrates the violation of the CHSH inequality." + ] + }, + { + "cell_type": "markdown", + "id": "9c7dcf81", + "metadata": {}, + "source": [ + "## Setup" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "53cb74e3", + "metadata": {}, + "outputs": [], + "source": [ + "# General\n", + "import numpy as np\n", + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "# Qiskit imports\n", + "from qiskit import QuantumCircuit\n", + "from qiskit.circuit import Parameter\n", + "from qiskit.quantum_info import SparsePauliOp\n", + "\n", + "# Qiskit Runtime imports\n", + "from qiskit_ibm_runtime import QiskitRuntimeService, Estimator, Batch\n", + "\n", + "# Plotting routines\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.ticker as tck" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "16f323fb", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ibmq_mumbai'" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", + "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", + "backend = service.least_busy(operational=True, simulator=False)\n", + "backend.name" + ] + }, + { + "cell_type": "markdown", + "id": "66d5e2e2", + "metadata": {}, + "source": [ + "## Step 1: Map classical inputs to a quantum problem" + ] + }, + { + "cell_type": "markdown", + "id": "1ab329f2", + "metadata": {}, + "source": [ + "### Create a parameterized CHSH circuit \n", + "\n", + "First, we write the circuit with the parameter $\\theta$, which we call `theta`. The [`Estimator` primitive](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator#estimator) can enormously simplify circuit building and output analysis by directly providing expectation values of observables. Many problems of interest, especially for near-term applications on noisy systems, can be formulated in terms of expectation values. For maximum generalization, the [`Estimator` primitive](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator#estimator) requires circuits with no measurements." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "6c77e40a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "theta = Parameter(\"$\\\\theta$\")\n", + "\n", + "chsh_circuit_no_meas = QuantumCircuit(2)\n", + "chsh_circuit_no_meas.h(0)\n", + "chsh_circuit_no_meas.cx(0, 1)\n", + "chsh_circuit_no_meas.ry(theta, 0)\n", + "chsh_circuit_no_meas.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" + ] + }, + { + "cell_type": "markdown", + "id": "de760250", + "metadata": {}, + "source": [ + "### Create a list of phase values to be assigned later\n", + "\n", + "After creating the parameterized CHSH circuit, you will create a list of phase values to be assigned to the circuit in the next step. You can use the following code to create a list of 21 phase values range from $0$ to $2 \\pi$ with equal spacing, that is, $0$, $0.1 \\pi$, $0.2 \\pi$, ..., $1.9 \\pi$, $2 \\pi$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "bcb3b32b", + "metadata": {}, + "outputs": [], + "source": [ + "number_of_phases = 21\n", + "phases = np.linspace(0, 2 * np.pi, number_of_phases)\n", + "# Phases need to be expressed as list of lists in order to work\n", + "individual_phases = [[ph] for ph in phases]" + ] + }, + { + "cell_type": "markdown", + "id": "6e559aed", + "metadata": {}, + "source": [ + "### Observables \n", + "\n", + "Now we need observables from which to compute the expectation values. In our case we are looking at orthogonal bases for each qubit, letting the parameterized $Y-$ rotation for the first qubit sweep the measurement basis nearly continuously with respect to the second qubit basis. We will therefore choose the observables $ZZ$, $ZX$, $XZ$, and $XX$." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "5873398f", + "metadata": {}, + "outputs": [], + "source": [ + "ZZ = SparsePauliOp.from_list([(\"ZZ\", 1)])\n", + "ZX = SparsePauliOp.from_list([(\"ZX\", 1)])\n", + "XZ = SparsePauliOp.from_list([(\"XZ\", 1)])\n", + "XX = SparsePauliOp.from_list([(\"XX\", 1)])\n", + "\n", + "ops = [ZZ, ZX, XZ, XX]\n", + "num_ops = len(ops)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Optimize problem for quantum execution." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "9a5561eb", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "\n", + "target = backend.target\n", + "pm = generate_preset_pass_manager(target=target, optimization_level=3)\n", + "\n", + "circuit_ibm = pm.run(chsh_circuit_no_meas)\n", + "circuit_ibm.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" + ] + }, + { + "cell_type": "markdown", + "id": "b7194399", + "metadata": {}, + "source": [ + "## Step 3: Execute using Qiskit Primitives.\n", + "\n", + "In order to execute the entire experiment in one call to the [`Estimator`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator#estimator) we need to batch the circuit and operators together, repeating each for the requested `number_of_phases` points." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "a3201a66", + "metadata": {}, + "outputs": [], + "source": [ + "batch_circuits = [circuit_ibm] * number_of_phases * num_ops\n", + "batch_ops = [op for op in ops for _ in individual_phases]" + ] + }, + { + "cell_type": "markdown", + "id": "2d8ad9e1", + "metadata": {}, + "source": [ + "We can create a [Qiskit Runtime `Estimator`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator#estimator) primitive to compute our expectation values, and the [`Batch`](https://docs.quantum-computing.ibm.com/run/run-primitives-batch) context manager to run our non-iterative workload." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "e73db51f", + "metadata": {}, + "outputs": [], + "source": [ + "# To run on a local simulator:\n", + "# 1. Use the Estimator from qiskit.primitives instead.\n", + "# 2. Remove the Batch context manager below.\n", + "\n", + "with Batch(backend=backend) as batch:\n", + " estimator = Estimator()\n", + "\n", + " batch_expvals = (\n", + " estimator.run(\n", + " batch_circuits,\n", + " batch_ops,\n", + " parameter_values=individual_phases * num_ops,\n", + " skip_transpilation=True,\n", + " shots=10000,\n", + " )\n", + " .result()\n", + " .values\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "02916dfd", + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.primitives import Estimator\n", + "\n", + "estimator = Estimator()" + ] + }, + { + "cell_type": "markdown", + "id": "ae4830b3", + "metadata": {}, + "source": [ + "The individual expectation values can then be extracted from the batched results:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "f478b954", + "metadata": {}, + "outputs": [], + "source": [ + "ZZ_expval, ZX_expval, XZ_expval, XX_expval = [\n", + " batch_expvals[kk * number_of_phases : (kk + 1) * number_of_phases] for kk in range(num_ops)\n", + "]" + ] + }, + { + "cell_type": "markdown", + "id": "ace7dc90", + "metadata": {}, + "source": [ + "## Step 4: Post-process, return result in classical format.\n", + "\n", + "After running the circuits, we need to build the CHSH witness functions. We first build the quantities $\\langle AB \\rangle$, $\\langle Ab \\rangle$, $\\langle aB \\rangle$, and $\\langle ab \\rangle$, by looking at the parity of the outcomes for the four families of circuits we built (two measurement bases for each of the two qubits). Then we use those quantities to build the witness functions as defined previously." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "3c3c0229", + "metadata": {}, + "outputs": [], + "source": [ + "# = - + + \n", + "chsh1_est = ZZ_expval - ZX_expval + XZ_expval + XX_expval\n", + "\n", + "# = + - + \n", + "chsh2_est = ZZ_expval + ZX_expval - XZ_expval + XX_expval" + ] + }, + { + "cell_type": "markdown", + "id": "a772c534", + "metadata": {}, + "source": [ + "Note that now we do not have to build the observables ourselves because they are returned to us! The computed expectation values are given in `result.values`. What comes back is a very small payload of data." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "f6267448", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(10, 6))\n", + "\n", + "# results from hardware\n", + "ax.plot(phases / np.pi, chsh1_est, \"o-\", label=\"CHSH1\", zorder=3)\n", + "ax.plot(phases / np.pi, chsh2_est, \"o-\", label=\"CHSH2\", zorder=3)\n", + "\n", + "# classical bound +-2\n", + "ax.axhline(y=2, color=\"0.9\", linestyle=\"--\")\n", + "ax.axhline(y=-2, color=\"0.9\", linestyle=\"--\")\n", + "\n", + "# quantum bound, +-2√2\n", + "ax.axhline(y=np.sqrt(2) * 2, color=\"0.9\", linestyle=\"-.\")\n", + "ax.axhline(y=-np.sqrt(2) * 2, color=\"0.9\", linestyle=\"-.\")\n", + "ax.fill_between(phases / np.pi, 2, 2 * np.sqrt(2), color=\"0.6\", alpha=0.7)\n", + "ax.fill_between(phases / np.pi, -2, -2 * np.sqrt(2), color=\"0.6\", alpha=0.7)\n", + "\n", + "# set x tick labels to the unit of pi\n", + "ax.xaxis.set_major_formatter(tck.FormatStrFormatter(\"%g $\\pi$\"))\n", + "ax.xaxis.set_major_locator(tck.MultipleLocator(base=0.5))\n", + "\n", + "# set labels, and legend\n", + "plt.xlabel(\"Theta\")\n", + "plt.ylabel(\"CHSH witness\")\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "63e63853", + "metadata": {}, + "source": [ + "In the figure, the red dashed lines delimit the classical bounds ($\\pm 2$) and the dash-dotted blue lines delimit the quantum bounds ($\\pm 2\\sqrt{2}$). You can see that the experimental results resemble the general trend of the simulated results and there are regions where the CHSH witness quantities exceeds the classical bounds. Congratulations! You have successfully demonstrated the violation of CHSH inequality in a real quantum system!" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "3eaa8f60", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'0.19.1'" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit_ibm_runtime\n", + "\n", + "qiskit_ibm_runtime.version.get_version_info()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "eb75a5c8", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.0.0rc1'" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit\n", + "\n", + "qiskit.version.get_version_info()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + }, + "vscode": { + "interpreter": { + "hash": "1910f834ba40d1043b9ae723a4d216fb6c2faf55822807adca52e5ece8e3f1c8" + } + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/tutorials/chsh_with_estimator.ipynb b/docs/tutorials/chsh_with_estimator.ipynb deleted file mode 100644 index fe4e2e380..000000000 --- a/docs/tutorials/chsh_with_estimator.ipynb +++ /dev/null @@ -1,478 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "bf7f865a", - "metadata": {}, - "source": [ - "# CHSH inequality" - ] - }, - { - "cell_type": "markdown", - "id": "98fa28f0", - "metadata": {}, - "source": [ - "## Background" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In this tutorial, you will run an experiment on a quantum computer to demonstrate the violation of the CHSH inequality with the Estimator primitive. \n", - "\n", - "The CHSH inequality, named after the authors Clauser, Horne, Shimony, and Holt, is used to experimentally prove Bell's theorem (1969). This theorem asserts that local hidden variable theories cannot account for some consequences of entanglement in quantum mechanics. The violation of the CHSH inequality is used to show that quantum mechanics is incompatible with local hidden-variable theories. This is an important experiment for understanding the foundation of quantum mechanics. \n", - "\n", - "The 2022 Nobel Prize for Physics was awarded to Alain Aspect, John Clauser and Anton Zeilinger in part for their pioneering work in quantum information science, and in particular, for their experiments with entangled photons demonstrating violation of Bell’s inequalities." - ] - }, - { - "cell_type": "markdown", - "id": "36669708", - "metadata": {}, - "source": [ - "For this experiment, we will create an entangled pair on which we measure each qubit on two different bases. We will label the bases for the first qubit $A$ and $a$ and the bases for the second qubit $B$ and $b$. This allows us to compute the CHSH quantity $S_1$:\n", - "\n", - "$$\n", - "S_1 = A(B-b) + a(B+b).\n", - "$$\n", - "\n", - "Each observable is either $+1$ or $-1$. Clearly, one of the terms $B\\pm b$ must be $0$, and the other must be $\\pm 2$. Therefore, $S_1 = \\pm 2$. The average value of $S_1$ must satisfy the inequality:\n", - "\n", - "$$\n", - "|\\langle S_1 \\rangle|\\leq 2.\n", - "$$\n", - "\n", - "Expanding $S_1$ in terms of $A$, $a$, $B$, and $b$ results in:\n", - "\n", - "$$\n", - "|\\langle S_1 \\rangle| = |\\langle AB \\rangle - \\langle Ab \\rangle + \\langle aB \\rangle + \\langle ab \\rangle| \\leq 2\n", - "$$\n", - "\n", - "You can define another CHSH quantity $S_2$:\n", - "\n", - "$$\n", - "S_2 = A(B+b) - a(B-b),\n", - "$$\n", - "\n", - "This leads to another inequality:\n", - "\n", - "$$\n", - "|\\langle S_2 \\rangle| = |\\langle AB \\rangle + \\langle Ab \\rangle - \\langle aB \\rangle + \\langle ab \\rangle| \\leq 2\n", - "$$\n", - "\n", - "If quantum mechanics can be described by local hidden variable theories, the previous inequalities must hold true. However, as is demonstrated in this notebook, these inequalities can be violated in a quantum computer. Therefore, quantum mechanics is not compatible with local hidden variable theories." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If you want to learn more theory, explore [Entanglement in Action](https://learning.quantum-computing.ibm.com/course/basics-of-quantum-information/entanglement-in-action#the-chsh-game) with John Watrous.\n", - "\n", - "" - ] - }, - { - "cell_type": "markdown", - "id": "d4cec8d8", - "metadata": {}, - "source": [ - "You will create an entangled pair between two qubits in a quantum computer by creating the Bell state $|\\Phi^+\\rangle = \\frac{|00\\rangle + |11\\rangle}{\\sqrt{2}}$. Using the Estimator primitive, you can directly obtain the expectation values needed ($\\langle AB \\rangle, \\langle Ab \\rangle, \\langle aB \\rangle$, and $\\langle ab \\rangle$) to calculate the expectation values of the two CHSH quantities $\\langle S_1\\rangle$ and $\\langle S_2\\rangle$. Before the introduction of the Estimator primitive, you would have to construct the expectation values from the measurement outcomes.\n", - "\n", - "You will measure the second qubit in the $Z$ and $X$ bases. The first qubit will be measured also in orthogonal bases, but with an angle with respect to the second qubit, which we are going to sweep between $0$ and $2\\pi$. As you will see, the Estimator primitive makes running parameterized circuits very easy. Rather than creating a series of CHSH circuits, you only need to create *one* CHSH circuit with a parameter specifying the measurement angle and a series of phase values for the parameter.\n", - "\n", - "Finally, you will analyze the results and plot them against the measurement angle. You will see that for certain range of measurement angles, the expectation values of CHSH quantities $|\\langle S_1\\rangle| > 2$ or $|\\langle S_2\\rangle| > 2$, which demonstrates the violation of the CHSH inequality." - ] - }, - { - "cell_type": "markdown", - "id": "9c7dcf81", - "metadata": {}, - "source": [ - "## Setup" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "id": "53cb74e3", - "metadata": {}, - "outputs": [], - "source": [ - "# General\n", - "import numpy as np\n", - "\n", - "# Qiskit imports\n", - "from qiskit import QuantumCircuit\n", - "from qiskit.circuit import Parameter\n", - "from qiskit.quantum_info import SparsePauliOp\n", - "\n", - "# Qiskit Runtime imports\n", - "from qiskit_ibm_runtime import QiskitRuntimeService, Estimator, Batch\n", - "\n", - "# Plotting routines\n", - "import matplotlib.pyplot as plt\n", - "import matplotlib.ticker as tck" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "16f323fb", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'ibmq_manila'" - ] - }, - "execution_count": 24, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", - "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", - "backend = service.least_busy(operational=True, simulator=False)\n", - "backend.name" - ] - }, - { - "cell_type": "markdown", - "id": "66d5e2e2", - "metadata": {}, - "source": [ - "## Step 1: Map classical inputs to a quantum problem" - ] - }, - { - "cell_type": "markdown", - "id": "1ab329f2", - "metadata": {}, - "source": [ - "### Create a parameterized CHSH circuit \n", - "\n", - "First, we write the circuit with the parameter $\\theta$, which we call `theta`. The [`Estimator` primitive](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator#estimator) can enormously simplify circuit building and output analysis by directly providing expectation values of observables. Many problems of interest, especially for near-term applications on noisy systems, can be formulated in terms of expectation values. For maximum generalization, the [`Estimator` primitive](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator#estimator) requires circuits with no measurements." - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "6c77e40a", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "theta = Parameter(\"$\\\\theta$\")\n", - "\n", - "chsh_circuit_no_meas = QuantumCircuit(2)\n", - "chsh_circuit_no_meas.h(0)\n", - "chsh_circuit_no_meas.cx(0, 1)\n", - "chsh_circuit_no_meas.ry(theta, 0)\n", - "chsh_circuit_no_meas.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" - ] - }, - { - "cell_type": "markdown", - "id": "de760250", - "metadata": {}, - "source": [ - "### Create a list of phase values to be assigned later\n", - "\n", - "After creating the parameterized CHSH circuit, you will create a list of phase values to be assigned to the circuit in the next step. You can use the following code to create a list of 21 phase values range from $0$ to $2 \\pi$ with equal spacing, that is, $0$, $0.1 \\pi$, $0.2 \\pi$, ..., $1.9 \\pi$, $2 \\pi$." - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "bcb3b32b", - "metadata": {}, - "outputs": [], - "source": [ - "number_of_phases = 21\n", - "phases = np.linspace(0, 2 * np.pi, number_of_phases)\n", - "# Phases need to be expressed as list of lists in order to work\n", - "individual_phases = [[ph] for ph in phases]" - ] - }, - { - "cell_type": "markdown", - "id": "6e559aed", - "metadata": {}, - "source": [ - "### Observables \n", - "\n", - "Now we need observables from which to compute the expectation values. In our case we are looking at orthogonal bases for each qubit, letting the parameterized $Y-$ rotation for the first qubit sweep the measurement basis nearly continuously with respect to the second qubit basis. We will therefore choose the observables $ZZ$, $ZX$, $XZ$, and $XX$." - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "5873398f", - "metadata": {}, - "outputs": [], - "source": [ - "ZZ = SparsePauliOp.from_list([(\"ZZ\", 1)])\n", - "ZX = SparsePauliOp.from_list([(\"ZX\", 1)])\n", - "XZ = SparsePauliOp.from_list([(\"XZ\", 1)])\n", - "XX = SparsePauliOp.from_list([(\"XX\", 1)])\n", - "\n", - "ops = [ZZ, ZX, XZ, XX]\n", - "num_ops = len(ops)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 2: Optimize problem for quantum execution.\n", - "\n", - "For this example, the circuit and the operators are simple, so no optimizations are needed." - ] - }, - { - "cell_type": "markdown", - "id": "b7194399", - "metadata": {}, - "source": [ - "## Step 3: Execute using Qiskit Primitives.\n", - "\n", - "In order to execute the entire experiment in one call to the [`Estimator`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator#estimator) we need to batch the circuit and operators together, repeating each for the requested `number_of_phases` points." - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "id": "a3201a66", - "metadata": {}, - "outputs": [], - "source": [ - "batch_circuits = [chsh_circuit_no_meas] * number_of_phases * num_ops\n", - "batch_ops = [op for op in ops for _ in individual_phases]" - ] - }, - { - "cell_type": "markdown", - "id": "2d8ad9e1", - "metadata": {}, - "source": [ - "We can create a [Qiskit Runtime `Estimator`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator#estimator) primitive to compute our expectation values, and the [`Batch`](https://docs.quantum-computing.ibm.com/run/run-primitives-batch) context manager to run our non-iterative workload." - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "id": "e73db51f", - "metadata": {}, - "outputs": [], - "source": [ - "# To run on a local simulator:\n", - "# 1. Use the Estimator from qiskit.primitives instead.\n", - "# 2. Remove the Batch context manager below.\n", - "\n", - "with Batch(backend=backend) as batch:\n", - " estimator = Estimator()\n", - "\n", - " batch_expvals = (\n", - " estimator.run(\n", - " batch_circuits, batch_ops, parameter_values=individual_phases * num_ops, shots=10000\n", - " )\n", - " .result()\n", - " .values\n", - " )" - ] - }, - { - "cell_type": "markdown", - "id": "ae4830b3", - "metadata": {}, - "source": [ - "The individual expectation values can then be extracted from the batched results:" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "id": "f478b954", - "metadata": {}, - "outputs": [], - "source": [ - "ZZ_expval, ZX_expval, XZ_expval, XX_expval = [\n", - " batch_expvals[kk * number_of_phases : (kk + 1) * number_of_phases] for kk in range(num_ops)\n", - "]" - ] - }, - { - "cell_type": "markdown", - "id": "ace7dc90", - "metadata": {}, - "source": [ - "## Step 4: Post-process, return result in classical format.\n", - "\n", - "After running the circuits, we need to build the CHSH witness functions. We first build the quantities $\\langle AB \\rangle$, $\\langle Ab \\rangle$, $\\langle aB \\rangle$, and $\\langle ab \\rangle$, by looking at the parity of the outcomes for the four families of circuits we built (two measurement bases for each of the two qubits). Then we use those quantities to build the witness functions as defined previously." - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "id": "3c3c0229", - "metadata": {}, - "outputs": [], - "source": [ - "# = - + + \n", - "chsh1_est = ZZ_expval - ZX_expval + XZ_expval + XX_expval\n", - "\n", - "# = + - + \n", - "chsh2_est = ZZ_expval + ZX_expval - XZ_expval + XX_expval" - ] - }, - { - "cell_type": "markdown", - "id": "a772c534", - "metadata": {}, - "source": [ - "Note that now we do not have to build the observables ourselves because they are returned to us! The computed expectation values are given in `result.values`. What comes back is a very small payload of data." - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "id": "f6267448", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots(figsize=(10, 6))\n", - "\n", - "# results from hardware\n", - "ax.plot(phases / np.pi, chsh1_est, \"o-\", label=\"CHSH1\", zorder=3)\n", - "ax.plot(phases / np.pi, chsh2_est, \"o-\", label=\"CHSH2\", zorder=3)\n", - "\n", - "# classical bound +-2\n", - "ax.axhline(y=2, color=\"0.9\", linestyle=\"--\")\n", - "ax.axhline(y=-2, color=\"0.9\", linestyle=\"--\")\n", - "\n", - "# quantum bound, +-2√2\n", - "ax.axhline(y=np.sqrt(2) * 2, color=\"0.9\", linestyle=\"-.\")\n", - "ax.axhline(y=-np.sqrt(2) * 2, color=\"0.9\", linestyle=\"-.\")\n", - "ax.fill_between(phases / np.pi, 2, 2 * np.sqrt(2), color=\"0.6\", alpha=0.7)\n", - "ax.fill_between(phases / np.pi, -2, -2 * np.sqrt(2), color=\"0.6\", alpha=0.7)\n", - "\n", - "# set x tick labels to the unit of pi\n", - "ax.xaxis.set_major_formatter(tck.FormatStrFormatter(\"%g $\\pi$\"))\n", - "ax.xaxis.set_major_locator(tck.MultipleLocator(base=0.5))\n", - "\n", - "# set labels, and legend\n", - "plt.xlabel(\"Theta\")\n", - "plt.ylabel(\"CHSH witness\")\n", - "plt.legend()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "id": "63e63853", - "metadata": {}, - "source": [ - "In the figure, the red dashed lines delimit the classical bounds ($\\pm 2$) and the dash-dotted blue lines delimit the quantum bounds ($\\pm 2\\sqrt{2}$). You can see that the experimental results resemble the general trend of the simulated results and there are regions where the CHSH witness quantities exceeds the classical bounds. Congratulations! You have successfully demonstrated the violation of CHSH inequality in a real quantum system!" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3eaa8f60", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.14.1'" - ] - }, - "execution_count": 1, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit_ibm_runtime\n", - "\n", - "qiskit_ibm_runtime.version.get_version_info()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "eb75a5c8", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.45.0'" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit\n", - "\n", - "qiskit.version.get_version_info()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.6" - }, - "vscode": { - "interpreter": { - "hash": "1910f834ba40d1043b9ae723a4d216fb6c2faf55822807adca52e5ece8e3f1c8" - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/docs/tutorials/grover_with_sampler.ipynb b/docs/tutorials/grover_with_sampler.ipynb deleted file mode 100644 index de017a145..000000000 --- a/docs/tutorials/grover_with_sampler.ipynb +++ /dev/null @@ -1,391 +0,0 @@ -{ - "cells": [ - { - "attachments": {}, - "cell_type": "markdown", - "id": "db78a668", - "metadata": {}, - "source": [ - "# Grover's algorithm" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "e57d1e6b", - "metadata": {}, - "source": [ - "## Background\n", - "\n", - "Amplitude amplification is a general purpose quantum algorithm, or subroutine, that can be used to obtain a quadratic speedup over a handful of classical algorithms. [Grover’s algorithm](https://arxiv.org/abs/quant-ph/9605043) was the first to demonstrate this speedup on unstructured search problems. Formulating a Grover's search problem requires an oracle function that marks one or more computational basis states as the states we are interested in finding, and an amplification circuit that increases the amplitude of marked states, consequently suppressing the remaining states. \n", - "\n", - "Here, we demonstrate how to construct Grover oracles and use the `GroverOperator` from the Qiskit circuit library to easily set up a Grover's search instance. The runtime `Sampler` primitive allows seamless execution of Grover circuits, including automatic compilation, error suppression, and readout error mitigation techniques." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "54602708", - "metadata": {}, - "source": [ - "## Setup\n", - "\n", - "Here we import the small number of tools we need for this tutorial." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "e2cb0472", - "metadata": {}, - "outputs": [], - "source": [ - "# Built-in modules\n", - "import math\n", - "\n", - "# Imports from Qiskit\n", - "from qiskit import QuantumCircuit\n", - "from qiskit.circuit.library import GroverOperator, MCMT, ZGate\n", - "from qiskit.visualization import plot_distribution\n", - "\n", - "# Imports from Qiskit Runtime\n", - "from qiskit_ibm_runtime import QiskitRuntimeService, Sampler, Batch" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "8668ab00", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'ibm_nairobi'" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", - "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", - "backend = service.least_busy(operational=True, simulator=False)\n", - "backend.name" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "d4845f4d", - "metadata": {}, - "source": [ - "## Step 1: Map classical inputs to a quantum problem\n", - "\n", - "Grover's algorithm requires an [oracle](https://learning.quantum-computing.ibm.com/course/fundamentals-of-quantum-algorithms/grovers-algorithm) that specifies one or more marked computational basis states, where \"marked\" means a state with a phase of -1. A controlled-Z gate, or its multi-controlled generalization over $N$ qubits, marks the $2^{N}-1$ state (`'1'`*$N$ bit-string). Marking basis states with one or more `'0'` in the binary representation requires applying X-gates on the corresponding qubits before and after the controlled-Z gate; equivalent to having an open-control on that qubit. In the following code, we define an oracle that does just that, marking one or more input basis states defined through their bit-string representation. The `MCMT` gate is used to implement the multi-controlled Z-gate." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "7d27e3b4", - "metadata": {}, - "outputs": [], - "source": [ - "def grover_oracle(marked_states):\n", - " \"\"\"Build a Grover oracle for multiple marked states\n", - "\n", - " Here we assume all input marked states have the same number of bits\n", - "\n", - " Parameters:\n", - " marked_states (str or list): Marked states of oracle\n", - "\n", - " Returns:\n", - " QuantumCircuit: Quantum circuit representing Grover oracle\n", - " \"\"\"\n", - " if not isinstance(marked_states, list):\n", - " marked_states = [marked_states]\n", - " # Compute the number of qubits in circuit\n", - " num_qubits = len(marked_states[0])\n", - "\n", - " qc = QuantumCircuit(num_qubits)\n", - " # Mark each target state in the input list\n", - " for target in marked_states:\n", - " # Flip target bit-string to match Qiskit bit-ordering\n", - " rev_target = target[::-1]\n", - " # Find the indices of all the '0' elements in bit-string\n", - " zero_inds = [ind for ind in range(num_qubits) if rev_target.startswith(\"0\", ind)]\n", - " # Add a multi-controlled Z-gate with pre- and post-applied X-gates (open-controls)\n", - " # where the target bit-string has a '0' entry\n", - " qc.x(zero_inds)\n", - " qc.compose(MCMT(ZGate(), num_qubits - 1, 1), inplace=True)\n", - " qc.x(zero_inds)\n", - " return qc" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "bca14740", - "metadata": {}, - "source": [ - "### Specific Grover's instance\n", - "\n", - "Now that we have the oracle function, we can define a specific instance of Grover search. In this example we will mark two computational states out of the eight available in a three-qubit computational space:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "c150298f", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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MmjULvXr16rCPu7s7gLZBduLECXz55Zfw8fHBmDFjbFIrWdel5hYUffaDxeMKN3ynQDX24+2PD+Fw4VksXxiLla+Oxe2Rt2DRyp9RVHJO7dKsrubXUvy2P9+iMZcutuBE+o/KFGQHtDz/mg2y3bt3AwDi4+Ov26es7PI79muDbMKECaisrMTWrVsxZcoUZYskRVT89AsunKm1eFzprhzNviMHAJNJRmJKJtx6OOGFR8OQpTfgw78eVbssRRRv/rFL405s6do4EWh5/p3VLkApp0+fBgAEBAR02G4ymbBv3z4AbYNMp7N+tsfExMBgaL/ZgJQRax6I+zHU4nGyWcbYkbehSmpSoCrLmOECeKdY/bjn6ptxsfkSXF2csCOrFNbcgR4SGgodWqx3wG54xByMKPS3eFxFfjH8/f0VqMhySqwBJecf6N4a8PHxQW5ubpfGajbIGhoaAABNTR2flNLT02E0GuHp6YmhQy0/6VnCYDCgvLxc0Z9BV9W69wB6d23sb1W/ocJkB1dlkivgbf3Drl8yHq4uTsgvrkHK3FHY/N0pnCyzzr+3sqICkO1j92dj70GAu+XjLpnNKDfYye+qAmtAyfkH1FsDmg0yHx8f1NTUQK/XY+zYsW3aKisr8fLLLwMAoqKiFN/Q4ePjo+jx6Xdkd6ALGxAvQYbHLX3hJ6m/g9UMF1Ra+ZjznwhHfOwgvLYiF9/uOQ19+gysWzIek57eYZXj+w4aZDdXZM1m56ufF7NAna4Ffn5+1i+oC6y9BpSef6B7a6A750nNBtmUKVNQUFCAtLQ0TJ06FaGhoQCAnJwcPPXUUzAajQBs80Horl4uU9eYW0zYEvMnNFXVWjQu6L44HF/7pTJFWaihsQW94jZa7XjBQ7yQuiAGB/POIG3dEZjNMhav1iN1wRjMfyIcKz+3bGNER44XFaGnh4sVqu2+2qIyfDPxJYvH3f/Wi3h17nTrF9QF1lwDtph/QL01oNnNHsnJyejXrx9KS0sRERGByMhIhISEIDY2FkFBQZg8eTKAts/HSBt0Ls4IfXKqxeOGz7lbgWrUJ0nAhrcnwEknITHlp9at1svW5yHn6BmkLohBkL/nTY4ilj6h/vAZN9KiMU5urgh+ZJIyBanIEeZfs0Hm7++PrKwsTJs2DW5ubigpKYG3tzfWrFmDjIwMFBUVAWCQaVXEH6ejz4ghne4fNHM8fO+MVLAi9SxMjMS4WwfijY/0KDx1dau12SxjzuuZcHbSYd2S8Tc4gphil8yBS6/OPyiLfWsOevTp+KM6InOE+ddskAFAWFgYtm/fjrq6OtTV1eHAgQOYO3cuGhoaUFJSAp1Oh5EjLXvXRmJw9eqJuzaloG94x7tWrzV0xjiM++AFTX74fcTQ3nj7xduw/5cqvP9p+63W+cW1WLxaj4kxvpj/RLgKFSrHOzwQUz5b1KlwGvNmIobPvssGVdmWo8y/JDvgV0AfOHAAcXFxGD58OAoLC9u1f/HFFwCAzZs3Y8uWLdiyZQsAIDAwEDExMTatlbqnpaEJJ/53Dwo3fIdzJ9ruRvMZNxIj5tyNgPtuh6TAxy66w9rPyGyhPnu23Twju1ZDxVkUbvgbjn/+Ay6cPd+mLWjmeIx4+l7cMjpUpequj2ug8xwyyD755BM899xzeOSRR5Cent6u/XrvzBMTE7FhwwaFqyMlyLKM6rxT2HZP8uXdbBIwp+ILtcu6Lp7ErO/SxRYYD5/Azn99nWtAIWqtAc3uWryRvLzL36l3vedjDpjtmidJEvpFBUGSJMiyrMnbiHRjTj1cMPD2MK4BDbKv+yk2crMgIyIicTjkFdmV72EkIiLxOeQVGRERaQeDjIiIhMYgIyIioTHIiIhIaAwyIiISGoOMiIiExiAjIiKhMciIiEhoDDIiIhIag4yIiITGICMiIqE55HctEtk7D3dn1GfPVrsMi3i483RiTVwDnceVR2SHJEmy67/tRcrjGug83lokIiKhMciIiEhoDDIiIhIag4yIiITGICMiIqExyIiISGgMMiIiEhqDjIiIhMYgIyIioTHIiIhIaAwyIiISGoOMiIiExiAjIiKhMciIiEhoDDIiIhIag4yIiITGICMiIqHxL0TbKVmW0dhkUruMTvNwd4YkSWqXoRmizT/ANUDqYZDZqcYmE3rFbVS7jE6rz57NP8tuRaLNP8A1QOrhrUUiIhIag4yIiITGICMiIqExyIiISGgMMiIiEhqDjIiIhMYgIyIioTHIiIhIaAwyIiISGoOMiIiExiAjIiKhMciIiEhoDDIiIhIag4yIiITmEEFmNBqRnJyM4OBguLm5YfDgwViwYAEaGhrwzDPPQJIkrFq1Su0yFbE0aTTkI8/gDzNCOmzfs/Y+XMidg4jgvjauzHaaztTilw+/xDcTX4JslgEAslnG8U0/wNR4UeXqlMc1ANT8WorsV/8bW8Y832YNlO0+BNlsVrk66i7N/z2yw4cP495774XBYEDPnj0RHh6OiooKrFixAsXFxaiurgYAjBo1St1CFbL4o0NImDgEH/z5duzaX47y3xpb2156MgKTxvjilQ9zcOxEjYpVKkOWZfzywRYc+c8vYW651K5937+tRs6S/8GdH76IIXePUaFC23DkNdDSeAF7k1bhdEZ2h+3fz1qK3sF+iF+XjD4hfjaujqxF01dkRqMRCQkJMBgMWLhwISorK6HX62EwGJCWloaMjAzk5ORAkiRERUWpXa4iWkxmJKZkoqe7C9YuHt/6emhgbyydH4PsI1V4b0OeihUqQ5ZlHHxjAw4v39xhiF3RXFuPPU8vQ8m2f9iwOtty1DVgarqIvz/2H9cNsSvOnSjHzvsXobaozEaVkbVpOsiSkpJQVlaGefPmYfny5fD09GxtS05ORnR0NEwmEwIDA+Hl5aVipco6VHAWqWt/wd3j/PHcg8Oh00nYuHQCJAlITMmE+Z+3WrTk9Pb9KPgko1N9ZbOMzHkrUVdapXBV6nHENfDz0r+iKqewU30v1tZj99PLeJtRUJoNsoKCAqSnp6N///5ITU3tsM/o0aMBANHR0a2vffHFF3jwwQcREBAADw8PjBgxAosWLUJ9fb1N6lbK2x8fwuHCs1i+MBYrXx2L2yNvwaKVP6Oo5JzapSki/793WNTf3NyCov/5u0LV2AdHWgPN5xtwfNNui8acL65A+Z7DyhREitJskG3atAlmsxmzZs1Cr169Ouzj7u4OoG2QLV++HE5OTnjnnXewc+dOPP/881i9ejXuuecemAV+t2YyyUhMyYRbDye88GgYsvQGfPjXo2qXpYjq/JJOvxO/1vHPf8Cliy0KVGQfHGkNFH+R2aWNPIWffqdANaQ0zW722L378rux+Pj46/YpK7t8T/zaINu2bRsGDBjQ+v8TJ07EgAEDMGvWLOzduxcTJkywuJaYmBgYDAaLxpjhAninWPyzbuRcfTMuNl+Cq4sTdmSVQrbi3aSQ0FDoYB8hcJt5AGZimMXjLpw9j1uDRqBaUn8noxLzDzjOGphpHobbMODmHX+n4O/7McffX4GK6GZ8fHyQm5vbpbGaDbLTp08DAAICAjpsN5lM2LdvH4C2QXZtiF0RExMDACgvL+9SLQaDwfKxkivg3aUfd13rl4yHq4sT8otrkDJ3FDZ/dwony+qscuzKigpAbrbKsbprhIcb0MVHnrVVZ1FusoNbbQrMP+A4a8DU2x9wt3ycs1lCuaFrv+ekHs0GWUNDAwCgqampw/b09HQYjUZ4enpi6NChNzzWnj17AABhYWFdqsXHx8fiMWa4oLJLP61j858IR3zsILy2Ihff7jkNffoMrFsyHpOetuxZ0vX4DhpkN+/G3cy9AAuvNGTIkCDB6xZv+Ekd34q2JWvPP+BYa0BndrF4DQDARZ0Zfn7chq+Grpwnr9BskPn4+KCmpgZ6vR5jx45t01ZZWYmXX34ZABAVFQVJkq57nPLycrz++uu45557uvxZs65cLjc0tqBX3MYu/bzfCx7ihdQFMTiYdwZp647AbJaxeLUeqQvGYP4T4Vj5eX63f8bxoiL09HCxQrXd1/hbDbbE/Amy6frb7n9PgoQ+of7I+3HLDdeDrVhz/gHHWwOndxzAnmfes3hc7FPTUbZsmwIVkZI0u9ljypQpAIC0tDQUFRW1vp6Tk4P4+HgYjUYAN/4gdH19PR544AG4urpi3bp1itarFEkCNrw9AU46CYkpP7Vus162Pg85R88gdUEMgvw9b3IUsXgM7IuA+263eNzwOXfbRYhZmyOugcF3xcDD1/J7syMS71agGlKaZoMsOTkZ/fr1Q2lpKSIiIhAZGYmQkBDExsYiKCgIkydPBtD2+di1mpqakJCQgFOnTmHXrl3w9fW1ZflWszAxEuNuHYg3PtKj8NTVZz9ms4w5r2fC2UmHdUvG3+AIYhr5/P3QuXb+hkNPv/4Y9tBEBStSjyOuAZ2zE6KSZlo0ZvBdMfCOCFSmIFKUZoPM398fWVlZmDZtGtzc3FBSUgJvb2+sWbMGGRkZrVdpHQVZS0sLHnroIeTm5mLnzp0IDw+3dflWMWJob7z94m3Y/0sV3v+0/Tbr/OJaLF6tx8QYX8x/Qsx/4/X0HxWMCauSIDk73bSvW//emPrZIrh6etigMtty5DUwPPFuRPwxoVN9+98ajAl/WaBwRaQUSZatuQFXDPX19fDy8oIkSairq4OHx9UTmNlsxmOPPYatW7dix44drVdutmbtZyRKq8+ebTfPR65VkXUEuUs2ovpoSftGSYJf/CjEpT4LzyEDbV7bjYg2/4B9rgFZllG44W/IW/E1Gg3V7dqd3FwR/MgkxLw5Gy4ebipUSNag2c0eN3Ls2DHIsozQ0NA2IQYAL774IrZs2YJXXnkFHh4eyM6++j1tw4YN63B7PtmvQeOjkLDrPZz5uQgnv96Lpqoa6Jyd4Bngg5DHJ8MzwL4CjKxLkiSE/eFeDH9yKkp35aLsBz2azzXA2aMHvCODEPzIJPToo/4uVeoehwyyvLzLX5Da0W3FnTt3AgDeffddvPvuu23a1q9fjzlz5iheH1mXJEm4JWY4bokZrnYppBKdizMCpsUhYFqc2qWQAhhkv1NSUmLjaoiIqDs0u9njRm4UZEREJBaHvCK78j2MREQkPoe8IiMiIu1gkBERkdAYZEREJDQGGRERCY1BRkREQmOQERGR0BhkREQkNAYZEREJjUFGRERCY5AREZHQHPLvkYlAlmU0NpnULqPTPNydIUmS2mVohmjzD3ANkHoYZEREJDTeWiQiIqExyIiISGgMMiIiEhqDjIiIhMYgIyIioTHIiIhIaAwyIiISGoOMiIiExiAjIiKhMciIiEhoDDIiIhIag4yIiITGICMiIqExyIiISGgMMiIiEhqDjIiIhMYgIyIioTHIiIhIaAwyIiISGoOMiIiExiAjIiKhMciIiEhoDDIiIhIag4yIiITGICMiIqH9P1i/7V/0x5bZAAAAAElFTkSuQmCC", - "text/plain": [ - "
" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "marked_states = [\"011\", \"100\"]\n", - "\n", - "oracle = grover_oracle(marked_states)\n", - "oracle.draw(output=\"mpl\", style=\"iqp\")" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "25487b93", - "metadata": {}, - "source": [ - "### GroverOperator\n", - "\n", - "The built-in Qiskit `GroverOperator` takes an oracle circuit and returns a circuit that is composed of the oracle circuit itself and a circuit that amplifies the states marked by the oracle. Here, we `decompose` the circuit to see the gates within the operator:" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "283d5265", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "grover_op = GroverOperator(oracle)\n", - "grover_op.decompose().draw(output=\"mpl\", style=\"iqp\")" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "83c34dc9", - "metadata": {}, - "source": [ - "Repeated applications of this `grover_op` circuit amplify the marked states, making them the most probable bit-strings in the output distribution from the circuit. There is an optimal number of such applications that is determined by the ratio of marked states to total number of possible computational states:" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "f4c3d4b5", - "metadata": {}, - "outputs": [], - "source": [ - "optimal_num_iterations = math.floor(\n", - " math.pi / (4 * math.asin(math.sqrt(len(marked_states) / 2**grover_op.num_qubits)))\n", - ")" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "e06c8238", - "metadata": {}, - "source": [ - "### Full Grover circuit\n", - "\n", - "A complete Grover experiment starts with a Hadamard gate on each qubit; creating an even superposition of all computational basis states, followed the Grover operator (`grover_op`) repeated the optimal number of times. Here we make use of the `QuantumCircuit.power(INT)` method to repeatedly apply the Grover operator." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "4933ae44", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc = QuantumCircuit(grover_op.num_qubits)\n", - "# Create even superposition of all basis states\n", - "qc.h(range(grover_op.num_qubits))\n", - "# Apply Grover operator the optimal number of times\n", - "qc.compose(grover_op.power(optimal_num_iterations), inplace=True)\n", - "# Measure all qubits\n", - "qc.measure_all()\n", - "qc.draw(output=\"mpl\", style=\"iqp\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 2: Optimize problem for quantum execution.\n", - "\n", - "For this example, the circuit the operators are simple, so no optimizations are needed." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "c5edec73", - "metadata": {}, - "source": [ - "## Step 3: Execute using Qiskit Primitives.\n", - "\n", - "Amplitude amplification is a sampling problem that is suitable for execution with the [`Sampler`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Sampler#sampler) runtime primitive. Because we have a single circuit, we instantiate the [`Batch`](https://docs.quantum-computing.ibm.com/run/run-primitives-batch) context manager to run our non-iterative workload." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "# To run on local simulator:\n", - "# 1. Use the Sampler from qiskit.primitives instead\n", - "# 2. Remove the Batch context manager below\n", - "\n", - "with Batch(backend=backend) as batch:\n", - " sampler = Sampler()\n", - " dist = sampler.run(qc, shots=10000).result().quasi_dists[0]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 4: Post-process, return result in classical format." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "a5ef9913", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plot_distribution(dist.binary_probabilities())" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "0e4223d0", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.14.1'" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit_ibm_runtime\n", - "\n", - "qiskit_ibm_runtime.version.get_version_info()" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "5e6db65c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.45.0'" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit\n", - "\n", - "qiskit.version.get_version_info()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/docs/tutorials/grovers_algorithm/grover_with_sampler.ipynb b/docs/tutorials/grovers_algorithm/grover_with_sampler.ipynb new file mode 100644 index 000000000..5d33ce155 --- /dev/null +++ b/docs/tutorials/grovers_algorithm/grover_with_sampler.ipynb @@ -0,0 +1,411 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "e57d1e6b", + "metadata": {}, + "source": [ + "## Background\n", + "\n", + "Amplitude amplification is a general purpose quantum algorithm, or subroutine, that can be used to obtain a quadratic speedup over a handful of classical algorithms. [Grover’s algorithm](https://arxiv.org/abs/quant-ph/9605043) was the first to demonstrate this speedup on unstructured search problems. Formulating a Grover's search problem requires an oracle function that marks one or more computational basis states as the states we are interested in finding, and an amplification circuit that increases the amplitude of marked states, consequently suppressing the remaining states. \n", + "\n", + "Here, we demonstrate how to construct Grover oracles and use the `GroverOperator` from the Qiskit circuit library to easily set up a Grover's search instance. The runtime `Sampler` primitive allows seamless execution of Grover circuits, including automatic compilation, error suppression, and readout error mitigation techniques." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "54602708", + "metadata": {}, + "source": [ + "## Setup\n", + "\n", + "Here we import the small number of tools we need for this tutorial." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "e2cb0472", + "metadata": {}, + "outputs": [], + "source": [ + "# Built-in modules\n", + "import math\n", + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "# Imports from Qiskit\n", + "from qiskit import QuantumCircuit\n", + "from qiskit.circuit.library import GroverOperator, MCMT, ZGate\n", + "from qiskit.visualization import plot_distribution\n", + "\n", + "# Imports from Qiskit Runtime\n", + "from qiskit_ibm_runtime import QiskitRuntimeService, Sampler, Batch" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "8668ab00", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ibmq_mumbai'" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", + "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", + "backend = service.least_busy(operational=True, simulator=False)\n", + "backend.name" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "d4845f4d", + "metadata": {}, + "source": [ + "## Step 1: Map classical inputs to a quantum problem\n", + "\n", + "Grover's algorithm requires an [oracle](https://learning.quantum-computing.ibm.com/course/fundamentals-of-quantum-algorithms/grovers-algorithm) that specifies one or more marked computational basis states, where \"marked\" means a state with a phase of -1. A controlled-Z gate, or its multi-controlled generalization over $N$ qubits, marks the $2^{N}-1$ state (`'1'`*$N$ bit-string). Marking basis states with one or more `'0'` in the binary representation requires applying X-gates on the corresponding qubits before and after the controlled-Z gate; equivalent to having an open-control on that qubit. In the following code, we define an oracle that does just that, marking one or more input basis states defined through their bit-string representation. The `MCMT` gate is used to implement the multi-controlled Z-gate." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "7d27e3b4", + "metadata": {}, + "outputs": [], + "source": [ + "def grover_oracle(marked_states):\n", + " \"\"\"Build a Grover oracle for multiple marked states\n", + "\n", + " Here we assume all input marked states have the same number of bits\n", + "\n", + " Parameters:\n", + " marked_states (str or list): Marked states of oracle\n", + "\n", + " Returns:\n", + " QuantumCircuit: Quantum circuit representing Grover oracle\n", + " \"\"\"\n", + " if not isinstance(marked_states, list):\n", + " marked_states = [marked_states]\n", + " # Compute the number of qubits in circuit\n", + " num_qubits = len(marked_states[0])\n", + "\n", + " qc = QuantumCircuit(num_qubits)\n", + " # Mark each target state in the input list\n", + " for target in marked_states:\n", + " # Flip target bit-string to match Qiskit bit-ordering\n", + " rev_target = target[::-1]\n", + " # Find the indices of all the '0' elements in bit-string\n", + " zero_inds = [ind for ind in range(num_qubits) if rev_target.startswith(\"0\", ind)]\n", + " # Add a multi-controlled Z-gate with pre- and post-applied X-gates (open-controls)\n", + " # where the target bit-string has a '0' entry\n", + " qc.x(zero_inds)\n", + " qc.compose(MCMT(ZGate(), num_qubits - 1, 1), inplace=True)\n", + " qc.x(zero_inds)\n", + " return qc" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "bca14740", + "metadata": {}, + "source": [ + "### Specific Grover's instance\n", + "\n", + "Now that we have the oracle function, we can define a specific instance of Grover search. In this example we will mark two computational states out of the eight available in a three-qubit computational space:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "c150298f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "marked_states = [\"011\", \"100\"]\n", + "\n", + "oracle = grover_oracle(marked_states)\n", + "oracle.draw(output=\"mpl\", style=\"iqp\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "25487b93", + "metadata": {}, + "source": [ + "### GroverOperator\n", + "\n", + "The built-in Qiskit `GroverOperator` takes an oracle circuit and returns a circuit that is composed of the oracle circuit itself and a circuit that amplifies the states marked by the oracle. Here, we `decompose` the circuit to see the gates within the operator:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "283d5265", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "grover_op = GroverOperator(oracle)\n", + "grover_op.decompose().draw(output=\"mpl\", style=\"iqp\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "83c34dc9", + "metadata": {}, + "source": [ + "Repeated applications of this `grover_op` circuit amplify the marked states, making them the most probable bit-strings in the output distribution from the circuit. There is an optimal number of such applications that is determined by the ratio of marked states to total number of possible computational states:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "f4c3d4b5", + "metadata": {}, + "outputs": [], + "source": [ + "optimal_num_iterations = math.floor(\n", + " math.pi / (4 * math.asin(math.sqrt(len(marked_states) / 2**grover_op.num_qubits)))\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "e06c8238", + "metadata": {}, + "source": [ + "### Full Grover circuit\n", + "\n", + "A complete Grover experiment starts with a Hadamard gate on each qubit; creating an even superposition of all computational basis states, followed the Grover operator (`grover_op`) repeated the optimal number of times. Here we make use of the `QuantumCircuit.power(INT)` method to repeatedly apply the Grover operator." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "4933ae44", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc = QuantumCircuit(grover_op.num_qubits)\n", + "# Create even superposition of all basis states\n", + "qc.h(range(grover_op.num_qubits))\n", + "# Apply Grover operator the optimal number of times\n", + "qc.compose(grover_op.power(optimal_num_iterations), inplace=True)\n", + "# Measure all qubits\n", + "qc.measure_all()\n", + "qc.draw(output=\"mpl\", style=\"iqp\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Optimize problem for quantum execution." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "c9a3020e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "\n", + "target = backend.target\n", + "pm = generate_preset_pass_manager(target=target, optimization_level=3)\n", + "\n", + "circuit_ibm = pm.run(qc)\n", + "circuit_ibm.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "c5edec73", + "metadata": {}, + "source": [ + "## Step 3: Execute using Qiskit Primitives.\n", + "\n", + "Amplitude amplification is a sampling problem that is suitable for execution with the [`Sampler`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Sampler#sampler) runtime primitive. Because we have a single circuit, we instantiate the [`Batch`](https://docs.quantum-computing.ibm.com/run/run-primitives-batch) context manager to run our non-iterative workload." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# To run on local simulator:\n", + "# 1. Use the Sampler from qiskit.primitives instead\n", + "# 2. Remove the Batch context manager below\n", + "\n", + "with Batch(backend=backend) as batch:\n", + " sampler = Sampler()\n", + " dist = sampler.run(circuit_ibm, skip_transpilation=True, shots=10000).result().quasi_dists[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 4: Post-process, return result in classical format." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "a5ef9913", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_distribution(dist.binary_probabilities())" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "0e4223d0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'0.19.1'" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit_ibm_runtime\n", + "\n", + "qiskit_ibm_runtime.version.get_version_info()" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "5e6db65c", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.0.0rc1'" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit\n", + "\n", + "qiskit.version.get_version_info()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/tutorials/learning-api.conf.yaml b/docs/tutorials/learning-api.conf.yaml new file mode 100644 index 000000000..822b6d10e --- /dev/null +++ b/docs/tutorials/learning-api.conf.yaml @@ -0,0 +1,15 @@ +# These tutorials are uploaded to the IBM Quantum Learning app +# https://learning.quantum.ibm.com/catalog/tutorials +# urlProduction refers to a link in the Learning CMS +lessons: + - path: variational_quantum_eigensolver + urlProduction: tutorials/5e01f54c-0ef4-4003-8793-d6e5717110bb + - path: chsh_inequality + urlProduction: tutorials/da7dbfe7-4ae7-4889-b78d-5dfd5263fb02 + - path: grovers_algorithm + urlProduction: tutorials/76db794e-a4a7-466e-bd2b-d5d5950a9279 + - path: quantum_approximate_optimization_algorithm + urlProduction: tutorials/8c5868ac-d82f-4ca4-ba9d-70d3d6344e80 + - path: submitting_transpiled_circuits + urlProduction: tutorials/0f49821a-9de4-4932-a77a-ec3faf23cf55 + \ No newline at end of file diff --git a/docs/tutorials/qaoa_with_primitives.ipynb b/docs/tutorials/qaoa_with_primitives.ipynb deleted file mode 100644 index 835495c25..000000000 --- a/docs/tutorials/qaoa_with_primitives.ipynb +++ /dev/null @@ -1,598 +0,0 @@ -{ - "cells": [ - { - "attachments": {}, - "cell_type": "markdown", - "id": "644fe680", - "metadata": {}, - "source": [ - "# Quantum Approximate Optimization Algorithm\n" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "f028436d", - "metadata": {}, - "source": [ - "## Background\n", - "\n", - "The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid iterative method for solving combinatorial optimization problems. In this tutorial, we demonstrate how to implement the QAOA algorithm using Qiskit Runtime for solving a simple max-cut problem.\n", - "\n", - "In a max-cut problem, we want to partition nodes of a graph in a way that maximizes the number of edges between nodes in differing groups. The desired max-cut partition for the following graph is clear: the 0th-node on the left should be separated from the rest of the nodes on the right by a cut. We will find this answer by applying QAOA by using Qiskit Runtime primitives and sessions." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "e291b6c0", - "metadata": {}, - "source": [ - "## Setup" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "id": "4a7d432c", - "metadata": {}, - "outputs": [], - "source": [ - "# General imports\n", - "import numpy as np\n", - "\n", - "# Pre-defined ansatz circuit, operator class and visualization tools\n", - "from qiskit.circuit.library import QAOAAnsatz\n", - "from qiskit.quantum_info import SparsePauliOp\n", - "from qiskit.visualization import plot_distribution\n", - "\n", - "# Qiskit Runtime\n", - "from qiskit_ibm_runtime import QiskitRuntimeService\n", - "from qiskit_ibm_runtime import Estimator, Sampler, Session, Options\n", - "\n", - "# SciPy minimizer routine\n", - "from scipy.optimize import minimize\n", - "\n", - "# rustworkx graph library\n", - "import rustworkx as rx\n", - "from rustworkx.visualization import mpl_draw" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "metadata": {}, - "outputs": [], - "source": [ - "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", - "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", - "backend = service.least_busy(operational=True, simulator=False)\n", - "backend.name" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 1: Map classical inputs to a quantum problem\n", - "\n", - "To demonstrate max-cut, we'll create a graph using the [rustworkx library](https://github.com/Qiskit/rustworkx), and create Pauli Hamiltonian that encodes the cost in a manner such that the minimum expectation value of the operator corresponds to the maximum number of edges between the nodes in two different groups." - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "num_nodes = 5\n", - "# The edge syntax is (start, end, weight)\n", - "edges = [(0, 1, 1), (0, 2, 1), (0, 3, 1), (0, 4, 1)]\n", - "\n", - "G = rx.PyGraph()\n", - "G.add_nodes_from(range(num_nodes))\n", - "G.add_edges_from(edges)\n", - "mpl_draw(\n", - " G, pos=rx.bipartite_layout(G, {0}), with_labels=True, node_color=\"#EE5396\", font_color=\"#F4F4F4\"\n", - ")" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "987e72fd", - "metadata": {}, - "source": [ - "For this simple example, the operator is a linear combination of terms with `Z` operators on nodes connected by an edge (recall that the 0th qubit is farthest right): $IIIZZ + IIZIZ + IZIIZ + ZIIIZ$. Once the operator is constructed, the ansatz for the QAOA algorithm can easily be built by using the [`QAOAAnsatz`](https://docs.quantum-computing.ibm.com/api/qiskit/qiskit.circuit.library.QAOAAnsatz#qaoaansatz) circuit from the Qiskit circuit library." - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "b6dabf56", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "execution_count": 25, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Problem to Hamiltonian operator\n", - "hamiltonian = SparsePauliOp.from_list([(\"IIIZZ\", 1), (\"IIZIZ\", 1), (\"IZIIZ\", 1), (\"ZIIIZ\", 1)])\n", - "# QAOA ansatz circuit\n", - "ansatz = QAOAAnsatz(hamiltonian, reps=2)\n", - "\n", - "ansatz.decompose(reps=3).draw(output=\"mpl\", style=\"iqp\")" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "da92068c", - "metadata": {}, - "source": [ - "The previous image illustrates the ansatz in basic gates for clarity. However, it can be expressed in multiple levels of decomposition by changing the `reps` argument or by drawing the circuit without the `decompose` method. For example, the following representation directly shows the QAOA structure with the default `reps` value, which is `reps=1`. " - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "8fbe14ff", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "execution_count": 26, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ansatz.decompose().draw(output=\"mpl\", style=\"iqp\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 2: Optimize problem for quantum execution.\n", - "\n", - "We can schedule a series of [qiskit.transpiler](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler) passes to optimize our circuit for a selected backend. This includes a few components:\n", - "\n", - "- [`optimization_level`](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler_preset#preset-pass-manager-generation): The lowest optimization level does the bare minimum needed to get the circuit running on the device; it maps the circuit qubits to the device qubits and adds swap gates to allow all 2-qubit operations. The highest optimization level is much smarter and uses lots of tricks to reduce the overall gate count. Since multi-qubit gates have high error rates and qubits decohere over time, the shorter circuits should give better results.\n", - "- [Dynamical Decoupling](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_provider.transpiler.passes.scheduling.PadDynamicalDecoupling): We can apply a sequence of gates to idling qubits. This cancels out some unwanted interactions with the environment." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit.transpiler import PassManager\n", - "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", - "from qiskit_ibm_runtime.transpiler.passes.scheduling import (\n", - " ALAPScheduleAnalysis,\n", - " PadDynamicalDecoupling,\n", - ")\n", - "from qiskit.circuit.library import XGate\n", - "\n", - "target = backend.target\n", - "pm = generate_preset_pass_manager(target=target, optimization_level=3)\n", - "pm.scheduling = PassManager(\n", - " [\n", - " ALAPScheduleAnalysis(durations=target.durations()),\n", - " PadDynamicalDecoupling(\n", - " durations=target.durations(),\n", - " dd_sequences=[XGate(), XGate()],\n", - " pulse_alignment=target.pulse_alignment,\n", - " ),\n", - " ]\n", - ")\n", - "\n", - "ansatz_ibm = pm.run(ansatz)" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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p168fqampjB49Ol8CiyM8//zzPPLII1bPvfjii8TGxvL8888zZ84ci8ScSZMm0aZNG7KysggKCjKPl4LqMzG1w63vVUVS1jG+9957jBo1itjYWHr27GkeM470448/snbtWiC3/6T46gz7Bzg5E7/8n1bPn5n/DDmZaQRNWFK2gd2uDAYwgDEnx+LwgTlfc+nIaTpNfwyPOj4W51qMG0hAl1AOzFnJ5WNnyzLaMqExKCIiIiIiIiIiInJ7KZMtLX799VcA8xfh9jh69CgADRo0MB8r7Mt/00T4rdscwM1J9P79+1tMcpsEBQURGBjI2bNniYuLo1mzZhblbq3TdNxWLJC7fQDcXJXhVo5qFyhZ26Snp7Nu3TrzEvIpKSnk/P/JEVOig5ubm0UZ04T10KFD6d+/f746MzIyAPJNktvTbo7o52HDhpmTNfJydXUF4MEHH+Tee+/Nd97FJfeVuHXZelO9q1atypcY4uLiwrhx45gwYYJ53JhERESwfPlyAgICmDVrltXnMT1nXFyc+djhw4dZvXo13t7eVssZDAY6dOhARESE1XayNm6zsrLIyMggOzub3377jfvuu89qPNbqKWi1jeI8n6neXr168fjjj9u8f2HvEGB1dZRu3brx008/MWTIENauXcvEiRMZMGBAvr4rDUeOHGHlypX4+fnZbJP27dtz8OBBq2O4IKZ2OHfuXInjLC2OjDE2Ntau66ZPn05cXBybN2+mZ8+ebNmyJd/vyOI6ceIEo0aNAnITWfJu5SJF514nGJ9uw0nesoyUiG1UD725Ysa579/nyp4fuGNOGE5VtHWII/i3DebC/uh8x3Mys9g24UMGrp9F1/+M55dH/g2AV5O6tJv8COf3RnF4/rqyDrdMaAyKiIiIiIiIiIiI3F5KPeEhOzvbPGnVtGlTu8pkZWWZl7Lv3LkzABcvXiQ2Npbq1avb3KfdNFFe0ES4aeUBa0xfWlerVi1fuVsnfO2ZuDft+X7r1/fguHaBkrXNpk2bePzxxzl7tuCvOBs3bmzxsynhYdiwYVavP3Ysd/nsW5+tsHZzVD8PHz7catnIyMgCzx8/fhzAInEhJyfHvKVH27Zt8fDwwGg0Eh8fT0xMDFlZWURFReVrI4AVK1aQk5NDdna21QQMuJkcknfVjq+++gqj0cjIkSPzbdthUqVKFaDgdsjbzi4uLjzwwAN88803DBw4kF69ejF06FAGDRpEYGCg1XsU1l/FfT5TvaaJZFsKeocKYzAYmD17NmvXriU6OppDhw5ZrNBRWkxtMnLkSIvfJXmZVusoasKDqZypXSoiR8ZYnO0jYmJiePTRRx2ypUZiYiL33nsvycnJ9OvXjzlz5pS4ToGAh14nedsK4pf/k2YzcxP/UsJ/JfbL1wj55waq1A4q3wArqdqdm3Mu7BjG7JurOQT2bEvEoh+sXp986BThH3zHnX9/iKaP9uH48s10e/8FALZN+DDfqhC3E41BERERERERERERkdtHqSc8XLt2zbxagK3Jv1tt2LCBixcvAvDwww8DllsKWPtKOycnx+Yy/tnZ2Rw+fBgnJyebqylkZ2dz5swZ4ObqCZmZmURGRuLk5JRvotSehAdfX18SEhK4dOlSvnOOahcoftvs2rWLAQMGkJmZyZNPPsnIkSNp2bIlNWvWxMXFhaNHj9K8eXNcXFxo3ry5uVx6erp5pQlb7VncRJGS9LOpvwDuueceq2XDw8Ntnjcajebzees+duwY169fB2Dz5s0Wq1Zs2LCBwYMHs2nTJpYsWcLYsWMt6ty8eTOQu1KBabUCW4KCgvKV6927t83r4+PjgfyT5gWN2y+//JIWLVqwePFiNm/ezObNm3nuuefo0aMHb731lkUiDRTeX8V5vrz9VNgqEwW9Q/Zo1qwZPj4+JCcnc/z48TJJeDC1Sc+ePW1eY0p2KmrCQ3JyMpDbLhWVI2Ns1apVvtVlbLl48aJ5O4u8v6+Ky5TkEB0dTdeuXfnuu+/MK8RIwaq36kH7tUab56vWb07777LNP6cnxXDy3YepN+ZdqrfqUQYR3n6CBnWh63vPsumxt0nccXMLKlcvDzJTrtssd3DuKhr060CHf47GJzQI/3Yh7J6+hKsn4ssi7FKjMSgiIiIiIiIiIiLy51HqCQ/Vq1fH2dmZ7OxsuyYtjUYj//537tLKffr0ITQ0FLg58dq2bVur5Xbt2kVqaire3t40bNjQ4tyxY8e4ceMGtWrVsvm1/B9//EFKSgqhoaEEBAQAuUvTZ2RkEBISYvF1et54Ckp4qFWrFgkJCeYJwLwc1S55Yylq20yZMoWMjAzefvttXnvttXzl1q9fD0CLFi3MqwlA7ioJWVlZNGjQwOakpq1tKQprt5L0s6m/GjZsSM2aNfOVPX78OKmpqQQGBuLv75/v/KlTp7hy5QoBAQHUrl0737M0bNgw3xYd/fv3Z+zYscyfP5/PPvssX8KDaWI7JiYmX7wFMa24YWtZ/uzsbHbt2gXknzQvaNy6u7szffp03njjDQ4cOMDatWtZuHAhv/76K3379uXo0aMWqz0U1l/Feb68/WStH/Iq6B2yl2mSOisrq9h1FMXp06cBbLZH3pVaiprwYEp4qlWrVgkiLF2OjHHdunUWiUC2xMbG0r17dyB31Zn58+eX6L5Xr17l3nvv5dChQ7Rr147169fn2+amuEJCQnBycnJIXfYwuFWl9n+Pl9n9iion/TonZj1AjU6DqHXf8+UdDk2bhmDMuFHeYZi5Gp14g06FXhezbgdejQKo/9eO5oQHz0A/UmMLTkQzZmXnbm2x4W3uGHMvSbuOELlofYlibhrSlEyD41aHKO0x7OgxWNHGkIiIiIiIiIiIiEhlERAQwJ49e4pcrtQTHpycnGjTpg379u1j586dPProowVeP2fOHHbv3o2rq6vF8uGmL8LzTvTntXz5csD6BKJpRQDT0vrWfPzxxwCMGDHCfMzWZG9SUhJJSUl4e3sXOBnXtm1bDh48SGRkJAMHDrQ456h2geK1TXZ2tnnJ98cffzxfmZycHJYtW2Z+jrxM7WkrKSE1NZXjx4/j6upKy5YtzcftabeS9HNhyRL2ni9qksZjjz3G/Pnz2bVrF3FxcRYJA6mpqUDRl/c3lbM1Sb927VrOnz9PrVq1qFOnTpHihdztHtq2bUvbtm2ZOHEirVu35uzZs+zevZshQ4YA9vVXcZ6vsH7Iq6B3yB7nz5/n3LlzANSrV6/I5YvD1CY3blif8Fq5ciUXLlygevXqNGrUqEh1m96Pdu3alSzIUlTWMcbFxdGzZ09OnjzJ0KFDWbp0Kc7OzsWu7/r16wwcOJCwsDCaN2/O//73P2rUqOGweBMSEhxWlz2cqnhQu/DLys2lHd9y49RB0uKiuLR9Zb7zoR9G4uZvPfGrNMTHx5OTbntFhLLmZnDG3g48vWE3vZe8RtgbSwCo37cDZ38u/B+GmVevk5ORhbObK7Gb9oHR9soI9ohPiCfDmF34hXYq7THs6DFY0caQiIiIiIiIiIiIyO2u1BMeIPeL23379rF06VKmTp1qMSGc16pVq5g2bRoA77zzjsWk9uXLlwGsbnOwY8cOc8JCQRPhly9fJioqiqZNm1qc37p1K8uWLcPX15cXXnjBfNzW1gnHjh0DyFfPrbp168aSJUvYvXu31fOOaBfTc0HR2iY1NZXs7NwJCWuT1e+99555ZYOiJjyEh4eTk5NDy5YtLZajt6fdStLPhcVV2ES7rf62tVqFSceOHalduzZJSUl8//33PPPMM+ZzDRo0IDk5mY0bN9KsWTOr5a2pU6cOly5dYu/evdx1110W5y5dusSrr74KFNwOBSU85OXt7W3up7xf5dvTX8V5vsL6Ka/C3qHCvPfeexiNRmrUqEHHjh2LVUdRBQQEcOnSJfbt28df/vIXi3MJCQnmvrO1bUtBTKt6mFYzqIjKOsYZM2YQHR3NkCFDWLFiBS4uxf9rLSMjgyFDhrBt2zaaNGnCxo0b8fPzc2C0ue92Wa/wUJH59hyFb89R5R2GWd26dSvU1/muRiewc7GEK1GxYATvpvW4HBVL9UYBpCxJKrRc1/8+h5OrC5ejztJ64oPErNtByunCy9lSt05dh6/wUJocPQYr2hgSERERERERERERqSxMuzAUVZkkPIwfP57Fixdz/Phx+vXrx5dffkn79u3N50+dOsV//vMfPvroI4xGI9OmTWPixIkWdZi+MP/kk08YOnQovr6+5OTksGbNGp5++mnc3NzIysoqMOHB1dWV8ePH8+2335q/2F23bp15hYMlS5ZYbHlhKndrnaZtAmJjY0lNTc23bYBJ3759cXJyYseOHeTk5OSb5HJEuxS3bby8vAgMDCQuLo6ZM2cyf/58nJ2dycjIYN68efzjH//AxcWFrKysIic82EqUsKfdHNHPRY3r1vJFXeHBYDDQv39/lixZki/hYejQoRw4cIApU6ZQu3Zthg4dalE2OjqaZcuW0b17d3r06GE+3qdPHyIjI3nrrbfo3r27ecWLo0ePMmrUKE6ePAkUnOCT99wXX3xBZGQkjz32GC1atDAfv3TpEpMnT+bEiRPccccddO7c2XzOnv4qzvMVZYWHwt6hX375hU2bNjF27FiaNGliPn79+nXmzJnDO++8A+Ru35I3+QZy33fTu28s4RfNefXp04cjR44we/Zs+vbta04YCQsLY9SoUVy4cAGwPyHF5OrVqxw8eBAvL698iRRQes9TFIXFaK/u3bvj5+dn83drXvPmzaNevXpMmTKlRMkO2dnZjBgxgp9//pl69eqxceNG6tatW+z6bDl+/Lhdz+UoN7Kg249ldrtKLyrqOFXL5F9G9sm8nsayJgWvAJXX2V/2UP+vHbkWe4HMa4VPujd/cgB1urZk76zlnP1pN/f//C5d547np7+9UeyYo45H4erhXuzyt6psY7iijSERERERERERERGR253BWEYzY9HR0QwcOND81XhQUBD+/v7ExcWRkJCA0WjE19eX+fPn8/DDD+crHx4eTvv27cnKysLd3Z2goCCSkpK4cuUK//rXv/jyyy+Jiopi7969+ZZSDwgIICkpiU8++YSnn34aDw8PmjdvTkJCArGxsTg5OfH+++/z3HPPWZTz8/Pj4sWLxMbGWqy+kJaWRrNmzThz5gw+Pj40bdoUZ2dnHn30UYvJboABAwawYcMGNm3aRK9evRzeLiVpmwULFjB+/HgAateuTf369Tl+/DjXr1/no48+4tlnnyUnJ4fLly/j5eVlLufr60tycjJnzpyhfv36+eIZO3YsixcvZu7cuRYJGva0W0n62dRfZ8+etbp9gWkcnDp1yuoWDQ0bNuTMmTMcPXrUvFpBbGys+RltlYPcVTgeeugh3N3duXDhgnlC88aNG/z1r39l27ZtAPj4+BAUFEROTg5nz57l4sWLAJw8edJie4O4uDjatGnDxYsXcXZ2Nk+aHz16lLZt2xIQEMCPP/7I8uXLeeSRR6y2Q95x+8QTT/D5558D4O/vT8OGDbl+/TonT54kLS2NevXq8b///c8iGcKe/irO8xXWT7cq6B1as2aNeQuOOnXqEBgYSE5ODkeOHDFvKTFu3Dg+/vjjfKsplFaCQGxsLHfeeScXL17ExcWFO+64g7S0NKKjo+nfvz85OTn873//Y9GiRYwdO9buej///HOeeOIJnnnmGRYsWJDvvKOe5/fff2fw4MHmn69fv86NGzeoUqUK1apVMx9fu3YtXbt2LVKMFdmKFSvMWxo1btw431Yxea1atapIWYapqanmtrt27ZoSHiqwbQOoUJPVRU14COgSSrspIzi8YB1pF69ybtcRm9dWbxTAoI1zuHzsLD8OfB1jTg6tXhhC+6kj2TXtM458WryBM/LE0j91wkNFG0MiIiIiIiIiIiIit7syW1c7ODiY/fv38/7779O9e3dSUlLYu3cv8fHxGI1Ghg8fTkxMjM1J/datW7N+/Xo6deqEs7MzycnJ9O7dm+3bt/Pyyy8THR2Ni4uL+Ut4k8TERJKSkvDx8eGpp55i3bp1NG/enMOHD5OWlsbf/vY3/vjjj3zJDrGxsVy8eBE/P798W024u7uzYcMGBg8ejKurK7t27eL333+3mAw0MU0ML126tFTapSRt8+yzz7Jo0SJCQkJITk4mPj6egQMHsnfvXjp16kR2djaNGze2SHaIjY0lOTkZX19fq8kOYHsLCHvarbjPkre/rE2im8aBt7e31aSFy5cvc+bMGTw8PAgJCTEfN61GYKucSb9+/XB1dSUtLY2ff/7ZfLxq1aps2rSJefPm0blzZ7Kysjh06BBJSUkEBQUxYcIEfvnlF4tkB4DAwEC2b9/O/fffj4eHhzm2uXPnsnPnTsLDwwG4++67bbZD3nE7btw4pkyZQteuXXFzcyM8PJwzZ84QGhrKv/71Lw4fPmyR7AD29VdRn6+wfrKmoHeoffv2TJs2jd69e+Pm5kZkZCQRERH4+/szbNgwNm7cyMKFC61uHZGYmAjYt9JEUdSrV49t27Zx33334e7uTkxMDD4+PixcuJD169cTFRUFWF+doyDLli0DcvvSGkc9T2ZmJhcvXjT/MSWOpKenWxzPzMwscowVWXp6uvm/T548ye+//27zj7VtgEQqgqRdR/BqXIeG/TtxPuyY7QsNBu7+7/M4OTmxfcKHGHNyt6A4/NFaLhyIpt3UEVRvWLuMohYRERERERERERERKb4yW+HBlvfee49XXnkFX19f9u/fb3MSvbIyGo20b9+eo0ePcvLkSbu/Cr7d20WKb/v27XTr1o127dqxd+/e8g6n1BX3HSrMwIEDWb9+PV9//TUPPfSQQ+oszLVr1/Dy8sJgMJCSkoKHh4dd5Q4dOkSbNm0YMGAAP/zwg9VryuN58rInxj8rrfBQeVS0r/OLusIDQLePJkBODtte+MDmNaHPDqLjP0ez583/4/D8tRbnvJvW4/6f3+X8vqhibW2hFR4q1hgSERERERERERERud2V2QoPtrz88ssMGjSIixcvMmzYMKtfDVdmBoOBOXPmcOPGDWbPnm13udu9XaR4rl+/bl7x4IUXXijnaMpGcd+hghiNRnbs2EHTpk158MEHHVKnPSIiIjAajYSEhNid7AAwY8YMnJycbD5/eT1PXoXFKCJl48yG3Zz5Kczm+RohgbSbNJxze44R8fH3+c5fjorlwHtfE/CXUJo/OaA0QxURERERERERERERKbEK8Q3aF198wbx58zAajURGRhZ5qfeKrlevXnz44YekpqYWqdzt3i5i27Rp0xg/fjx169Y1H4uMjGT8+PFERETQrVs3Ro8eXY4Rlq3ivkO2HDlyhEuXLvHOO+/g5FR2eV+HDh0CiradRXp6Oq1bt+b+++/Pt5WLSXk9j4k9MUrFkJORxsk5w0k7G4mTW1VcatSiwbMLcK8TnO/atPjjxPz3MbJSLuDsUYOgCUuo2iAUo9GIwWAgfsV0fHuNwa1WQ/O2MVf2/Ejs569gcHXDya0qQRO+wD2wKQB7Bxtwb9iSeqNnU6PDAM4sepErYevIOHea5nP349H4TvO9j73ekxsxB6kz7J/UHjSxLJrmtnH6h50Fnr9yPI7/azSiwGsOffAdhz74zpFhiYiIiIiIiIiIiIiUinLf0kJELJ0+fZqgoCAMBgPBwcH4+Phw7tw5Tp06BUCXLl1Yu3Ytfn5+5RypFNWECRN4//33mTlzJlOnTi3vcKSMVKQtLXIy0kgJ34xX+/4YDAbOrf+QSztW0Wzmb/nKRk3rhU/P0fj1HsOl31eRuHo2zd8L49Lvq0iNDsOYmY7nHV24snsd9Z+ah4uXL4fGNqLhc4vwurMvccv+Qc6Na9R/ai6Qm/DQZtklXKp5A5ASsZUqtRtzbMrdNJmyxiLhASBm3hiqNrqz0ISHY6/3IOjFJVSpHVT8hvr/Ktp2BMXZ0qK8lfeWFofGBmFwqYJTlaoABDw4BZ9uwwotd+n3VVwN30T9J+fanRRkTUUbQyIiIiIiIiIiIiK3O/0vWZEKxsPDg5deeolffvmFuLg4Tp06hbe3N3369GHEiBGMGjUKFxe9upVRcVZ4EHEkJzd3anS4uU2BZ9POJK2Zk++6zMvnSI3eQ8iMnwHw7vIgZxY9T1pCNDW7DsWtVkOi/tGb66cOEvLGBpzccie4M86fxiO4A9lpqVw/sZca7frbjKV66D0Ofjrbsq5dJvLFluRk3MDNrz7GzHTSE0/i02MUQS8sLrM4pGw0fnVlvgSawlz+4zt8euaunOTfb5xFUtDpD5+ymhQkIiIiIiIiIiIiIuVPs6YiFYy/vz//+c9/yjsMKQWbN28u7xBELJz7YR7enQbnO55x4SyuNetgcM79Z4LBYMDNvwEZ589wIyac1Khd+PV+HM/mXTn90TjqPzkXFy9fMBq5duR3Ts0ZjpN7Neo/+d8yfiLrXKp543PPCJyrVqfOsH9wZd//SFz1lpId/kQKSnpp+OwCrh39naAJSzC4uNqVFCQiIiIiIiIiIiIiFYMSHkRERP6EEr55i/SEaBq+ualI5bw7D6HmX/5G/IrpeIZ0ombXhzAYDObz1ZrfzZ0rrnJ51xqOTelG6Pxj5m0sHOXU3NHcOB0OQHpCNNH/GoDB1Q2AJlPWWN3e4vqpA9Qa+GLuf5/Yi0fjtg6NSSqOmP+OxogRz5BOBI5+G9ca/gUmvVzd/zOed3TB4OKary5bSUEiIiIiIiIiIiIiUjEo4UFERORPJvG7OVzeuZqQf23EqYpHvvNufvXJvJSAMTsLg7MLRqORjPNncPNvYE5uqPvIdJv1G5yccpMilr5OenwULk07OTT+Ri99af7vY6/3IOjFJVaTHPK6ceqAOcnh+om9eHca5NCYpGJo9tZW3PwbYMzKJG7ZNGLmPUbIP38EbCe9XN61hpqdh+Srq7hJQSIiIiIiIiIiIiJSdpzKOwAREREpO0lr/8OlbSsI+dcvNldecPWuhUeTdlz8bSkAl3d8i5tvPdzrBBda/5U96wHIOH+GzEuJVLGjTGnLuBgHGHDzDQTgRkw4VRu2Kt+gpFS4+TcAwODiSu37J3ItYpv53K1JLx6N22I0Grmy/394tetvUY8pKSj4nxusJgWJiIiIiIiIiIiISMWghAcREZE/iYwLscR+9jJZqZeJmtaTyIl3cuSVu8znYz54isu71gHQ8NmFXPjfQg4/25TEb98m6MXP7brH+fUfcHj8HRyf0Z/64z7ApbqP1etOz3+a8CfqkXEhluPT/8rhp0svMeL6yf0WW1g4e3pz7sf5pXY/KR/ZaalkXbts/jl52wpzv9tKerketZuq9ZrjXLWauZw9SUEiIiIiIiIiIiIiUjFoSwsREZE/CTe/erRfa7R5PuiFxeb/dq/XjDve2VnkewS/8ZNdk8QNxy8sct3WNJv5W6HXeHcciHfHgeafm78X5pB7S8WSdTmJE28/CDnZGDFSpXZjgibmbn9iK+nFxcsP77seMB83JQW5BTQmalpPAAwuVWg+Z1eZPouIiIiIiIiIiIiI2EcJDyIiIlLqXLxrE/V6dwJHzaJGhwEFXnvs9Z5knIvBs3nXMopObgdVAhrT4r/7rZ6zlfQS8Xwotf/9q/l4YUlBIiIiIiIiIiIiIlKxKOFBREREHKKgieI2XyTaXU+zmb8WfpGIA4R+GFHeIYiIiIiIiIiIiIhICTiVdwAiIiIiIiIiIiIiIiIiIiIiRaWEBxEREREREREREREREREREal0lPAgIiIiIiIiIiIiIiIiIiIilY4SHkRERERERERERERERERERKTSMRiNRmN5ByEiInK7Sk1NpVq1agBcu3YNT0/PMru30Qhp2WV2u0rP3RkMhvKO4iaj0UjWjfTyDqNIXKpWweDARqxsY7iijSERERERERERERGR251LeQcgIiIipcNggKr6m77SMhgMuHq4l3cY5UpjWEREREREREREREQKoi0tREREREREREREREREREREpNJRwoOIiIiIiIiIiIiIiIiIiIhUOkp4EBERERERERERERERERERkUpHCQ8iIiIiIiIiIiIiIiIiIiJS6SjhQURERERERERERERERERERCodJTyIiIiIiIiIiIiIiIiIiIhIpaOEBxEREREREREREREREREREal0lPAgIiIiIiIiIiIiIiIiIiIilY4SHkRERERERERERERERERERKTSUcKDiIiIiIiIiIiIiIiIiIiIVDpKeBAREREREREREREREREREZFKRwkPIiIiIiIiIiIiIiIiIiIiUuko4UFEREREREREREREREREREQqHSU8iIiIiIiIiIiIiIiIiIiISKWjhAcRERERERERERERERERERGpdJTwICIiIiIiIiIiIiIiIiIiIpWOEh5ERERERERERERERERERESk0nEp7wBERESkdBiNkJZd3lFUHu7OYDCUdxQ3GY1Gsm6kl3cYReJStQoGBzZiZRvDFW0MiYiIiIiIiIiIiNzulPAgIiJym0rLhm4/lncUlce2AVC1Av3LKOtGOsuaPFreYRTJyBNLcfVwd1h9lW0MV7QxJCIiIiIiIiIiInK705YWIiIiIiIiIiIiIiIiIiIiUuko4UFEREREREREREREREREREQqHSU8iIiIiIiIiIiIiIiIiIiISKWjhAcRERERERERERERERERERGpdJTwICIiIiIiIiIiIiIiIiIiIpWOEh5ERERERERERERERERERESk0lHCg4iIiIiIiIiIiIiIiIiIiFQ6LuUdgIhIZRYdHc22bdt4/PHHK2R9ImUt5dBvRE3raXHMyd2TKnWb4ttjFLUGvoDBWf/8kNKjMSgiIiIiIiIiIiLy5/GnW+HB398fg8FAbGys3WWMRiM1atTAYDBw/vz5It/zypUr+Pv7065dO4xGY5HLixRHScdtRVKR36FXXnmFJ554wmFtfGt96enp1KtXj+DgYDIzMx1yD0erDDFK2at5zyMEvfR/BE38kjrD3sCYnUnsZ3/nzMfjyzs0+ZPQGBQRERERERERERG5/ZXb521nzpxh6dKlrFu3jtOnT5OcnEzNmjXp0KEDjz76KA8//DBOTo7Nx4iNjeXChQv4+PhQr149u8udPn2aq1evEhAQgL+/v8W5OXPmcO3aNV566SVq1KhhtfzMmTO5cOECn376KQaDocB7lUe7lAd72q2i2bhxI3379s133MPDg6ZNm/LII48wceJE3NzcyiG6/Aoat0VV3v1V0Ds0ZswYvvjiiwLLHzlyhDvuuMPhcWVnZ/Pbb7/RpUuXErexrfqqVKnCa6+9xosvvsiCBQt48cUXS3yfgqxbt44NGzawd+9e4uLiuHDhAm5ubjRp0oQBAwbw97//HT8/P4syZR1jaSnOs4ttHo3b4dvjUfPP/gPGEzH+Di78spi6j87EtUbJ3xmx35iEVQ6ra0mdoQ6rqzRpDIqIiIiIiIiIiIjc/gzGMv5cOjs7m3fffZcZM2aQlpaGs7Mz9evXx8/Pj9OnT5u/au7duzerVq3C29vbYff+4YcfuP/+++nRowe//vqr3eW2bt3KuHHj6Ny5M0uWLDEfv3LlCjVr1sTd3Z2UlBScnZ3zlT179iwhISHccccdHDhwwOY9yrNdypo97VYRvfvuu0yaNAlfX1/z5HlWVhbR0dFcvHgRgH79+vHTTz8VmthSFmyN26Iq7/4q7B0yJTyEhIRQq1Ytq3UsX76cBg0aODy2Xbt20blzZ7744gtGjx5davWlp6fTsGFDsrOziYmJwdPTs8T3sqVHjx5s2bIFNzc36tati5+fH+fOnePs2bMYjUb8/f35+eefufPOOy3KlWWMpaW4z16Y1NRUqlWrBsC1a9fKtG1uZEG3H8vsdsDN7QQCx7xLwJBXLM6dmP0Ql3esotk7O6nWrHPZBmaHbQOgagXa6SDzehrLmjxa+IWF8Az0o+F9nYlc9IMDoirYyBNLcfVwd1h9xRnD5TkGK9oYEhEREREREREREbndlelSAdnZ2YwYMYIpU6bg7OzMrFmzOHfuHKdOnSIsLIykpCRWr15NzZo12bRpEyNGjHDo/U2Tpa1bty5SuXvuuYejR4/mmzTet28fRqORVq1a2ZwEXrhwIenp6Tz++OM26y/vdilr9rRbRWQaPyNHjmT79u1s376dP/74g8TERF599VUAfv75ZzZs2FCOUd5ka9wWVXn3lz3vEMDUqVPN/XLrn9JIdgDYvHkzNWvW5OGHHy7V+qpUqcLw4cO5cOECK1ascMi9bHniiSfYtGkTKSkp5t9Bp0+f5uDBg7Rs2ZLz589b/R1UljGWluI+u9gvPfEEAC7VfMo5kj+X+n07cPbnPeUdRoWgMSgiIiIiIiIiIiJyeynThIdnnnmGr7/+mtq1a7N161YmT56Mj8/N/+FsMBgYMmQIq1blLru8YcMGh04eHzx4EIA2bdo4pL59+/YB0LZtW6vns7Ky+Pzzz3F2dmb48OE26ynvdilrhbVbRbV//34gf8KMi4sLs2bNMvfZ77//Xuaxlaby7C9736HysnnzZh577DHc3R3zNXNB9Y0cORKATz75xCH3smX06NH06tUr39YsrVq14tNPPwVytwg5cuRIucVYWkry7JJfTvp1sq5eIPPKeW7EHOLMx89x4+R+PEI64R7YtLzD+1PxahxASkxieYdR5jQGRURERERERERERG5/ZZbw8P3337N48WIMBgPLli2jXbt2Nq/t1asXd911FwArV640H4+JicFgMFCnTh2bZdu3b4/BYGD79u35zuVd4WHnzp0MGTIEf39/PDw86NKlCz///LPVOoOCgjAYDBw9ehSAb7/9FoPBwCuv5C6TvHDhQgwGg/nPW2+9BeRuKRAfH0/Hjh2pXbt2qbVLSdsmJiaGd999l3vvvZcmTZrg6emJh4cHbdq04e233yYjI8NqfQEBARgMBmJiYjhw4ACjRo0iMDAQT09P7rzzTr766iuL6+1tt5L2s6m/jhw5wo4dO8z97OXlRZ8+fQgPDzdfu2vXLoYOHUrt2rXx9vamb9++RERE5Kvzxo0bREVFAdZXCHF2djavIpCenm415oyMDD755BP69OmDr68vVapUITg4mMmTJ3Pt2jWbz5qYmMiECRNo1KgR7u7uhISE8M4775CTk8OYMWMwGAwsXrzYZjuYxq1Jeno68+bN4+6776ZmzZq4ubkREBBAp06dmDRpEvHx8YD9/VXc58sb35YtWxg0aBD+/v4YDAY+//xzwL53qLykp6ezY8cOxo0bZ/OaCxcuMGnSJIKDg3F3d6d+/fpMmDCB1NRUnnzySQwGAx9++KFd9XXs2JGAgAB2797NyZMnS+WZCtO8eXPzf1+/fj3f+fKKsSx2Zirs2SW/hBVvcHCUP+GjaxE5oTXnN8zH+y9/I/j1teUd2p+Ki4c7mdfSyjuMcqExKCIiIiIiIiIiInL7K5NdhnNycsyTpk8//TS9e/cutEyXLl3YtWuX+at6uPmFva0vzTMzMzl8+DAGgyHfKg7Xrl3jxIkTODs7s2nTJqZOnYqfnx/16tXj2LFj7Ny5k/79+/Pdd98xaNAgc7nLly9z+vRpPDw8aNo092vA1NRUunbtyt69e0lLS6Nt27Z4eHhYxA6wZcsWADp16lSq7VLStnnzzTf57LPP8PT0pG7duoSGhnLu3DnCw8MJDw8nLCyMb7/91qJMUlISSUlJeHl5sWbNGl555RV8fX1p0KABaWlpHDx4kEceeQQfHx/69etXpHYrybOY+qtKlSr88MMPTJ48mTp16lC/fn0iIyPZtGkTffv25ciRI3z22WdMnjyZgIAAAgMDiYyMZOPGjfTt25eoqCiqVatmrjc8PJzs7GycnJxo2bJlvpiys7M5ffo0AKGhofnOR0dH88ADDxAREYGLiwuNGzemVq1aREdHM3v2bH755Re2bdtm0R6Qm5AxYMAAkpOTqVatGqGhocTGxvLaa69x6tQp85fmd955p9V2yDtuAc6fP29O+nBxcaFRo0YEBwcTFxfHnj17CAsLY+zYsUXqr+I8nym+qlWrsnLlSmbMmIGvry9BQUE4OTmZk0oKe4fyWrVqFWvWrOHq1av4+fnRuXNnRo0ahb+/f6Fli2Pnzp106NDBYiI8rwMHDtC/f38SExPx9PSkRYsWxMfH8/7773PixAmSk5OBm31XWH0Ad911F2vXrmXLli00btzY4c9UGNPqJZ6enjRr1szqNY6IsUePHmzZsoVTp04RFBRU4LXh4eGMHj2aVatWERwcXKz72cOeZxdLfn8dR80uD2HMzuTG6UMkrp5NxoVYDK43VzBJidhG9L/65ytrzMrAmJNN+++yyzLk21Ld7q2J23KwvMMoFxqDIiIiIiIiIiIiIre/Mlnh4YcffiAqKgpnZ2emTp1qVxnT9gCXLl0yHzNNhN86uWsSERFBRkYGjRo1onr16hbnDh48aP4K+N///jeffvop8fHx7N+/n4SEBHr37k1OTg4vvfSSxdfCplUhWrVqhZNTbnONHj2arVu3mn/evHkz27dvN//p0aMHcHOCrEOHDqXaLlCytunXrx979+4lJSWFqKgodu/eTUxMDGFhYdSuXZvVq1dz6NAhizKm7UHS0tKYMWMGy5YtIzExkbCwMOLi4hg4cCCAeRl4sL/dSvIspv7Kzs7m7bffZvXq1cTGxrJv3z4OHTpEjRo1OHfuHKNGjWLmzJl888035vMRERHUrFmThIQE1q9fb7Xe4OBgqlatmi+mBQsWcOnSJfz8/HjwwQctziUnJ9O/f38iIiJ46qmniIuL49ixYxw5coTIyEiaN2/Ovn37mDt3rkW5xMREBg8eTHJyMpMnT+bcuXPs3buXxMRE3nzzTRYuXMiBAwdwdnbOl4RhbdwCvPzyy4SHhzNixAhiY2OJiooiLCyM+Ph4zp49y+zZs82Txvb2V3GezxRfeno6s2bN4uOPPzaPn4SEBHOyS2HvUF7r169n7dq1/Prrr3zzzTe8/PLLNGrUiKVLlxZatjgOHz7MM888Y/XchQsXuP/++0lMTOTll18mISGBffv2kZiYyOzZs1m/fj1hYWEYDAZzckdB9ZmYEj+2bt3q2IcpQE5ODgkJCXz55ZeMGTMGgLfeessiISivso7x888/5+DBg/Ts2dPhq0oU9dnFUpU6IXjd2Yca7fsT8LdJBL/+Pdejwziz4OY4rx7ajbYrr1n8CZ0fhUt1P+qOeLMco7991Op4B+fDjlkcazdlBGMSVhE8vJfVMvd+O4NRMSvwbla/LEIsNRqDIiIiIiIiIiIiIre/Mkl4WL16NQDdu3enfn37/ud5SkoKkPs1rYlpktTWl//79u0DrE+Umybos7OzzZNXzs7OANSoUYPFixfj5OTEyZMnzVsX5C13a51RUVFcv36dhg0b4u3tbTWemJgYAOrWrWv1vKPaBUrWNsOGDaNdu3YYDAaL4x06dKBv374A+bZ5MLVLZmYmy5cvZ9iwYeby7u7uPPvsswDmVQ9M7Gk3R/XzV199xeDBg83nQkJCzD9v2LCBFStWMGTIEPP5Jk2acP/99wNw6tQpi3pNSRh5t7PIyMggIiKCCRMmMHHiRLy8vPj666/x8vKyKDthwgSio6OZMGECn3zyCbVq1bKI6YMPPgBgzZo1FuWef/55kpKSeO6555g1a5Y50cJgMPD666/TokULMjIyaNq0Ke7u7hZlbY3b1atX4+zszKJFi/JtEREYGMikSZMsxoE9/VWc5zPFl5OTw4IFCxg3bpz5fXRycjInWRT2DgE0bdqUuXPncuDAAS5fvkxqaipbt26lX79+pKamMnr06HwJLI7w/PPP88gjj1g99+KLLxIbG8vzzz/PnDlzLBJzJk2aRJs2bcjKyiIoKMg8Xgqqz8TUDre+V6Xh448/xmAw4OzsTN26dXnssceoV68e33//PS+++GKFiBHgvffeY9SoUcTGxtKzZ0/zmCmJ4j67FKxa8y749BjFpe0ruXZkh9VrcjLTOfn236jW4m7qPGRfIqAUwGAAAxhzciwOH5jzNZeOnKbT9MfwqONjca7FuIEEdAnlwJyVXD52tiyjLXUagyIiIiIiIiIiIiK3nzJJePj1118BzF+E2+Po0aMANGjQwHyssC//TRPht25zADcn0fv3728xyW0SFBREYGAgAHFxcfnK3Vqn6bitWCB3+wC4uSrDrRzVLlCytklPT+ebb77h+eef57777uOee+7h7rvv5u677+aHH34AwM3NzaKMacJ66NCh9O+ffynojIwMgHyT5Pa0myP6ediwYeZkjbxcXV0BePDBB7n33nvznXdxyd3l5datJUz1rlq1CoPBgMFgoEqVKrRs2ZL58+czbtw4du/eTc+ePS3KRUREsHz5cgICApg1a5bV5zE9Z95xd/jwYVavXo23t7fVcgaDwbzqgbV2sjZus7KyyMjIIDs7m99++81qLLbqKWi1jeI8n6neXr168fjjj9u8f2HvEMDUqVOZOHEibdq0oUaNGnh4eNCtWzd++uknBg8ejNFoZOLEiRYrt5SmI0eOsHLlSvz8/Gy2Sfv27QHrY7ggpnY4d+5cyYK0Q506dejatSt33XUXdevWxWAwEB4ezvLly7ly5UqZxBgbG0tMTEyBf86cOcP06dPp1asXZ86coWfPnpw5c6ZE9y3us0vh6gz7Bzg5E7/8n1bPn5n/DDmZaQRNWFK2gd2m/NsGc2F/dL7jOZlZbJvwIS4eVej6n/Hm415N6tJu8iOc3xvF4fnryjLUMqMxKCIiIiIiIiIiInJ7cSntG2RnZxMbGwvkfoltj6ysLPNS9p07dwbg4sWLxMbGUr16dZv7tJsmyguaCDetPGCN6UvrvMuV25rwtWfiPi0tDSDf1/fguHaBkrXNpk2bePzxxzl7tuCvOBs3bmzxsynhYdiwYVavP3Ysd/nsW5+tsHZzVD8PHz7catnIyMgCzx8/fhyAZs2amY/l5OSYt/Ro27YtHh4eGI1G4uPjiYmJISsri6ioqHxtBLBixQpycnLIzs62moABN5ND8q7a8dVXX2E0Ghk5cmS+bTtMqlSpAhTcDnnb2cXFhQceeIBvvvmGgQMH0qtXL4YOHcqgQYPMyT721OOI5zPVO2rUKKtlTAp6hwpjMBiYPXs2a9euJTo6mkOHDlms0FFaTG0ycuRIm1sfmFbrKGrCg6mcqV1K0+DBgy1WSDl06BDPPfccK1as4MyZM2zfvr3UY+zWrVuRy8TExPDoo4+WaEuN4j67FM69TjA+3YaTvGUZKRHbqB56s4/Pff8+V/b8wB1zwnCq4lFALWJN7c7NORd2DGP2zdUcAnu2JWLRD1avTz50ivAPvuPOvz9E00f7cHz5Zrq9/wIA2yZ8mG9ViNuFxqCIiIiIiIiIiIjI7aXUEx6uXbtGzv//n+b27nu+YcMGLl68CMDDDz8MWG4pcOvWC5A7KW1rGf/s7GwOHz6Mk5OTzdUUsrOzzV8Fm1ZPyMzMJDIyEicnp3wTpfYkPPj6+pKQkMClS5fynXNUu0Dx22bXrl0MGDCAzMxMnnzySUaOHEnLli2pWbMmLi4uHD16lObNm+Pi4kLz5s3N5dLT080rTdhqz+ImipSkn039BXDPPfdYLRseHm7zvNFoNJ/PW/exY8e4fv06AJs3b7ZYtWLDhg0MHjyYTZs2sWTJEsaOHWtR5+bNm4HclQpMqxXYEhQUlK9c7969bV4fHx8P5J80L2jcfvnll7Ro0YLFixezefNmNm/ezHPPPUePHj146623LBJpoPD+Ks7z5e2n++67r8AyBb1D9mjWrBk+Pj4kJydz/PjxMkl4MLXJrat95GVKdipqwkNycjKQ2y5lrVWrVqxfv57GjRvz+++/s3HjRvr06ZPvOkfG2KpVq3yry9hy8eJF83YWeX9fOYK9zy72CXjodZK3rSB++T9pNjN3paOU8F+J/fI1Qv65gSq1g8o3wEooaFAXur73LJsee5vEHTe3oHL18iAz5brNcgfnrqJBvw50+OdofEKD8G8Xwu7pS7h6Ir4swi43GoMiIiIiIiIiIiIit49ST3ioXr06zs7OZGdn2zVpaTQa+fe//w1Anz59CA0NBW5OvLZt29ZquV27dpGamoq3tzcNGza0OHfs2DFu3LhBrVq1bH4t/8cff5CSkkJoaCgBAQFA7tL0GRkZhISEWHydnjeeghIeatWqRUJCgnkCMC9HtUveWIraNlOmTCEjI4O3336b1157LV+59evXA9CiRQvzagKQu0pCVlYWDRo0sDmpaWtbisLarST9bOqvhg0bUrNmzXxljx8/TmpqKoGBgfj7++c7f+rUKa5cuUJAQAC1a9fO9ywNGzbMt0VH//79GTt2LPPnz+ezzz7Ll/BgmtiOiYnJF29BTCtu3Lp1iUl2dja7du0C8k+aFzRu3d3dmT59Om+88QYHDhxg7dq1LFy4kF9//ZW+ffty9OhRi9UeCuuv4jxf3n6y1g95FfQO2cu0jUlWVlax6yiK06dPA9hsj7wrtRQ14cGU8FSrVq0SRFh81atXp3v37nz77bccPHjQ6qS/I2Nct26dRSKQLbGxsXTv3h3IXXVm/vz5Jb73rex5dnuEhITg5FQmu0kBYHCrSu3/Hi+z+wFUb9WD9mttbyFTtX5z2n+Xbf45PSmGk+8+TL0x71K9VY8yiNC2pk1DMGbcKNcY8nI1OvEGnQq9LmbdDrwaBVD/rx3NCQ+egX6kxhaciGbMymbbhA8ZuOFt7hhzL0m7jhC5aH2JYm4a0pRMg+NWhyjOGC7PMVjRxpCIiIiIiIiIiIhIZREQEMCePXuKXK7UEx6cnJxo06YN+/btY+fOnTz66KMFXj9nzhx2796Nq6src+bMMR83fRGed6I/r+XLlwPWJxBNKwKYlta35uOPPwZgxIgR5mO2JnuTkpJISkrC29u7wMm4tm3bcvDgQSIjIxk4cKDFOUe1CxSvbbKzs81Lvj/++OP5yuTk5LBs2TLzc+Rlak9bSQmpqakcP34cV1dXWrZsaT5uT7uVpJ8LS5aw93xRkzQee+wx5s+fz65du4iLi7NIGEhNTQWKvry/qZytSfq1a9dy/vx5atWqRZ06dYoUL+Ru99C2bVvatm3LxIkTad26NWfPnmX37t0MGTIEsK+/ivN8hfVDXgW9Q/Y4f/48586dA6BevXpFLl8cpja5ccP6hNfKlSu5cOEC1atXp1GjRkWq2/R+tGvXrmRBloBpTGZnZ1s9X9YxxsXF0bNnT06ePMnQoUNZunQpzs7OpXKvwp7dHgkJCY4Kxy5OVTyoXfhl5SYn/TonZj1AjU6DqHXf8+UdDvHx8eSk214Roay5GZyxtwNPb9hN7yWvEfbGEgDq9+3A2Z8L/4dh5tXr5GRk4ezmSuymfWC0nShgj/iEeDKMxX9HblXaY9jRY7CijSERERERERERERGR212pJzxA7he3+/btY+nSpUydOtViQjivVatWMW3aNADeeecdi0nty5cvA1jd5mDHjh3mhIWCJsIvX75MVFQUTZs2tTi/detWli1bhq+vLy+88IL5uK2tE44dOwaQr55bdevWjSVLlrB7926r5x3RLqbngqK1TWpqqnnSztpk9XvvvWde2aCoCQ/h4eHk5OTQsmVLi+Xo7Wm3kvRzYXEVNtFuq79trVZh0rFjR2rXrk1SUhLff/89zzzzjPlcgwYNSE5OZuPGjTRr1sxqeWvq1KnDpUuX2Lt3L3fddZfFuUuXLvHqq68CBbdDQQkPeXl7e5v7Ke9X+fb0V3Ger7B+yquwd6gw7733HkajkRo1atCxY8di1VFUAQEBXLp0iX379vGXv/zF4lxCQoK572xt21IQ06oeptUMylpycjJbtmwBbI+vso5xxowZREdHM2TIEFasWIGLS+n8tWbPs9ujTp06Zb7CQ0V2ace33Dh1kLS4KC5tX5nvfOiHkbj5W1/ppjTUrVu3Qn2d72p0AjsXS7gSFQtG8G5aj8tRsVRvFEDKkqRCy3X973M4ubpwOeosrSc+SMy6HaScLrycLXXr1HX4Cg+lydFjsKKNIREREREREREREZHKwrQLQ1GVScLD+PHjWbx4McePH6dfv358+eWXtG/f3nz+1KlT/Oc//+Gjjz7CaDQybdo0Jk6caFGH6QvzTz75hKFDh+Lr60tOTg5r1qzh6aefxs3NjaysrAITHlxdXRk/fjzffvstNWrUAHKXTDetcLBkyRKLLS9M5W6t07RNQGxsLKmpqfm2DTDp27cvTk5O7Nixg5ycnHyTXI5ol+K2jZeXF4GBgcTFxTFz5kzmz5+Ps7MzGRkZzJs3j3/84x+4uLiQlZVV5IQHW4kS9rSbI/q5qHHdWr6oKzwYDAb69+/PkiVL8iU8DB06lAMHDjBlyhRq167N0KFDLcpGR0ezbNkyunfvTo8ePczH+/TpQ2RkJG+99Rbdu3c3r3hx9OhRRo0axcmTJ4GCE3zynvviiy+IjIzkscceo0WLFubjly5dYvLkyZw4cYI77riDzp07m8/Z01/Feb6irPBQ2Dv0yy+/sGnTJsaOHUuTJk3Mx69fv86cOXN45513gNztW/Im30Du+256940l/KI5rz59+nDkyBFmz55N3759zQkjYWFhjBo1igsXLgBFnzS/evUqBw8exMvLK18iBTjmefbs2cO6desYPXo0wcHBFuf279/PM888w+XLl2nVqhW9e/cucoz26t69O35+fjZ/t+Y1b9486tWrx5QpU0qU7FDSZ7fX8ePH7XouR7mRBd1+LLPbFZlvz1H49hxV3mGYRUUdp2qZ/MvIPpnX01jWpOAVoPI6+8se6v+1I9diL5B5rfBJ9+ZPDqBO15bsnbWcsz/t5v6f36Xr3PH89Lc3ih1z1PEoXD3ci13+VqU9hh09BivaGBIRERERERERERG53RmMjpzpK0B0dDQDBw40fzUeFBSEv78/cXFxJCQkYDQa8fX1Zf78+Tz88MP5yoeHh9O+fXuysrJwd3cnKCiIpKQkrly5wr/+9S++/PJLoqKi2Lt3b76l1AMCAkhKSuKTTz7h6aefxsPDg+bNm5OQkEBsbCxOTk68//77PPfccxbl/Pz8uHjxIrGxsRarL6SlpdGsWTPOnDmDj48PTZs2xdnZmUcffdRishtgwIABbNiwgU2bNtGrVy+Ht0tJ2mbBggWMHz8egNq1a1O/fn2OHz/O9evX+eijj3j22WfJycnh8uXLeHl5mcv5+vqSnJzMmTNnqF+/fr54xo4dy+LFi5k7d65FgoY97VaSfjb119mzZ61uX2AaB6dOnbK6RUPDhg05c+YMR48eNa9WEBsba35GW+UgdxWOhx56CHd3dy5cuGCe0Lxx4wZ//etf2bZtGwA+Pj4EBQWRk5PD2bNnuXjxIgAnT5602N4gLi6ONm3acPHiRZydnc2T5kePHqVt27YEBATw448/snz5ch555BGr7ZB33D7xxBN8/vnnAPj7+9OwYUOuX7/OyZMnSUtLo169evzvf/+zSIawp7+K83yF9dOtCnqH1qxZY96Co06dOgQGBpKTk8ORI0fMW0qMGzeOjz/+ON9qCqWV8BAbG8udd97JxYsXcXFx4Y477iAtLY3o6Gj69+9PTk4O//vf/1i0aBFjx461u97PP/+cJ554gmeeeYYFCxbkO++I5/ntt9/o2bMnkLvaR/369XF2diY2Npb4+Hggd8WPDRs20Lhx4yLHWJGV9NkLkpqaSrVq1QC4du2aEh4qsG0DqFCT1UVNeAjoEkq7KSM4vGAdaRevcm7XEZvXVm8UwKCNc7h87Cw/DnwdY04OrV4YQvupI9k17TOOfFq8gTPyxNJKlfDgaBVtDImIiIiIiIiIiIjc7spsXe3g4GD279/P+++/T/fu3UlJSWHv3r3Ex8djNBoZPnw4MTExNif1W7duzfr16+nUqRPOzs4kJyfTu3dvtm/fzssvv0x0dDQuLi7mL+FNEhMTSUpKwsfHh6eeeop169bRvHlzDh8+TFpaGn/729/4448/8iU7xMbGcvHiRfz8/PJtNeHu7s6GDRsYPHgwrq6u7Nq1i99//908oZWXaWJ46dKlpdIuJWmbZ599lkWLFhESEkJycjLx8fEMHDiQvXv30qlTJ7Kzs2ncuLFFskNsbCzJycn4+vpaTXYA21tA2NNuxX2WvP1lbRLdNA68vb2tJi1cvnyZM2fO4OHhQUhIiPm4aTUCW+VM+vXrh6urK2lpafz888/m41WrVmXTpk3MmzePzp07k5WVxaFDh0hKSiIoKIgJEybwyy+/WCQ7AAQGBrJ9+3buv/9+PDw8zLHNnTuXnTt3Eh4eDsDdd99tsx3yjttx48YxZcoUunbtipubG+Hh4Zw5c4bQ0FD+9a9/cfjwYYtkB7Cvv4r6fIX1kzUFvUPt27dn2rRp9O7dGzc3NyIjI4mIiMDf359hw4axceNGFi5caHXriMTERMC+lSaKol69emzbto377rsPd3d3YmJi8PHxYeHChaxfv56oqCjA+uocBVm2bBmQ25fWOOJ52rRpw7x583jggQfw8vIiKiqK/fv3k52dTZ8+ffjoo484ePCgzQn/wmKsyEr67CIVQdKuI3g1rkPD/p04H3bM9oUGA3f/93mcnJzYPuFDjDm5W1Ac/mgtFw5E027qCKo3rF1GUYuIiIiIiIiIiIiIFF+ZrfBgy3vvvccrr7yCr68v+/fvtzmJXlkZjUbat2/P0aNHOXnypN17j9zu7SLFt337drp160a7du3Yu3dveYdT6or7DhVm4MCBrF+/nq+//pqHHnrIIXUW5tq1a3h5eWEwGEhJScHDw8OucocOHaJNmzYMGDCAH374weo15fE8edkT45+VVnioPCra1/lFXeEBoNtHEyAnh20vfGDzmtBnB9Hxn6PZ8+b/cXj+Wotz3k3rcf/P73J+X1SxtrbQCg8VawyJiIiIiIiIiIiI3O7KbIUHW15++WUGDRrExYsXGTZsGJmZmeUdkkMZDAbmzJnDjRs3mD17tt3lbvd2keK5fv26ecWDF154oZyjKRvFfYcKYjQa2bFjB02bNuXBBx90SJ32iIiIwGg0EhISYneyA8CMGTNwcnKy+fzl9Tx5FRajiJSNMxt2c+anMJvna4QE0m7ScM7tOUbEx9/nO385KpYD731NwF9Caf7kgNIMVURERERERERERESkxCrEN2hffPEF8+bNw2g0EhkZWeSl3iu6Xr168eGHH5Kamlqkcrd7u4ht06ZNY/z48dStW9d8LDIykvHjxxMREUG3bt0YPXp0OUZYtor7Dtly5MgRLl26xDvvvIOTU9nlfR06dAgo2nYW6enptG7dmvvvvz/fVi4m5fU8JvbEKCJl4/QPOws8f+V4HP/XaESB1xz64DsOffCdI8MSERERERERERERESkV5b6lhYhYOn36NEFBQRgMBoKDg/Hx8eHcuXOcOnUKgC5durB27Vr8/PzKOVIpqgkTJvD+++8zc+ZMpk6dWt7hSBmpSFta5GSkcXLOcNLORuLkVhWXGrVo8OwC3OsE5yubFn+cmP8+RlbKBZw9ahA0YQlVG4RiNBoxGAzEr5iOb68xuNVqiMFgAODKnh+J/fwVDK5uOLlVJWjCF7gHNgVg72AD7g1bUm/0bGp0GMCZRS9yJWwdGedO03zufjwa32m+97HXe3Ij5iB1hv2T2oMmlmYTWaho2xEUZ0uL8lbeW1ocGhuEwaUKTlWqAhDw4BR8ug0rtNyl31dxNXwT9Z+ca/c7Yk1FG0MiIiIiIiIiIiIit7ty39JCRCx5eHjw0ksvERoayoULF9i7dy8pKSn06dOHzz77jC1btijZoZIqzgoPIo7m328cofOP0WLeQbzvGszpD5+yet2Z+U/j99dxtFwQRcDfXiNm3hgALu/4ltgvXiM79TKpx3cTM3cUWVcv5pZZ+Bz1x86jxX8PUL1NH85vWGBRZ7O3tlGjQ+42CTW7DqXZrO241WqY797NZv6Kd6dBdj3Psdd7kJ4UY+fTy59B41dX0uK/B2jx3wN2JTsAXP7jO7zvegCw/x0RERERERERERERkfKnb9BEKhh/f3/+85//lHcYUgo2b95c3iHIn5yTm7s54QDAs2lnktbMyXdd5uVzpEbvIWTGzwB4d3mQM4ueJy0hmppdh+JWqyFR/+jN9VMHCXljA05uuV/0Z5w/jUdwB7LTUrl+Yi812vW3GUv10Hsc/HS2ZV27TOSLLcnJuIGbX32MmemkJ57Ep8cogl5YXGZxSPkpaAw0fHYB147+TtCEJRhcXO16R0RERERERERERESkYlDCg4iIyJ/UuR/m4d1pcL7jGRfO4lqzDgbn3H8mGAwG3PwbkHH+DDdiwkmN2oVf78fxbN6V0x+No/6Tc3Hx8gWjkWtHfufUnOE4uVej/pP/LeMnss6lmjc+94zAuWp16gz7B1f2/Y/EVW8p2eE2FfPf0Rgx4hnSicDRb+Naw7/AMXB1/8943tEFg4trvrpsvSMiIiIiIiIiIiIiUjEo4UFERORPKOGbt0hPiKbhm5uKVM678xBq/uVvxK+YjmdIJ2p2fQiDwWA+X6353dy54iqXd63h2JRuhM4/hks1b4fGfmruaG6cDgcgPSGa6H8NwODqBkCTKWuoUjsoX5nrpw5Qa+CLuf99Yi8ejds6NCapGJq9tRU3/wYYszKJWzaNmHmPEfLPHwHbY+DyrjXU7DwkX13FfUdEREREREREREREpOwo4UFERORPJvG7OVzeuZqQf23EqYpHvvNufvXJvJSAMTsLg7MLRqORjPNncPNvYE5uqPvIdJv1G5yccpMilr5OenwULk07OTT+Ri99af7vY6/3IOjFJVaTHPK6ceqAeYL7+om9eHca5NCYpGJw828AgMHFldr3T+Tws03N56yNAaPRyJX9/yPwsXcs6insHRERERERERERERGRisGpvAMQERGRspO09j9c2raCkH/9YnPlBVfvWng0acfF35YCcHnHt7j51sO9TnCh9V/Zsx6AjPNnyLyUSBU7ypS2jItxgAE330AAbsSEU7Vhq/INShwuOy2VrGuXzT8nb1thTnCwNQauR+2mar3mOFetZi5nzzsiIiIiIiIiIiIiIhWDVngQERH5k8i4EEvsZy/jFtCYqGk9ATC4VKH5nF0AxHzwFN6dBuF91yAaPruQmPfHkLjqLZyrehH04ud23eP8+g9I+PpNDE7O1B/3AS7Vfaxed3r+01zZs57MS4kcn/5XnKtWp+XCaMc86C2un9xvsYWFs6c3536cT9ALi0vlflI+si4nceLtByEnGyNGqtRuTNDE3NVAbI0BFy8/vO96wHy8sHdERERERERERERERCoWg9FoNJZ3ECIiIrer1NRUqlXL/Xr82rVreHp6ltm9b2RBtx/L7HbsHWygzbJLVr+KL+icNTHzxlC10Z3UHjTRoTEWZNsAqFqBUkEzr6exrMmj5R1GkYw8sRRXD3eH1VfaYzji+VCa/vtXXL1rOaS+ijaGRERERERERERERG532tJCRERESp2Ld22iXu/OlT2Fz14fe70nKYe34ORedskh8ucU+mGEw5IdRERERERERERERKTs6Rs0ERERcYj2a20vGtXmi0S762k281dHhCMiIiIiIiIiIiIiIrc5rfAgIiIiIiIiIiIiIiIiIiIilY4SHkRERERERERERERERERERKTSUcKDiIiIiIiIiIiIiIiIiIiIVDoGo9Foe8NtERERKZHU1FSqVasGwLVr1/D09CyzexuNkJZdZrer9NydwWAo7yhuMhqNZN1IL+8wisSlahUMDmzEyjaGK9oYEhEREREREREREbnduZR3ACIiIlI6DAaoqr/pKy2DwYCrh3t5h1GuNIZFREREREREREREpCDa0kJEREREREREREREREREREQqHSU8iIiIiIiIiIiIiIiIiIiISKWjhAcRERERERERERERERERERGpdJTwICIiIiIiIiIiIiIiIiIiIpWOEh5ERERERERERERERERERESk0lHCg4iIiIiIiIiIiIiIiIiIiFQ6SngQERERERERERERERERERGRSkcJDyIiIiIiIiIiIiIiIiIiIlLpKOFBREREREREREREREREREREKh0lPIiIiIiIiIiIiIiIiIiIiEilo4QHERERERERERERERERERERqXSU8CAiIiIiIiIiIiIiIiIiIiKVjhIeREREREREREREREREREREpNJRwoOIiIiIiIiIiIiIiIiIiIhUOkp4EBERERERERERERERERERkUpHCQ8iIiIiIiIiIiIiIiIiIiJS6SjhQURERERERERERERERERERCodl/IOQEREREqH0Qhp2eUdReXh7gwGQ3lHcZPRaCTrRnp5h1EkLlWrYHBgI1a2MVzRxpCIiIiIiIiIiIjI7U4JDyIiIreptGzo9mN5R1F5bBsAVSvQv4yybqSzrMmj5R1GkYw8sRRXD3eH1VfZxnBFG0MiIiIiIiIiIiIitzttaSEiIiIiIiIiIiIiIiIiIiKVjhIeREREREREREREREREREREpNJRwoOIiIiIiIiIiIiIiIiIiIhUOkp4EBERERERERERERERERERkUpHCQ8iIiIiIiIiIiIiIiIiIiJS6SjhQURERERERERERERERERERCodJTyIiIiIiIiIiIiIiIiIiIhIpeNS3gGIiFRW0dHRbNu2jccff7xC1idSHlIO/UbUtJ4Wx5zcPalStym+PUZRa+ALGJz1zw8pPRqDIiIiIiIiIiIiIn8ef6oVHvz9/TEYDMTGxtpdxmg0UqNGDQwGA+fPny/yPa9cuYK/vz/t2rXDaDQWubxIcZR03FYkFfkdeuWVV3jiiScc1sa31peenk69evUIDg4mMzPTIfdwtMoQo5SPmvc8QtBL/0fQxC+pM+wNjNmZxH72d858PL68Q5M/CY1BERERERERERERkdtfuSQ8nDlzhrfeeovOnTtTp04dqlSpQkBAAAMHDuSrr74iJyfH4feMjY3lwoUL+Pj4UK9ePbvLnT59mqtXrxIQEIC/v7/FuTlz5jB9+nSuXLlis/zMmTO5cOEC06dPx2AwFHiv8miX8mBPu1U0GzduxGAw5Pvj6elJ27Zteeedd8jIyCjvMM0KGrdFVd79VdA7NGbMGKv9kvfP0aNHSyWu7OxsfvvtN7p06VLiNrZVX5UqVXjttdc4ceIECxYsKPE9iuOTTz4xt2WPHj3yna8IMZaWwp5dCubRuB2+PR7Ft+coAv72Kne88weuvvW48MtiMq9U7kQsqRw0BkVERERERERERERuf2W6nm92djbvvvsuM2bMIC0tDWdnZ+rXr0/r1q05ffo069evZ/369SxevJhVq1bh7e3tsHsfOHAAgNatWxep3JkzZ2jWrBmdO3e2OH7lyhUmTZqEu7s7//jHP6yWPXv2LO+//z5t2rRh0KBBNu9Rnu1S1uxpt4po//79APj6+nLHHXcAkJWVRXR0NAcOHODAgQNs2rSJn376qdDElrJga9wWVXn3l73vUEhICLVq1bJ6zsPDo1Ri27NnD1euXOHpp58u1frGjRvHzJkzefPNN3nyySfx9PR0yP3skZiYyKRJkwq9rjxjLC32PrvYz9ndE89mnbm8YxXpiSdwrVHyRCGx35iEVQ6ra0mdoQ6rqyxpDIqIiIiIiIiIiIjcfsos4SE7O5sRI0bw9ddf4+npyaxZsxg3bhw+Pj5A7hL8a9as4cknn2TTpk2MGDGCH3/80WH3L27Cwz333GP1C/F9+/ZhNBpp1aoVzs7OVssuXLiQ9PR0Hn/8cZv1l3e7lDV72q0iMo2fkSNHMm/ePPPxrKwspk6dyrvvvsvPP//Mhg0bGDBgQDlFeZOtcVtU5d1f9rxDAFOnTmXMmDFlE9T/t3nzZmrWrMnDDz9cqvVVqVKF4cOHM2/ePFasWMFTTz3lkPvZ44UXXuDq1asMHDiQH374weZ15RljabH32aVo0hNPAOBSzaecI/lz8Qz0Y/cbS4hcpLGsMSgiIiIiIiIiIiJyeymzLS2eeeYZvv76a2rXrs3WrVuZPHmyeVIfwGAwMGTIEFatyv0CccOGDWzYsMFh9z948CAAbdq0cUh9+/btA6Bt27ZWz2dlZfH555/j7OzM8OHDbdZT3u1S1gprt4rKtMLDrQkzLi4uzJo1y9xnv//+e5nHVprKs7/sfYfKy+bNm3nsscdwd3cv9fpGjhwJ5G6xUFbWrVvHqlWreO6552jfvn2h15dHjKWlqM8u1uWkXyfr6gUyr5znRswhznz8HDdO7scjpBPugU3LO7w/lfp9O3D25z3lHUaZ0xgUERERERERERERuf2VScLD999/z+LFizEYDCxbtox27drZvLZXr17cddddAKxcudJ8PCYmBoPBQJ06dWyWbd++PQaDge3bt+c7l3eFh507dzJkyBD8/f3x8PCgS5cu/Pzzz1brDAoKwmAwmL+W//bbbzEYDLzyyitA7hfopj3eDQYDb731FgBbt24lPj6ejh07Urt27VJrl5K2TUxMDO+++y733nsvTZo0wdPTEw8PD9q0acPbb79NRkaG1foCAgIwGAzExMRw4MABRo0aRWBgIJ6entx555189dVXFtfb224l7WdTfx05coQdO3aY+9nLy4s+ffoQHh5uvnbXrl0MHTqU2rVr4+3tTd++fYmIiMhX540bN4iKigKsrxDi7OxMgwYNAEhPT7cac0ZGBp988gl9+vTB19eXKlWqEBwczOTJk7l27ZrNZ01MTGTChAk0atQId3d3QkJCeOedd8jJyWHMmDEYDAYWL15ssx1uXeUhPT2defPmcffdd1OzZk3c3NwICAigU6dOTJo0ifj4eMD+/iru8+WNb8uWLQwaNAh/f38MBgOff/45YN87VF7S09PZsWMH48aNs3nNhQsXmDRpEsHBwbi7u1O/fn0mTJhAamoqTz75JAaDgQ8//NCu+jp27EhAQAC7d+/m5MmTpfJMeaWkpPDcc89Rt25d/v3vf9tVpqxjNDEajQ6trzjPLtYlrHiDg6P8CR9di8gJrTm/YT7ef/kbwa+vLe/Q/nS8GgeQEpNY3mGUOY1BERERERERERERkdtfqW9pkZOTY540ffrpp+ndu3ehZbp06cKuXbvMX9XDzS/sbX1pnpmZyeHDhzEYDPlWcbh27RonTpzA2dmZTZs2MXXqVPz8/KhXrx7Hjh1j586d9O/fn++++45BgwaZy12+fJnTp0/j4eFB06a5XwKmpqbStWtX9u7dS1paGm3btsXDw8MidoAtW7YA0KlTp1Jtl5K2zZtvvslnn32Gp6cndevWJTQ0lHPnzhEeHk54eDhhYWF8++23FmWSkpJISkrCy8uLNWvW8Morr+Dr60uDBg1IS0vj4MGDPPLII/j4+NCvX78itVtJnsXUX1WqVOGHH35g8uTJ1KlTh/r16xMZGcmmTZvo27cvR44c4bPPPmPy5MkEBAQQGBhIZGQkGzdupG/fvkRFRVGtWjVzveHh4WRnZ+Pk5ETLli3zxZSdnc3p06cBCA0NzXc+OjqaBx54gIiICFxcXGjcuDG1atUiOjqa2bNn88svv7Bt2zaL9oDchIwBAwaQnJxMtWrVCA0NJTY2ltdee41Tp05x5MgRAO68806r7ZB33AKcP3/enPTh4uJCo0aNCA4OJi4ujj179hAWFsbYsWOL1F/FeT5TfFWrVmXlypXMmDEDX19fgoKCcHJyMieVFPYO5bVq1SrWrFnD1atX8fPzo3PnzowaNQp//9LZn33nzp106NCB5s2bWz1/4MAB+vfvT2JiIp6enrRo0YL4+Hjef/99Tpw4QXJyMnCz7wqrD+Cuu+5i7dq1bNmyhcaNGzv8mfKaMmUKsbGxfP3113h5edldzhEx9ujRgy1btnDq1CmCgoIKvDY8PJzRo0ezatUqgoODi3W/WxX32SU/v7+Oo2aXhzBmZ3Lj9CESV88m40IsBtebq5ikRGwj+l/985U1ZmVgzMmm/XfZZRnybcnFw53Ma2nlHUa50BgUERERERERERERuf2V+goPP/zwA1FRUTg7OzN16lS7ypi2B7h06ZL5mGki/NbJXZOIiAgyMjJo1KgR1atXtzh38OBB81fA//73v/n000+Jj49n//79JCQk0Lt3b3JycnjppZcsvhY2rQrRqlUrnJxym2r06NFs3brV/PPmzZvZvn27+U+PHj2Am1sbdOjQoVTbBUrWNv369WPv3r2kpKQQFRXF7t27iYmJISwsjNq1a7N69WoOHTpkUca0PUhaWhozZsxg2bJlJCYmEhYWRlxcHAMHDgTg008/NZext91K8iym/srOzubtt99m9erVxMbGsm/fPg4dOkSNGjU4d+4co0aNYubMmXzzzTfm8xEREdSsWZOEhATWr19vtd7g4GCqVq2aL6YFCxZw6dIl/Pz8ePDBBy3OJScn079/fyIiInjqqaeIi4vj2LFjHDlyhMjISJo3b86+ffuYO3euRbnExEQGDx5McnIykydP5ty5c+zdu5fExETefPNNFi5cyIEDB3B2ds6XhGFt3AK8/PLLhIeHM2LECGJjY4mKiiIsLIz4+HjOnj3L7NmzzZPG9vZXcZ7PFF96ejqzZs3i448/No+fhIQEc7JLYe9QXuvXr2ft2rX8+uuvfPPNN7z88ss0atSIpUuXFlq2OA4fPswzzzxj9dyFCxe4//77SUxM5OWXXyYhIYF9+/aRmJjI7NmzWb9+PWFhYRgMBnNyR0H1mZgSP7Zu3erYh7nFzp07WbBgAf379+ehhx4qUtmyitHk888/5+DBg/Ts2dMhq0qU5Nklvyp1QvC6sw812vcn4G+TCH79e65Hh3Fmwc2xXj20G21XXrP4Ezo/CpfqftQd8WY5Rn/7qNu9NXFbDpZ3GOVCY1BERERERERERETk9lfqCQ+rV68GoHv37tSvX9+uMikpKQB4enqaj5kmSW19+b9v3z7A+kS5aYI+OzubL7/8kjFjxuDs7AxAjRo1WLx4MU5OTpw8edK8dUHecrfWGRUVxfXr12nYsCHe3t5W44mJiQGgbt26Vs87ql2gZG0zbNgw2rVrh8FgsDjeoUMH+vbtC5BvmwdTu2RmZrJ8+XKGDRtmLu/u7s6zzz4LYF71wMSednNUP3/11VcMHjzYfC4kJMT884YNG1ixYgVDhgwxn2/SpAn3338/AKdOnbKo15SEkXc7i4yMDCIiIpgwYQITJ07Ey8vL6hfhEyZMIDo6mgkTJvDJJ59Qq1Yti5g++OADANasWWNR7vnnnycpKYnnnnuOWbNmmRMtDAYDr7/+Oi1atCAjI4OmTZvi7u5uUdbWuF29ejXOzs4sWrQo3xYRgYGBTJo0yWIc2NNfxXk+U3w5OTksWLCAcePGmd9HJycnc5JFYe8QQNOmTZk7dy4HDhzg8uXLpKamsnXrVvr160dqaiqjR4/Ol8DiCM8//zyPPPKI1XMvvvgisbGxPP/888yZM8ciMWfSpEm0adOGrKwsgoKCzOOloPpMTO1w63vlSJmZmYwdO5YqVaqYt9soirKIMa/33nuPUaNGERsbS8+ePc1jpjhK+uxSuGrNu+DTYxSXtq/k2pEdVq/JyUzn5Nt/o1qLu6nzkH3JgFKwWh3v4HzYMYtj7aaMYEzCKoKH97Ja5t5vZzAqZgXezez790lloTEoIiIiIiIiIiIicvsp9S0tfv31VwDzF+H2OHr0KAANGjQwHyvsy3/TRPit2xzAzUn0/v37W0xymwQFBREYGMjZs2eJi4ujWbNmFuVurdN03FYskLt9ANxcleFWjmoXKFnbpKens27dOvMS8ikpKeTk5AA3Ex3c3NwsypgmrIcOHUr//vmXgc7IyADIN0luT7s5op+HDRtmTtbIy9XVFYAHH3yQe++9N995F5fc1+HWrSVM9a5atSpfYoiLiwvjxo1jwoQJ5nFjEhERwfLlywkICGDWrFlWn8f0nHFxceZjhw8fZvXq1Xh7e1stZzAY6NChAxEREVbbydq4zcrKIiMjg+zsbH777Tfuu+8+q/FYq6eg1TaK83ymenv16sXjjz9u8/6FvUOA1dVRunXrxk8//cSQIUNYu3YtEydOZMCAAfn6rjQcOXKElStX4ufnZ7NN2rdvz8GDB62O4YKY2uHcuXMljtOWt99+m4iICGbOnFmsLSkcGWNsbKxd102fPp24uDg2b95Mz5492bJlS77fkfYo6bOLfeoM+wfJW5YRv/yfNH1zY77zZ+Y/Q05mGkETlpR9cLcjgwEMYPz/f6+bHJjzNfX7tqfT9MeI33KA6wnJ5nMtxg0koEsoe2cu5fKxs2UdcanTGBQRERERERERERG5vZRqwkN2drZ50qpp06Z2lcnKyjIvZd+5c2cALl68SGxsLNWrV7e5T7tporygiXDTygPWmL60rlatWr5yt0742jNxn5aWu1/2rV/fg+PaBUrWNps2beLxxx/n7NmCJzRunfwzJTwMGzbM6vXHjuV+SXrrsxXWbo7q5+HDh1stGxkZWeD548ePA1gkLuTk5Ji39Gjbti0eHh4YjUbi4+OJiYkhKyuLqKgoqxOkK1asICcnh+zsbKsJGHAzOSTvqh1fffUVRqORkSNH5tu2w6RKlSpAwe2Qt51dXFx44IEH+Oabbxg4cCC9evVi6NChDBo0iMDAQKv3KKy/ivt8pnpHjRpltYxJQe9QYQwGA7Nnz2bt2rVER0dz6NAhixU6SoupTUaOHGnxuyQv02odRU14MJUztYujHTt2jJkzZ9K8eXNeffXVYtXhyBi7detW5DIxMTE8+uijRd5SwxHPLvZxrxOMT7fhJG9ZRkrENqqH3uznc9+/z5U9P3DHnDCcqngUUIvYy79tMBf2R+c7npOZxbYJHzJw/Sy6/mc8vzzybwC8mtSl3eRHOL83isPz15V1uGVCY1BERERERERERETk9lKqCQ/Xrl0zrxZga/LvVhs2bODixYsAPPzww4DllgLWvtLOycmxuYx/dnY2hw8fxsnJyeZqCtnZ2Zw5cwa4uXpCZmYmkZGRODk55ZsotSfhwdfXl4SEBC5dupTvnKPaBYrfNrt27WLAgAFkZmby5JNPMnLkSFq2bEnNmjVxcXHh6NGjNG/eHBcXF5o3b24ul56ebl5pwlZ7FjdRpCT9bOovgHvuucdq2fDwcJvnjUaj+Xzeuo8dO8b169cB2Lx5s8WqFRs2bGDw4MFs2rSJJUuWMHbsWIs6N2/eDOSuVGBarcCWoKCgfOV69+5t8/r4+Hgg/6R5QeP2yy+/pEWLFixevJjNmzezefNmnnvuOXr06MFbb71lkUgDhfdXcZ4vbz8VtspEQe+QPZo1a4aPjw/JyckcP368TBIeTG3Ss2dPm9eYkp2KmvCQnJz7Bbavr28xoyvYs88+S3p6Oh9//LF5NZSicmSMrVq1yre6jC0XL140b2eR9/eVvRzx7GK/gIdeJ3nbCuKX/5NmM3NXO0oJ/5XYL18j5J8bqFI7qHwDrKRqd27OubBjGLNvruYQ2LMtEYt+sHp98qFThH/wHXf+/SGaPtqH48s30+39FwDYNuHDfKtC3E40BkVERERERERERERuH6Wa8FC9enWcnZ3Jzs62a9LSaDTy73/nfmXYp08fQkNDgZsTr23btrVabteuXaSmpuLt7U3Dhg0tzh07dowbN25Qq1Ytm1/L//HHH6SkpBAaGkpAQACQuzR9RkYGISEhFl+n542noISHWrVqkZCQYJ4AzMtR7ZI3lqK2zZQpU8jIyODtt9/mtddey1du/fr1ALRo0cK8mgDkrpKQlZVFgwYNbE5q2tqWorB2K0k/m/qrYcOG1KxZM1/Z48ePk5qaSmBgIP7+/vnOnzp1iitXrhAQEEDt2rXzPUvDhg3zbdHRv39/xo4dy/z58/nss8/yJTyYJrZjYmLyxVsQ04obtpblz87OZteuXUD+SfOCxq27uzvTp0/njTfe4MCBA6xdu5aFCxfy66+/0rdvX44ePWqx2kNh/VWc58vbT9b6Ia+C3iF7mSavs7Kyil1HUZw+fRrAZnvkXamlqAkPpoSnWrVqlSBC2/bt24eTk5NFQpXJtWvXANixY4f5d2RUVJR5ZZzSiHHdunUWiUC2xMbG0r17dyB31Zn58+cX+V6OeHZ7hYSE4OTkVKyyxWFwq0rt/x4vs/sBVG/Vg/ZrjTbPV63fnPbfZZt/Tk+K4eS7D1NvzLtUb9WjDCK0rWnTEIwZN8o1hrxcjU68QadCrwsa1IWu7z3LpsfeJnFHxM3yXh5kply3We7g3FU06NeBDv8cjU9oEP7tQtg9fQlXT8QXO+amIU3JNDguWaI4Y7g8x2BFG0MiIiIiIiIiIiIilUVAQAB79uwpcrlSTXhwcnKiTZs27Nu3j507d/Loo48WeP2cOXPYvXs3rq6uzJkzx3zc9EV43on+vJYvXw5Yn0A0rQhgWlrfmo8//hiAESNGmI/ZmuxNSkoiKSkJb2/vAifj2rZty8GDB4mMjGTgwIEW5xzVLlC8tsnOzjYv+f7444/nK5OTk8OyZcvMz5GXqT1tJSWkpqZy/PhxXF1dadmypfm4Pe1Wkn4uLFnC3vNFTdJ47LHHmD9/Prt27SIuLs4iYSA1NRUo+vL+pnK2JunXrl3L+fPnqVWrFnXq1ClSvJC73UPbtm1p27YtEydOpHXr1pw9e5bdu3czZMgQwL7+Ks7zFdYPeRX0Dtnj/PnznDt3DoB69eoVuXxxmNrkxg3rk10rV67kwoULVK9enUaNGhWpbtP70a5du5IFWYCcnBySkpJsns/MzDSfz7Hy9XdZxJhXXFwcPXv25OTJkwwdOpSlS5fi7OxcrLpK+uz2SkhIKHbZ4nCq4kHtwi8rNznp1zkx6wFqdBpErfueL+9wiI+PJyfddoJAWXMzOGNPB8as24FXowDq/7WjOeHBM9CP1NiCV98xZmXnbm2x4W3uGHMvSbuOELlofYlijk+IJ8OYXfiFdirtMezoMVjRxpCIiIiIiIiIiIjI7a5UEx4g94vbffv2sXTpUqZOnWoxIZzXqlWrmDZtGgDvvPOOxaT25cuXAaxuc7Bjxw5zwkJBE+GXL18mKiqKpk2bWpzfunUry5Ytw9fXlxdeeMF83NbWCceOHQPIV8+tunXrxpIlS9i9e7fV845oF9NzQdHaJjU1lezs3MkIa5PV7733nnllg6ImPISHh5OTk0PLli0tlqO3p91K0s+FxVXYRLut/ra1WoVJx44dqV27NklJSXz//fc888wz5nMNGjQgOTmZjRs30qxZM6vlralTpw6XLl1i79693HXXXRbnLl26xKuvvgoU3A4FJTzk5e3tbe6nvF/l29NfxXm+wvopr8LeocK89957GI1GatSoQceOHYtVR1EFBARw6dIl9u3bx1/+8heLcwkJCea+s7VtS0FMq3qYVjNwNNP7Z8306dOZMWMG3bt357fffrN5XWnHeKsZM2YQHR3NkCFDWLFiBS4uxfsrzRHPXhAPDw+uXbvG3Xffzblz54rc9yVhcKtaZvcqjks7vuXGqYOkxUVxafvKfOdDP4zEzd/6ajeloW7duhXq63xXoxPYmV9zesNuei95jbA3lgBQv28Hzv5ceCZs5tXr5GRk4ezmSuymfWC0vTKCPerWqevwFR5Kk6PHYEUbQyIiIiIiIiIiIiKVhWml7aIq9YSH8ePHs3jxYo4fP06/fv348ssvad++vfn8qVOn+M9//sNHH32E0Whk2rRpTJw40aIO0xfmn3zyCUOHDsXX15ecnBzWrFnD008/jZubG1lZWQUmPLi6ujJ+/Hi+/fZbatSoAeQumW5a4WDJkiUWW16Yyt1ap2mbgNjYWFJTU/NtG2DSt29fnJyc2LFjBzk5OfmWMHdEuxS3bby8vAgMDCQuLo6ZM2cyf/58nJ2dycjIYN68efzjH//AxcWFrKysIic82EqUsKfdHNHPRY3r1vJFXeHBYDDQv39/lixZki/hYejQoRw4cIApU6ZQu3Zthg4dalE2OjqaZcuW0b17d3r06GE+3qdPHyIjI3nrrbfo3r27ecWLo0ePMmrUKE6ePAkUnOCT99wXX3xBZGQkjz32GC1atDAfv3TpEpMnT+bEiRPccccddO7c2XzOnv4qzvMVZYWHwt6hX375hU2bNjF27FiaNGliPn79+nXmzJnDO++8A+Ru35I3+QZy33fTu28s4eReXn369OHIkSPMnj2bvn37mhNGwsLCGDVqFBcuXADsT0gxuXr1KgcPHsTLyytfIgWU3vMURWEx2qt79+74+fnZ/N2a17x586hXrx5TpkwpdrJDWTAYDHh6epp/D5WlG1nQ7ccyv63dfHuOwrfnqPIOwywq6jhVK9BQyryexrImBa8CZXIlKhaM4N20HpejYqneKICUJbZXLTHp+t/ncHJ14XLUWVpPfJCYdTtIOV14OVuijkfh6uFe7PK3Ku0x7OgxWNHGkIiIiIiIiIiIiMjtrtQ3Eq9WrRo//vgjzZo1IzIykg4dOtCoUSM6depEYGAgTZo04cMPP8THx4eVK1fy5ptv5qtjzJgxuLi4sHfvXurVq0fz5s3x8/PjoYceYuLEiebl6q1NIpom6OfPn8+vv/5KvXr16NSpE/Xr12fw4MFcvnyZDz74IN+S+ba+lA8NDaVBgwbEx8fToEED/vKXv3D33XebVx8wqV+/Pn/9619JSEiw+lWwI9qlJG3z+uuvA7Bo0SICAwPp2LEjtWrV4vXXX+eDDz7AaDRiMBjylbM34aE47eaIfnbklhaxsbF2TVDfd999AGzevNm8pQHA3//+d7p160ZKSgoPPfQQvr6+tG/fnrZt2+Ln50dISAjTp0+nYcOGFvVNmjQJX19f4uLiaNOmDS1atDD/ycnJYcCAAYD1bQOsjdstW7bwzjvvEBoaSq1atejYsSOhoaHUrVuXRYsWUa9ePb799luLrQDs6a/iPF9RVngo7B1KTU1l9uzZBAcHU7duXTp27Ej79u3x8/PjjTfewGg0Mm7cOCZNmlTovRzF1Hdnz54lNDSUVq1aERISQqdOnWjcuDG9evUCrCerFOTbb78lMzOTESNGULVqxfxi31Exzpgxg1WrVuHv71/otVWrVuWf//wnrq6uxb6fyO3k7C97qP/Xjrh4uJN5rfBVBpo/OYA6XVty4D/f8NvY93Bydqbr3PFlEKmIiIiIiIiIiIiIiGOUesIDQHBwMPv37+f999+ne/fupKSksHfvXuLj4zEajQwfPpyYmBgefvhhq+Vbt27N+vXr6dSpE87OziQnJ9O7d2+2b9/Oyy+/THR0NC4uLuYv4U0SExNJSkrCx8eHp556inXr1tG8eXMOHz5MWloaf/vb3/jjjz947rnnLMrFxsZy8eJF/Pz88m014e7uzoYNGxg8eDCurq7s2rWL33//nWrVquWL2/S1/9KlS0ulXUrSNs8++yyLFi0iJCSE5ORk4uPjGThwIHv37qVTp05kZ2fTuHFjvLy8LNolOTkZX19f6tevbzUeWwkP9rRbcZ8lb3+ZkiLyMo0Db29v8yoSeV2+fJkzZ87g4eFBSEiI+bgpCcJWOZN+/frh6upKWloaP//8s/l41apV2bRpE/PmzaNz585kZWVx6NAhkpKSCAoKYsKECfzyyy80atTIor7AwEC2b9/O/fffj4eHhzm2uXPnsnPnTsLDwwG4++67bbZD3nE7btw4pkyZQteuXXFzcyM8PJwzZ84QGhrKv/71Lw4fPmyx8gPY119Ffb7C+smagt6h9u3bM23aNHr37o2bmxuRkZFERETg7+/PsGHD2LhxIwsXLrS6fUBiYiJgX+JFUdSrV49t27Zx33334e7uTkxMDD4+PixcuJD169cTFRUFFD3hYdmyZUBuX1pTWs9TFIXFKCKl7+zPe6jfrwN1e7Qhfmt4gddWbxRAu6kjOL//OIc/XMPlqFgOvPc1AX8JpfmTA8ooYhERERERERERERGRkjEYy2v9c+C9997jlVdewdfXl/3799ucRK+sjEYj7du35+jRo5w8edLufUdu93aR4tu+fTvdunWjXbt27N27t7zDKXXFfYcKM3DgQNavX8/XX3/NQw895JA6C3Pt2jW8vLwwGAykpKTg4eFhV7lDhw7Rpk0bBgwYwA8//GD1mvJ4nrzsiVHKR0Xf0qKi2TaACrUdQVG2tAAwODsxLHwxcZv3s33CRxhzcmxcaKD/mjfxa92Ydf1e5crxuNzDTk7ct/4tajStx7peLxdra4uRJ5ZWqi0tHK2ijSERERERERERERGR212ZrPBgy8svv8ygQYO4ePEiw4YNIzMzszzDcTiDwcCcOXO4ceMGs2fPtrvc7d4uUjzXr183r3jwwgsvlHM0ZaO471BBjEYjO3bsoGnTpjz44IMOqdMeERERGI1GQkJC7E52gNwtHpycnGw+f3k9T16FxSgiZcOYnUPcb7lbB9lMdgBCn7mf2p3uYP+7K83JDqYy2yd8qK0tRERERERERERERKTSKNeEB4AvvviC6dOn069fPyIjI8s7HIfr1asXH374IXXq1ClSudu9XcS2adOmER8fb3EsMjKSAQMGEBERQbdu3Rg9enQ5RVf2ivsO2XLkyBEuXbrEq6++ipNT2f0KPHToEFC07SzS09Np3bo1n376ab6tXEzK63lM7IlRRMrOmQ27OfNTmM3zNUICaTdpOOf2HCPi4+/zndfWFiIiIiIiIiIiIiJSmZTrlhYiYun06dMEBQVhMBgIDg7Gx8eHc+fOcerUKQC6dOnC2rVr8fPzK+dIpagmTJjA+++/z8yZM5k6dWp5hyN/ErduB5CTkcbJOcNJOxuJk1tVXGrUosGzC3CvE5yvbFr8cWL++xhZKRdw9qhB0IQlVG0QitFoxGAwEL9iOr69xuBWqyEGgwGAK3t+JPbzVzC4uuHkVpWgCV/gHtgUgL2DDbg3bEm90bOp0WEAZxa9yJWwdWScO03zufvxaHyn+d7HXu/JjZiD1Bn2T2oPmliaTWShom1HUNQtLSqC8t7S4tDYIAwuVXCqUhWAgAen4NPt/7V397FalnUcwL/PeYPDix6UA5ryIgoE2DRzYJKmk+Vyha/N3nxpGs6lJGvNObRMk1xjvKThbI606ViliVvqtNSItHCQyLQCQQ6kAoJxeIcD+PQH2zHjHDi6A+fc8Pn89Zznfq7r/t3Pftd2tud7X/fl+x23/sVHs3HRc+l3zdQ2r5GWdLYeAgAAAAA41HX4Dg/AB7p165YJEyZkxIgRWbduXRYsWJBNmzZlzJgxmTlzZubMmSPsUFAfZ4cHOBDqvzAuI2YszvDpr6Zu1IVZce+1LX5u5Yzr0vv8cTn5viU55pKb0zD96iRJ40uP5a2Hbs7uLY3Z8sbLaZh6RXZtfG/PmPu/k37fnp7h0xam5yljsvbp+z4059BJc3Pk6Xt2Deg1+rIM/clfUtNnwF7nHnrXC6kbObZN17N44jnZsaahjVfP4WDQ93+d4dMWZvi0hW0KOyRJ498eT92oi5K0fY0AAAAAANDx3IMGnUh9fX2mTJnS0WVwADz//PMdXQKkoqZrc+AgSboPOSNrZk/e63M7G9/NlqXzM/hHzyZJ6s68NCt/cUO2r1qaXqMvS02fAVly23nZuvzVDP7h06mo2XNHf9PaFel20unZvX1Lti5bkCNP+2KrtfQccXY7X13rdm1uzD/Gn5z3m7alpne/lHfuyI7Vb+aoc67IwBsfOGh10HH21QMDrr8vm//1YgZ+98GUqqrbtEYAAAAAAOgcBB4A4DD17u+np27khXu937Tu36nudWxKlXv+TSiVSqmp75+mtSuzrWFRtiyZl97nfSvdh43Oip+PS79rpqbqiKOTcjmb//lilk/+aiq69ki/a6Yd5CtqWVWPuhx19tdTWdszx15+Wzb8/ZmsfnSSsMMhqmHalSmnnO6DR+a4K+9O9ZH1++yBja88m+6fPDOlquq95mptjQAAAAAA0DkIPADAYWjVbydlx6qlGXDncx9pXN0ZF6fXZy/JO7NuT/fBI9N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- "text/plain": [ - "
" - ] - }, - "execution_count": 37, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ansatz_ibm.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can also use `apply_layout` to transform our virtual observable to physical" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "SparsePauliOp(['IIIIIIIIIIIIIIIIIIIIIIIIIIIIZIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIIIIIIIIIIIIIZZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII', 'IIIIIIIIIIIIIIIIIZIIIIIIIIIIIIZIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII'],\n", - " coeffs=[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])" - ] - }, - "execution_count": 31, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "hamiltonian_ibm = hamiltonian.apply_layout(ansatz_ibm.layout)\n", - "hamiltonian_ibm" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "b58c33dc", - "metadata": {}, - "source": [ - "## Step 3: Execute using Qiskit Primitives." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "fe36b13c", - "metadata": {}, - "source": [ - "As with an iterative optimization procedure, we now need to define our cost function over which to minimize. We proceed in an identical manner to the [Variational Quantum Eigensolver tutorial](https://learning.quantum-computing.ibm.com/tutorial/variational-quantum-eigensolver), computing the expectation value of our Hamiltonian with respect to the parameterized ansatz circuit using the [Qiskit Runtime `Estimator`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator#estimator) primitive:" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "id": "2f3e4de4", - "metadata": {}, - "outputs": [], - "source": [ - "def cost_func(params, ansatz, hamiltonian, estimator):\n", - " \"\"\"Return estimate of energy from estimator\n", - "\n", - " Parameters:\n", - " params (ndarray): Array of ansatz parameters\n", - " ansatz (QuantumCircuit): Parameterized ansatz circuit\n", - " hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n", - " estimator (Estimator): Estimator primitive instance\n", - "\n", - " Returns:\n", - " float: Energy estimate\n", - " \"\"\"\n", - " cost = estimator.run(ansatz, hamiltonian, parameter_values=params).result().values[0]\n", - " return cost" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "32035dc8", - "metadata": {}, - "source": [ - "Any classical optimizer can be used to minimize the cost function. On a real quantum system, an optimizer designed for non-smooth cost function landscapes usually does better. Here we use the [COBYLA routine from SciPy through the minimize function](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html).\n", - "\n", - "Because we are iteratively executing many calls to Runtime, we use a [`Session`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Session) to execute all calls within a single block. Moreover, for QAOA, the solution is encoded in the output distribution of the ansatz circuit bound with the optimal parameters from the minimization. Therefore, we will need a [`Sampler`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Sampler) primitive as well, and will instantiate it with the same [`Session`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Session).\n" - ] - }, - { - "cell_type": "code", - "execution_count": 95, - "id": "f2fffe34", - "metadata": {}, - "outputs": [], - "source": [ - "# To run on local simulator:\n", - "# 1. Use the Estimator from qiskit.primitives instead.\n", - "# 2. Remove the Session context manager below.\n", - "\n", - "options = Options()\n", - "options.transpilation.skip_transpilation = True\n", - "options.execution.shots = 10000\n", - "\n", - "session = Session(backend=backend)\n", - "\n", - "estimator = Estimator(session=session, options={\"shots\": int(1e4)})\n", - "sampler = Sampler(session=session, options={\"shots\": int(1e4)})" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "b0b5aa51", - "metadata": {}, - "source": [ - "We can set an initial set of random parameters:" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "1631f250", - "metadata": {}, - "outputs": [], - "source": [ - "x0 = 2 * np.pi * np.random.rand(ansatz_ibm.num_parameters)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "43520f43", - "metadata": {}, - "source": [ - "We can run our minimization routine:" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "0076beb6", - "metadata": {}, - "outputs": [], - "source": [ - "res = minimize(cost_func, x0, args=(ansatz_ibm, hamiltonian_ibm, estimator), method=\"COBYLA\")" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "95404ae5", - "metadata": {}, - "source": [ - "In the end, we have a result in the standard [SciPy `OptimizeResult`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html) format." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "7a299ed5", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - " message: Optimization terminated successfully.\n", - " success: True\n", - " status: 1\n", - " fun: -3.1833650134933325\n", - " x: [ 5.739e+00 2.804e+00 9.282e-01 5.858e+00]\n", - " nfev: 62\n", - " maxcv: 0.0" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "res" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "d162e690", - "metadata": {}, - "source": [ - "## Step 4: Post-process, return result in classical format." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "677cf16b", - "metadata": {}, - "source": [ - "The solution vector of parameter angles (`x`), when plugged into the `ansatz` circuit, yields the graph partitioning that we were looking for." - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "29cff98d", - "metadata": {}, - "outputs": [], - "source": [ - "# Assign solution parameters to ansatz\n", - "qc = ansatz.assign_parameters(res.x)\n", - "# Add measurements to our circuit\n", - "qc.measure_all()" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "554563ff", - "metadata": {}, - "outputs": [], - "source": [ - "# Sample ansatz at optimal parameters\n", - "samp_dist = sampler.run(qc).result().quasi_dists[0]\n", - "# Close the session since we are now done with it\n", - "session.close()" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "38c59bdc", - "metadata": {}, - "source": [ - "For small problem instances, the solution can be visually obtained:" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "9c61fa56", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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1iVW2EavE8ffff0tycrK0atXKYb+V00kWwzBy/XiWWm4dz6zCKsezbt26iWEY0qBBA4dxt+N6YYVzvtRy89rISnKj805AQIC88MILMnjwYClTpoyULVtWRo4cKSIiHTt2zPlKcCFuO83nXn75ZTl8+LDEx8fLH3/8IfXr1zfHrV27VqZOneowfceOHWXPnj0SHx8v//zzj7Rr185hvGEY8sEHH0h0dLRcuXJFVq5cKZUrV06z3OnTp8vGjRtdUqa8KLduA/7ss89k586dEh4eLuHh4ebruGfOnCkfffSRU8uYWVapiyVLlojI1V+37XWRk7dmi1w78Th58qSIiHkbmau7d9sdP35cWrRoIY0aNTIPkrnJCuvG1q1bzR8lUm8nOd0mjRs3zpWu/6nj6NKlixiGYZ5w5UYMVqmLFi1aSGhoqBw4cECmTZsmu3btkhdffDHNCWnqX9JfffVVWbp0qYwePVp2794tQ4YMka1bt5qJodQnpAsWLJC///5bunXr5nBCumnTJhk7dqzs3LlTDh48KD/++KO89tpr8vTTT6e5bel21L9/f5k0aVKutUlcXJzYbDb59NNPHdrkdt1GrBCH/ULt7bffTnd5OcUwjFw/nt3KeV+vsdn73Ehu3cpmZ7XjWb169fLMeuFKVjjns0pdWEnnzp1l1KhRMmjQIAkJCZHw8PA0nXfsyWyRa513vv76a6lVq5bMnj073c47r7zyivTu3Vvq1asnFy5cSNN5Z+TIkdKlSxfp2rWr1KtXTw4fPiyrV6/Od+c6JN+AHJIbFwnBwcFSvXp182NPlN55551SunTpnK2AVKxUF6tWrZJVq1blWBx//PGHfPHFFxIeHi5RUVFSqVIlGTRokNx5553SsGHDHEsAHjt2TJo3by516tSRKVOmOPSCzU25vW7Url1batSoISLXtpPcaJPvvvsu157baY+jbt26UrduXVmzZk2uxWCVuqhTp46sWbMmx09Ivby8ZMaMGdKsWTO5++675aOPPpLXXnvNEslyK8iNi4TUbVK7dm3x9PSUu+66y2yT23kbsUIcdevWFTc3Nzl16pTDPHMqyZJabh/PrHLel5vPobba8WzKlCmsF6lQF9aUG513PDw8ZNSoUXLixAmJi4uTFStWyN133+2yMuYWbjsFckhu3gZsNVaqi9deey1H4/D19ZVffvlFBg8eLBcvXpSAgAA5c+aMDBgwQA4ePJgj3bvtJ4Jly5aVUaNGOVyk3OhCIidYYd147rnn5JVXXpEFCxaIl5dXrrVJz5495dVXX83Rrv/Xx7Fw4UJ59dVXpVKlStK6devbui5OnToljz/+uDz++OPpbidr165NM6xjx443vGXCfkL6wQcfpDv+nnvukc2bN2f4fVy9SMjoNtOcaJOZM2dK9+7dZcaMGbm6blplG8ntOD799FPZv3+//Prrr9KgQQMJCgrKtduRrXA8s4rcuJXNqsezZs2ayaBBg1gvhG0Etx9DUz/gxkK2bNkigwcPlt9//10SExOlRo0a0r9/f+nUqVOm5xEfHy+ffPKJfP/99xIZGSmFCxeWBx54QD788MNbfi5HXFycBAYGSmxsrAQEBNxqcSzLKvevZzcOK8Qgkjfu5c8M6iJnffHFFzJy5EjzxOOzzz4zf2Vq3ry5lCtXzuFXpp9//lnee+89iYiIkEqVKsmIESMcfmVSVRk8eLB8/fXX5onH+PHjzV+Zpk6dmubWi9TfzcjttF5YqU2Cg4MtEYenp2eux2CVurDoqZPJKtuqVeJwNfYX1o3jv//+k7Fjx8qsWbNk9+7dUrx48TRJlt9//12aNWsmH3/8sZlkGTZsmGzfvt28qP/kk0/k448/lmnTpplJlr/++kv+++8/86L+yJEjcubMGVmwYIGMHDlSNmzYICIiFStWlAIFCqQbn1XkxHm4lbYTKxzPrH4cEbl99uGZYYW6sEIMSF9mc0WWTL6tWbNGwsLCxNvbW7p06SL+/v4yZ84cOXz4sIwaNUpef/31m84jJSVF2rVrJ8uWLZMGDRpIs2bNZN++fTJ37lwpX768bN68WYoWLZrpmEi+ZcwKJ+hWiEEk/+zQqAukh/UCyBussq1aIQ4rxICcl9OJHhGRHj16pPuw9jVr1kjz5s1dVlZnsMJ5OKyH/ec1VqgLK8QgYp04rCSzuSLL3XaalJQkvXr1EpvNJuvXrze7dw8aNEhCQ0Nl4MCB8vjjj9/0tbPTpk2TZcuWyRNPPCE//vijGIYhIiITJkyQF198Ud577z2ZOHGiq4sD3DJOgK5h5470sF7AytiHA7kvp29HFrnay+n6ZyHdDMcz4MbYRpCfWC75tnr1ajlw4IA888wzZuJNRCQwMFAGDhxo/qo0aNCgG85n0qRJIiIyfPhwM/EmIvL888/LyJEj5ccff5SxY8eKj4+PS8oBIH/goA8AAICcwrknkD9ZLvlm/zWqTZs2acaFhYWJiMi6detuOI8rV67IH3/8IVWqVEnTQ84wDGndurVMnDhRtm7dKvfee69zAgcAF+JEzFqs0h75JQ4rxCDCNgLXscL6aYUYRKwTB6zFKuuFVeIAkP9YLvm2b98+ERGpVKlSmnFBQUFSoEABc5qMHDhwQFJSUtKdR+p579u3L8PkW3x8vMTHx5t/x8bGiojImTNnJDExUUREbDabuLm5SXJysqSkpJjT2ocnJSU5PEzTzc1NbDZbhsPt87Vzd7/aPElJSZka7uHhISkpKZKcnGwOMwxD3N3dMxyecCXd4t+SuDjJdpkSrnhkK4bTpxPNMmXUHjdrp+zGYI/DLqvtlHDFJtlxo/bIbDs5oy7OnEm64bqXmXZyZptkdXvKbnuIiJw9m/19hDPiiIuTW95HuKo9srPfc/a2mpV9uTPaIzb26jyzsy93Vl1k9/jkjH24XVb35c44nsXGaraPuQlXsndqdfp0YrbPI5y5jdzKPkLEsZ0Srrg5LQ67W92XO6Muzp5Nzvb5njPbJCvne85qjzNnsn8Om3DFkOyKi5Msn+/Z9Z+UvTYZ0+vG5xeZaSdnH8+yui/Pbpvc6Pwis+3krLrI7vWTM9skq/tyZxzPzp3L+vmePXZn7DPOnUvJ1nWuK9ojK/vy7B7bU8dhd6v7cmfEYG+P7Fy7O6tNsnvtfn3suZljOX/+vIhk4kUqajGtW7dWEdF9+/alO75kyZIaEBBww3ls3LhRRUSfeuqpdMd//fXXKiI6ZsyYDOcxePBgFRE+fPjw4cOHDx8+fPjw4cOHDx8+fDL8REZG3jBPZbmeb1bxzjvvSP/+/c2/U1JS5MyZM3LHHXc4PEMuP4uLi5MyZcpIZGRkrr7h1QpxWCEG4rBeDFaJwwoxWCUOK8RglTisEANxWC8Gq8RhhRisEocVYrBKHFaIwSpxWCEG4rBeDFaJwwoxWCUOK8RglTisEENuUFU5f/68lCxZ8obTWS75FhgYKCLXbvO8XlxcnBQqVCjb80g9XXq8vLzEy8vLYVjBggVvuNz8KiAgwBIbjxXisEIMxGG9GKwShxVisEocVojBKnFYIQbisF4MVonDCjFYJQ4rxGCVOKwQg1XisEIMxGG9GKwShxVisEocVojBKnFYIYacdqPckl32H1rjZKmfx3a96OhouXDhQobPcrOrUKGC2Gy2DJ8Nd6PnygEAAAAAAADOYrnkW7NmzUREZPny5WnGLVu2zGGajPj4+EhoaKjs2bNHDh8+7DBOVWXFihXi5+cndevWdVLUAAAAAAAAQFqWS761atVKKlSoINOnT5fw8HBzeGxsrAwbNkw8PT2lW7du5vCoqCjZvXt3mltMe/fuLSJXn92mqd46MXHiRDl48KA89dRT4uPj49rC5HFeXl4yePDgNLff3o5xWCEG4rBeDFaJwwoxWCUOK8RglTisEANxWC8Gq8RhhRisEocVYrBKHFaIwSpxWCEG4rBeDFaJwwoxWCUOK8RglTisEIOVGao3ex9qzluzZo2EhYWJt7e3dOnSRfz9/WXOnDly+PBhGTVqlLz++uvmtD169JBp06bJlClTpEePHubwlJQUadeunSxbtkwaNGggzZo1k/3798svv/wi5cqVkz/++EOKFi2aC6UDAAAAAADA7cJyPd9ERFq0aCG//fabNG7cWGbOnClfffWVFC9eXGbMmOGQeLsRm80m8+fPlyFDhsipU6fk008/lY0bN8qzzz4rmzZtIvEGAAAAAAAAl7NkzzcAAAAAAAAgP7BkzzcAAAAAAAAgPyD5BgAAAAAAALgIyTcAAAAAAADARUi+AQAAAAAAAC5C8g1ZlpKSIryvAwCA7ElJScntEAAAAOBCJN9wQ/bkWmJioiQnJ0t0dLRERkaKiIjNZhPDMERVb5sLh4ySjbdL+a9HfVxDIvoa1otrWC+uoS6uub4ubDZOx5CWqrLd/D/q4prb6bz7ZlgvrmG9cER9XJO6wwzbS+4ylBbATezevVu++uorWbhwoXh5eYmqSokSJeS+++6TLl26SIUKFXI7xByhqmIYhly+fFni4+PlyJEj4u3tLZUrV3aYLiUl5ba4kKI+rrHXRVxcnJw+fVr27NkjJUqUkJo1a4phGDkah4jk6DLTi4H14irWC8cYqItrMRiGISdPnpSIiAj5559/5M4775SyZcuKn5+fBAYGiqenZ47EIZK7dWGX0f7gdthPXC85OVnc3NxyOwxLoC6uoS6uoS6uoS4cUR/X3I7Hz7yA5BtuaM2aNdKvXz/5+++/5c4775TKlSvLX3/9JceOHTOnadu2rfTp00fuu+8+MzlnhZN5Z1NV2bp1qwwfPlw2btwoKSkpcvnyZQkKCpL27dvLE088IQ0aNMiVuHKjvq1YH7lVFykpKbJ27Vp5++23Ze/evRIXFyciIkWKFJH77rtPHn74YWnZsqUULVo0x+LMrYMu68U1rBeOy6UurkpOTpZff/1V+vXrJ9HR0ZKQkCAiIv7+/lKvXj1p06aN3HfffRISEiI2my1H4rTCSXpMTIxcvHhRIiIipGzZslKuXDlznL13i6tjtMr5y7FjxyQiIkKioqKkevXqcuedd4qHh4c5Pj9vH9ejLq7Zs2eP7NixQ86cOSN33323lCpVSgoWLCgFCxYUd3f3HInBKskN1otrWC8c5XZ9WKku/vzzT1m7dq1cvHhRKleuLEFBQVKqVCkpW7as+Pj4uHz5ycnJ5p1y+H8K3EDTpk21VKlSumTJEr18+bImJCSoqupff/2l77//vlaqVEkNw1A/Pz/94IMPXBZHZGSk7tu3T+Pj4122jJtZunSpVqxYUb28vPTee+/VZ555RmvWrKn+/v5qGIYahqE1atTQ7777Ti9evKiqqikpKU6PY9euXbpx40Y9f/68w/CUlBSXLC8jVqgPq9TFggULtHTp0nrHHXfo008/rW+//bY++OCDWr16dfX29lbDMPTOO+/U0aNHp4nVWbZs2aJz587VM2fOOAxPSUnR5OTkG37XmXXFenEN68U11MU1c+bM0aJFi2r58uV10KBBOmbMGH355Ze1ffv2WqZMGTUMQ0uUKKFvvvmmnjp1ymnLTW3NmjU6ceJEjY6OdhienJyco3WhqhoTE6MTJ07UKlWqqJ+fn3p7e6uHh4dWq1ZNBw0apP/9959Tl5dZObmvsDt27JgOHz5cCxcurO7u7uY+Mzg4WHv37q1LlizRS5cu5WiMmdk+XIG6uObgwYP65ptvqs1mM+vBMAwtWrSoPvTQQ/rVV1/p3r17zelzIkbWi2tYL67JrbpQtV595GZd7N69W5977jmHejAMQwsUKKChoaE6YMAAXb16tXke7uo4k5OTNSkpyaXLyCtIviFDkZGR6u7urh9++KF58ErvIDZ79mwNDQ1VwzB0wIABeuXKFafH0q5dO23RooWOGjVKN2zYoNHR0enuKFLHd+zYMafG0LhxY61QoYKuX7/eYfjevXv1yy+/1LCwMHPn1rNnTz19+rRTl2/XunVrvfvuu/WVV17Rn376SXfv3q2JiYkO01yfZDhw4IDT47BCfVilLho0aKBVq1bVLVu2OAw/cuSI/vzzz9q7d28tXry4GoahLVu21H///dfpMTRr1sw8wRg5cqRu3rw5zbZ4/YX1v//+6/QTU9aLa1gvrqEurgkNDdVatWppeHi4w/BTp07punXr9KOPPjKPqeXKldMVK1Y4dfmqqo0aNVLDMLRmzZr66quv6tKlS82TcLvrT5a3bdvmkgvZfv36qZeXl1aoUEG7d++uvXr10po1a6qfn5+5r2jVqpUuW7bMbBtXxLFo0SINDw9Ps07kZNK+d+/e6u3traGhoTp06FB999139aGHHtJq1aqpm5ubGoahderU0ZkzZ5pt44rYJk+erKtWrUp3naAursrJunj66afV19dXH3zwQZ0yZYqOGzdOX331VQ0LC9NixYqpYRhaqVIlHTdunEvrYvjw4Tpr1iyNjY11GJ6ZpL2zsF5cw3rhyAr1YZW6ePzxx9XPz0979+6ty5Yt0+nTp+unn36qvXr10rvuukvd3Ny0RIkSOmDAAJf94Pnqq6/qhAkT0vzgmZSUlGtJSSsg+YYMLViwQD08PPSLL75QVXXodXb9Sfnu3bu1Tp066uvrq9u3b3dqHJGRkQ5Z+6CgIO3YsaN+/fXXun37dj179mya7+zatUsfe+wx/fDDD50Sw9GjR9XDw0M/+OADc0d9/cW86tXeBPbkwjPPPKNxcXFOWX7qOAzDUG9vb3V3d1dfX19t1KiRDhw4UBctWqSRkZFpvvPPP/9okyZNtE+fPk6NI7frwyp1cezYMfX29tb333/fHJZeXWzdulW7du2qhmHogw8+qDExMU476NvrIjAwUL28vNQwDC1btqw++eSTOmnSJN21a1ea7+zcuVMrVaqkjzzyiFNisMfBenEV68U11MU1x48fV19fX33rrbfMYenVxa5du/SNN95QwzC0YcOG6a63WXXs2DE1DEOLFSumvr6+ahiGuru7a6NGjXTo0KFpEqSqqtu3b9eAgABt0KCB0+JQVY2IiFAPDw/t3LlzmouT8PBwHT58uNavX18Nw1AfHx8dN26cU5dvd/jwYfXz89NmzZrpW2+9pfPmzdOIiIg0619KSop57hMTE6O7d+92WgwRERHq7u6uzzzzTJpxe/fu1SlTpmjnzp3N3j6vvvqqXrhwwWnLtzty5IjabDatWrWqdurUScePH69///13mrpITk42193o6GjdsWOHqjrnYpa6uCYiIkJtNpu+/PLLacYdO3ZMly5dqgMGDNDy5curYRjarl07PXr0aLaXe70jR46oYRhasGBBrVevnr777ru6cePGNBfRSUlJ5l0ykZGR+vvvv6sq6wXrhevWC1Vr1IfV6uLNN99MM+7cuXMaHh6u48eP12bNmqlhGFq9enXduXOnU5ZtZ68L+7lGjx49dMmSJWl6v6Wui8OHD+vcuXM1JibGqbFYDck3ZOjgwYPq4eGhvXv3vuF09p3Fn3/+qYZh6GeffebUOH744Qc1DEOfffZZ/fzzz7VNmzZauHBhtdlsWqlSJX3++ed15syZunv3bvMi/uuvv1bDMHTChAlOiWH58uXq4+Ojw4cPV9W0icjUO9a4uDh96KGH1DAMXb16tVOWbzdz5kw1DENfeeUVXbx4sfbs2dM8kBQpUkTbtWunI0aM0PXr1+vJkydV9eqvc4Zh6FdffeW0OKxQH1api3Xr1mlAQIC+8847qqoOvSbS63Let29fNQxDZ8+e7bQY5syZo4Zh6FtvvaW7d+/WQYMGaUhIiBqGoTabTatXr659+vTRn3/+WQ8fPqyqqtOmTVPDMHT8+PFOi4P14hrWi2uoi2v+/PNPLVasmJnovXLlikPP8utPvseMGaOGYeikSZOcFsP8+fPVMAwdPHiwJiYm6sSJE7V58+bmiXJgYKC2a9dOv/jiCzO59OOPP6phGPrll186LQ5V1Y8//lgLFSqkq1atUlXHi1W7hIQEnTFjhtaoUUMNwzB/EHR2HPaLBJvNpoUKFdLWrVvrRx99pKtXr9YTJ06k+c6kSZO0VKlSunTpUqfEMHr0aA0MDDR7OiYmJqa5UElMTNRly5Zp48aN1TAMHTRokKo6t/fGiBEjzF6X9tu3qlatqr169dLp06drREREmu988cUXahiG/vzzz06Jgbq45rPPPlM/Pz9dsmSJql7dHq7fZyYnJ+umTZu0Q4cOahiGvvDCC5qYmOjUurDvi+666y6zLvz8/LR169Y6ZsyYdG8PHz16tBqGoVOmTHFKDKwX17BeOLJCfVilLr766iv18vLSX3/9VVWv1kV6PyT9+++/2qdPHzUMQx955BGH27Wz67PPPlPDMLRu3brq4+Njnl9UqlRJ33rrrXR/5LPX37fffuu0OKyI5BsyFB8fr126dFHDMPSdd97RI0eOpDudPWO9detWLVSokL7++utOjeOjjz5SwzDMXwYOHDigv/76q7799ttav3599fHxUS8vL61bt66+++67Om/ePH3ggQfUZrM57RevmJgY9ff31w4dOtxwOvtFw65du9TDw0MHDx7slOXb2Q/49guVU6dO6fbt23XChAn6yCOPaNGiRc0eHU8//bR+/vnn2rp1a6fWhao16sMqdXH58mUNCgrS+vXrp5lv6oOdvS4OHz6sgYGB+sorrzjtgD9u3Dg1DEMXLlyoqle33ZMnT+rSpUu1T58+Wq5cOTUMQ319fbVJkyb61ltvadOmTdUwDNYL1guXrxfUhaNq1app+fLlzSSfXXp1ERUVpSVKlNBu3bo57TaN8ePHp3sRuGfPHv3f//6nd999t3miXLp0aX3iiSfM3mfOrovXXntNAwMDzR4h9vMJ1bQJ++3bt2vJkiW1evXqTr9N5sknn1R3d3edPXu2/vjjj9qxY0cNCgpSwzC0VKlS2rFjR/3yyy/1jz/+0EuXLmlycrJ27tzZqXXy/vvvq5+fn/7222+q6vjjxfVJ6tOnT2udOnU0KCjI6c8F7NGjh7q5uenatWt106ZN+uqrr2rFihXVMAz18vLS0NBQfeutt3ThwoV67tw5VVV96qmnnLoPpS6uGTlypPr4+JhJ3uvr4vp95EMPPaTe3t4ZnrNnVe/evdVms+k///yjJ0+e1E8++URr167tcFdK586dderUqWayunv37urh4eG07ZX14hrWC0dWqA+r1MXXX3+tXl5e5jE+Pj7+hudSL7/8shqG4dTnq77yyitqGIaZiJ42bZq2aNHCrAvDMLRBgwY6cuRIsw169Oih7u7uLrsN1ipIvuGGtm3bphUrVlQ3Nzd99NFHdenSpRk+023SpEnq5uamCxYscNry4+Pj9d1331V3d3fdv3+/w7jLly/rf//9pz/++KM+//zzWrVqVXV3d9eCBQuqYRj6wAMPOC2O5ORkszfGk08+qTt27HC4SEgdr+rV22WKFSumL730ktNiSExM1DFjxmiJEiV0z549DuOSkpI0OjpaN2zYoMOGDdOmTZuaD66238LlTLldH1aqC1XVDz/8UA3D0CZNmuiKFSvSPbmy18Xff/+tpUqV0ueee84py05KStLvvvtOa9asme6BMyEhQQ8fPqzTp0/Xxx9/XAsXLmwe+FgvWC9yYr1QpS5SmzBhgnp7e2vFihX1p59+SvcFEPbj7D///KMVKlTQbt26OWXZKSkpunDhQm3VqpX+9ddf5rDrp9m4caO+9NJLWrJkSbMuHnroIafEkNrcuXMz1evUnoz86KOPtECBAmZy3RnOnDmjrVu31iJFiqjq1f3YyZMnddOmTTpq1Ci977771N/fX93c3LRq1ar60ksv6ZAhQ7RQoULatm1bp8WxevVqNQxDBw4ceMPp7NvJF198oX5+fjp37lynxXD27Flt3769+vv7m8MSExP16NGjOnv2bH3qqafMHzAKFiyo7dq10z59+qi/vz914aK62LZtm3lMvV7qbde+z5g6dar6+vrqd99957QYYmNjtUOHDurh4ZHmmL5lyxbt37+/BgcHm/uKqlWr6uOPP66+vr6sF6wXLl8vVHO/PqxUF3v27DFfepb6sS7XJ6jtdTF79mz18fFx2t0fcXFx2rFjRzUMI81jZY4ePaqffPKJw4983t7e2rRpU/Xy8nJ6XVgRyTfc1IEDB7Rbt27mc3Jq166tQ4cO1eXLl+vGjRt1y5YtOmPGDA0KCtIqVao4ffmnTp3S2bNnm79cpffrf2xsrP7555/67bffmr8yLFq0yKlxHDx4UBs0aKCGYWjjxo11woQJum/fPr148WKai5fx48erm5ubzp8/36kxnDt3TpcvX24+pD69XzKuXLmiERERumrVKvNXBmfXhWru14eV6iImJkYfeeQRNQxDK1asqG+//bauXr1ajx07luYg/Omnn6rNZnNqXVy4cEE3b95s/sKa0S9cFy9e1AMHDphd7lkvWC9Uc2a9oC6uuXz5spmk9vX11SeeeEKnTZum//zzj16+fNlhWnvSct68eU5b/pUrV3TXrl3p/rqcXiKue/fuLquLkydPau3atdVms+mQIUP04MGD6cZgT7599tln6ubmphs2bHBaDCdOnNCHH35YO3TokOYWtoSEBI2MjNTly5frwIEDtW7duurp6WneRmO/rSe7UlJS9Pz589q+fXs1jKvPwty2bVuabSN1XXz11Vdqs9l07dq1TolB9Wpi4cUXX9SuXbum+3b5K1eu6J49e3TChAl6//33q6+vr/mQe3uv0uyiLq5JTk7WhIQEffbZZ9UwDA0LC9MVK1ak+5B/e1188803arPZdOXKlU6JQfXq/vPDDz/UF1980bw17frt9MqVK7pkyRJ9+umnNSAgwLywZr1gvXDleqFqjfqwUl2oqg4cONC8Zk/vBRCpX3owZcoUdXNz02XLljklhvj4eP3222/1rbfeMs8zEhMT01y/h4eHa79+/bREiRJmXbjiPMNqSL4hQ/admerVB0J+/fXX2q5dOw0MDFTDMNTNzc2hh0BISIh5r31OuX7Hdvr0aW3WrJkGBga6ZHmXLl3SQYMGmb0BKlasqL1799ZJkybprFmzdPny5frpp59q4cKFtWbNmi6JIbNOnz6tLVu2dFldqOad+siJulC9ejCvWbOm2mw2LVasmD7wwAP67rvv6qeffqozZszQ1157Tf39/TU0NNSlcdxITEyMtmnThvVCWS9Sy4n1QpW6SG3JkiXaokULM5lTu3ZtffLJJ/XNN9/UcePG6WOPPaY+Pj7avHlzl8aRHvtJckxMjLZr104LFizosmUtWLBAixcvrjabTR955BGdNWuWHjlyRC9duuRwjD958qR26dJFCxUq5PQYDh8+rFu3bjUvzNJLzp4/f14PHz6sU6dO1aCgIJesHxs3btSqVauqYRhav359HTFihG7atEmjo6MdEoNRUVHaoUMHLVy4sNNjiI6O1v/++++GbwO0nx+uWrVKy5UrR124uC52796tLVu2NG8F79Onj86ePVv37t3r8IzEo0ePaps2bcxenM509uxZjYiISPcH8OvrZe/evVqtWjXWC9YLh79duV6o5n59WKkuTp48qc8995x5jd6uXTsdN26cbt261WE7OXTokDZq1EiLFSvm1OVfvnxZT548maYuUifH7c6ePau1atVy+TmXVZB8wy1JSEjQ9evX68iRI7Vfv3767LPP6iOPPKLffvutS96io+qYnU/vvn37NKqqS5cuVQ8PD+3evbtL4lC92rNm4cKF2qdPH7377rvV29vb/FXL/rn33nt13bp1To8hM88/stfV0qVL1TAMp92udP0y7InZ06dP6/z583O8PpKSksz6yOjV7jlRF6mXk5CQoFu3btURI0bo/fffr0FBQeZDV+2fBx54QLdu3eqSOG7EXj9LlixRwzC0a9euTl8G60X6y2G9uPbsrkuXLukff/yR43WR+mTz+meJ2eVEXdiXb3f06FGdNWuWPvfcc1qtWjWHenB3d9euXbvqP//845I4buT6unjqqadcurz9+/dr9+7dzd4ANWvW1L59++qECRP0+++/1zlz5ugjjzyinp6e5os7csvSpUvVz8/PabdFX+/SpUv63nvvadmyZdUwDA0ODtZHH31U33nnHR0xYoR+8cUX2rhxY/Xx8dEhQ4a4JIabsa8fS5cuVX9/f3322WddshzqwtHEiRM1JCREbTabBgQEaGhoqHbp0kX79++vb7/9tlatWlX9/f3Nlx7lNPtF9bJly7RgwYKsF8p6oZpz64Wdlesjp+ti0aJF2qJFC/P8u2TJklq/fn19+umn9cknn9TixYtr4cKF9dNPP3VpHOmx9xxdtmyZFi5c2OV1YRUk35BGYmKi/vPPPzpmzBidOHGiTp48WefPn5/m4dAZPfstp6R38fTdd99p6dKlc+QiNjk5Wf/++2+dMWOGjh07Vt9//3196aWXdPHixeYtb7np119/1Tp16ui2bdtyZHlJSUm6Y8cOnT59eq7WR+rki11O10VKSooePnxYN2zYoPPnz9cvv/xShw0bplu3bk3TDT6n/fbbb9quXTvzAeeuxnpxze20Xlxf19ffnpOcnKz79+/XtWvXuqwubhaDqqb7prOc3kZUr/7ye/DgQQ0PD9dZs2bpd999pwcPHkzzC3FO+/fff7VHjx4aHh7ukvmnrv/Dhw/rd999p127dtWKFSuaj7pI/Rk8eLDTH55uj8Muo6S93ZtvvqmGYejmzZudHoc9SRwbG6tr1qzR999/X5s2bapFihRJk5gdO3asnj171ukx3Io33njDJXWROll++vRpXblyZa7UReo40juGpOaqurg+jt27d+u3336rTzzxhPkmb8Mw1MfHR++44w6dOnVqmucs5bT+/fuzXvw/1otrXLFepH5buF1CQoL+999/OVYfqX/wtbvZeuGqbcQudSxxcXG6atUqfeONN7RmzZpmXRQpUkSrVaum8+bNy9Vz0Ndee00Nw9BNmzblWgw5yVBVFeD/HTp0SEaPHi3jx493GO7j4yOVKlWS5s2bS7t27aRRo0ZSoEABSUpKEjc3NzEMw+mxJCUlyZ49e2T58uXi5+cnHh4eUqxYMQkJCZFSpUql+50LFy7Ijh075N5773V6PHb2TSZ1mVXVJXWQHVeuXJH9+/dL9erVnTbPy5cvy++//y4rV64UDw8PEREpW7as3HvvvVK5cmVzuuTkZHFzc3Pacm8Ug2EYUr58ebn33nvlzjvvTPc7rqiLjFhxXUgtKSlJTpw4keE2lBWsFzd3O64XsbGx8ssvv8jGjRslOTlZUlJSpGrVqtK+fXupWbOm05ZzqzHcdddd0r59e4d2T71fd0VdpF7OrawHrlhvbnWely5dEl9fX6fGkFpCQoJ4eno6LO/vv/+WAwcOyMWLFyUqKkr8/Pzk/vvvl7vvvttlcSQmJpr7L5Gr9ZSSkuKwz7p48aKMGzdOfv/9d1m4cKHLYkkdU2RkpERFRcnFixflwIEDUrhwYWncuLGULl3a5cu/kfj4eJk+fbqsXr1avv/+e6fPPy4uTgICAhyWFxERISdPnpTLly/nWF1cH0d664Wr6+J6KSkpcu7cObl48aLExcXJrl27pHjx4lK9enUpVKiQy5d/I8nJybJ8+XJZsmSJfPbZZ06fP+tFxm7n9SIhIUHOnTsnxYoVc1jm6dOn5fLly3LhwgWX10d6MdjjsNls5nHX1XWRkZSUFLHZbBIdHS27du2SUqVKSZkyZcTHxyfHYkjPjh07ZN68eTJ06NBcjSOnkHyDg44dO8q8efOkV69eUr9+fXF3d5fY2FhZv369LF++XM6dOyclSpSQZ555Rvr27ZtmB+MsN0sCtmjRQh544AFp2LCh+Pr65tqFberl2hMLVr/Izqrdu3fLhx9+KNOnTxcREV9fX7l06ZKIiAQGBkqLFi2kU6dO0rZtWwkMDExzsMmJGFq1aiWdO3eWsLAwh5MiZ0tMTBQ3Nzex2WwZTpPeumE/8OVUDDmB9eIa1otrwsPDZdCgQWaComjRonLq1ClzfEhIiDz77LPSuXNnKVKkiEv2mzeLoXbt2vLcc89J586dpXDhwk5ddmpxcXHi7u6e6QSWK9aLW43B1Q4ePCiLFy+Wf//9Vzw9PcXX11fuvvtuadGihUuSnpmNw8/PT6pXry4tWrSQEiVKpPudc+fOSVxcnAQHB7ssrsxsD1Y417h8+bJcvnzZKduPqsrOnTvlxx9/lEOHDklSUpL4+flJ3bp1pUOHDlK+fPkbftdZdZFeHAUKFJB69epJhw4dpGzZsuku15l1kR3O3G9kJ4bExETx8vLK9rxYL5wjv60XIld/NPztt99kwoQJEhUVJXFxceLn5yf33nuvPProo1KvXr0bxuKM+sgohqZNm8pjjz0mderUMadNvV44uy5Su9F6n944V6wbVjg+WZaLe9YhDzl06JC6ubnpG2+8kW5X2WPHjulXX32l9erVU8MwtGXLlrpv3z6XxPL444+ru7u7vvjiizp16lT94Ycf9Msvv9TOnTtroUKFzPvW3333XT158qRLYhg1apSuWrUq12+vtUocDz30kHp5een777+vixcv1g0bNuivv/6qL7/8shYvXtzsxvzUU0+57HatW4nBVbdJqaq+//77+s033+jevXvNtxrdTGae15fXYlBlvUjNCm1ihRhUVe+//3718/PT0aNH659//qmRkZG6Y8cO/d///qd169Y126RRo0Yue7uVFWJQVe3bt6++9957umrVKj127FimbiVN77EKeT0GuxkzZmhwcLAahqE2m00LFChgtkWJEiW0Z8+eumzZMvM24evfZphTcTz77LO6cuVKc/mu2E6uf6lEelLfVmVvE2e3TWbicLWJEyeab70rXLhwmtsIW7VqpTNnzjTfCHz9m2lzKo777rtPf/755zRvJnamqKiodG+TT0/qZyE7e724lThchfXiGtYLRyNGjDDboUqVKub+3P6pUaOGjh8/Xi9cuJBrMdSsWVMnTJjg8ts603uDeUbPSU89zJnby63EkJqrtlmrIvkG0xdffKE+Pj7mRUhGO9Y9e/Zonz591DAM7dmzp9M3GiskAQ8dOmTuOO+66y4dPHiw/vXXX+lOaz+oHTt2TH/55Rfds2dPvosjIiJCbTabDhw4MMNpFi5cqG3atFF3d3cNCQlx+nP3rBCDPQ57m5QtW1Z79eqlCxYs0KNHj6a5SLS3SUREhH722Wf622+/5ZsY7PPM7TaxQgz2OHK7TawQg32eNptNBw8enOE0mzZt0i5duqiHh4eWK1fOfMW9sxIAVojBHoe9Te644w594IEH9LPPPtPNmzdrTEyMw7T25e7bt08HDBig8+bNyzcx2B05ckSLFCmilSpV0sWLF+u6det0+/btOnfuXO3atav6+vqaF7fvvPOOnjt3zqnLt1Icx44d0+7du+svv/yihw8fztTFrCueAWiFOA4fPqwFCxbUkJAQ3bRpk+7atUvPnDmjmzZt0rfeekurVKlirsNdunTRvXv3OnX5Vorj6NGj2rZtW/30009148aNevLkyQz3SfbhrkiEWCEOK7SHVeKwQntYKY6IiAgtUKCANmnSRP/991/zGcL//POPfvrppxoWFqbu7u5qGIY2aNDAJS/Bs0IMqqqRkZF6zz336KuvvqqzZs3SvXv3prk2v/7ZeM5OElshhryC5BtMEydOVMMwdM2aNap64wuQy5cva69evdQwDKcmeVStkQT87LPP1DAMveeeexx6ztx77706fvx4PXLkiDmtvZ7GjRunhmHonDlz8l0cEydOVG9vb507d66qqkNPgNT1fv78eR01apQahqFt27Z16q9NVohBVXX8+PFm0jc0NFQ9PT3NX9gGDhyo69ev11OnTjn80vjFF1+oYRj6008/5ZsYVK3RJlaIQdUabWKFGFRVJ0+erF5eXjpz5kxVvdYmycnJafbTc+bMUQ8PD61du7ZTezFbIQbVa8fVRx99VDt27Gjux4ODg7Vr16763Xff6d9//+3w4OevvvpKDcPQadOm5ZsY7N5//30tVqyYLly4MN3xCQkJOmXKFK1du7babDZ97LHHXNK73QpxvPvuu2oYhrq5uWnVqlX19ddf11WrVumJEycyvGhZtmyZDhs2TI8dO5av4hg0aJAWK1ZMly5dmuE0ixYt0ubNm6thGNq8eXM9cOCAU5ZttTjef/99NQxDPTw8tGTJktqlSxf99ttvNTw8PE0S2N4ev/zyi/bq1Uv379+fr+KwQntYJQ4rtIeV4hgyZIgWKVJEV6xYoarp9+777bfftGPHjmYPtO3btzvElR9iUFUdPHiwGoahXl5e6ufnp02aNDHvBDl69KjDtPblfv/999q6desMO3TkxRjyCpJvMO3cuVN9fX313nvvNXuSXX8Bq3rtIubnn39WNzc3nTp1qlPjsEISsE+fPmqz2fTPP//U3bt364cffqjNmzc3fw339fXVxx57TGfNmqXnz5/XpKQk7dKlixqG4dSLeqvEMXv2bDUMQ+fPn3/TaZOTk82T+T/++CNfxaB67a08mzdv1uPHj+vkyZO1R48eWqlSJfPA07x5cx01apT+/fffGh0dbR54ndUmVohB1RptYoUYVK3RJlaIQVV11apVahiGfvPNNxlOk/pNYGPGjFHDMHTJkiX5KgZV1bfeeksNw9Dff/9dL1y4oEuWLNGhQ4dq8+bN1d/fX93d3bV69erat29fXbhwof7999/62GOPObVNrBCDXatWrbRWrVpm0sbeg+r6pOihQ4e0a9euahiGjh492qkxWCWOZs2aqY+Pj3bu3Fnvvvtu84K2UaNG+vHHH+uWLVv03LlzZjxXrlzRhx9+WH18fJzaY8AKcbRv316rVaumkZGRqnrtNqTr2yMxMdHch/fv398py7ZaHK1bt1ZfX1997bXXNCwsTAsWLGgmRvv06aOzZ8/WvXv3mttmUlKSPvroo+rp6ZnpRw3klTis0B5WicMK7WGlODp27KgVKlTQiIgIczmqV9vk+iTYpEmT1DAMffzxx522fKvEoHp1/fTz89MRI0boc889Z976WrRoUX3wwQd11KhR+ttvvzn0dO/YsaPabDan3Q5rhRjyCpJvMF26dEl79+5t/kJ+/fOZkpOTHRJhU6dOVXd3dzPj7yy5nQSMjY3V9u3bq2EYDuW9ePGirly5Ut944w2tXbu22QutZMmS+vjjj6ufn5+2b9/eKTFYKQ5V1QMHDmjhwoW1WrVq+vvvv5vDr3+Vtv0CZunSperm5qZffvllvoohLi5OO3TooIZhODyD78qVK7p161YdO3asPvLIIxoUFGTestSqVSv19PR0WptYIQY7K7SJFWKwQptYIQa7qKgoDQ4O1qCgIJ03b16GF+j2Nlm3bp16enrqyJEj81UMFy9e1J49e6qXl5dDj4DExETdv3+/zpkzR1977TWtXbu2enp6qq+vr95zzz1qGIY+8MAD+SYGu4SEBO3Vq5cWKFAgU0mbCxcuaEhIiNaqVUtjY2PzVRzHjx/XmjVras2aNVVVNTw8XL/88kvt1KmTli5dWg3D0ICAAH3wwQd1woQJGhkZqatXr9agoCANCwtzSgxWiuOtt95SNze3ND0kUrNfzKakpGjLli21SpUqTu0BaIU4oqOj9Z577tFKlSqp6tXk7/z58/Wtt97SevXqqbe3t3p5eWn9+vV14MCBumHDBp03b54WK1ZM77//fqfEYKU4crs9rBKHVdrDKnGoqg4bNkwNw9Bt27ZlOE1SUpJ5jH/88ce1bNmyunv37nwVw4kTJzQ0NFTLlCmjqqpnzpzRrVu36vjx4/Whhx7SO+64Qw3D0PLly+tTTz2lP/zwg06bNk2LFi2qbdu2zTcx5CUk3+AgISFB+/btayZ02rZtqz/99JPD7SiqV3fAzZo102LFijk9htxOAiYkJOjnn3+uXbt21TNnzjg85NjuxIkTOmvWLH3mmWf0zjvvNOvLmQ/ttkocqlfrfOjQoWoYhjZu3FgXLFjgMP763onTpk1Td3d38xlK+SmGH374Qbt3727egnR9m5w9e1ZXrVqlQ4YM0VatWpkP8V68eHG+iSF1LFZoEyvEkNttYoUYUvvmm2/UMAytUKGCfv7553rixIkMp502bZq6ubk5vddZbseQkpKiv/76q77++ut66tQpc1hqFy9e1J07d+rkyZP12WefNW8JdVabWCGG1L7//ns1DEO7du1q9ha4/se11Me6559/Xu+44w6nP94it+PYtm2benl5aYcOHRyGx8XF6fr16/Wjjz7S1q1bmy+YKlWqlIaGhqphGPrrr786JQYrxbFo0SI1DENbt26t27ZtS/cxIqnbo3///hoQEKD//POP02KwQhz//fefli5dWh955BGH4ZcvX9Z//vlHv//+e+3Vq5dWrlxZ3dzctFChQlqtWjWnt4dV4sjt9rBKHFZpD6vEoaq6YcMGtdlsGhISoitWrEi3V13qh/2///776uvra972mV9iOHDggIaEhOhjjz3mMDwpKUmjoqJ03bp1+uGHH2qTJk3Ux8dHPT09zR9WnNUmVoghLyH5BpP9oHHixAkdO3asVqhQwUzm+Pn5aevWrfWdd97RTp06acmSJdXPz0/HjBnjkliskASMj49Pc5GS3v38f/75p1aqVEkLFizo9BisFIeq6siRI81fMGrVqqWff/65Hj9+XFXV7DZ84MABrV+/vpYoUSLfxpCe9Nrkr7/+0urVq2tgYGC+jsEKbWKFGNJzO68XM2bMME+8K1WqpAMHDtTff/9djx49qsePH9f4+Hjdtm2b1qpVy/zFND/GkJ70Hqewd+9erVOnTo6tF7kRw6lTp/S+++5TwzC0U6dON3z5ydmzZ7VHjx4aFBSU7+K4ePGiDhkyRCdMmKCJiYnpvhEuOjpaFyxYoG+//bb5dt5ChQo5LQYrxREfH69PP/20GoahTZo00dmzZ2d4y/O5c+e0R48eWrRoUafGYIU4Ll++rJ9//rn+8MMPZm+Z69vj3LlzunnzZp04caI+/PDDLmkPq8SR2+1hlTis0h5WicPu7bffNn9gGz16tO7evTvd3syxsbHavXt3veOOO/JdDPHx8Tp9+nSdN29ehi/CuXLlih48eFCXLVumffr0UU9PT6e2iRViyEtIvkFVM36u2rx587RDhw5apEgRdXNzM581VrduXZ05c6ZL7tO2UhIwIykpKeaLINauXav+/v767LPP5mgMORmHff2Ii4vTn376SVu1amW2iWEYGhoaqk8//bQ2bdpUfX19NTAw0Km39VklBtXMvRLbfkv0qlWr1NfX1+ltYoUYVK9tq7GxsTp9+nRt2bJljreJFWJQ1TRvE73RNK5qEyvEoHptW01ISNBVq1Zpz549HV4YU6VKFW3atKlWrVpVDcPQ4sWL67fffpvvYlDN3LZqP1ldvny5enl55cr+wtUxpBYXF6fPPvus2RbNmzfXH374QWNiYvTKlSt65swZVb360oeAgAB98cUX83Uc10svWT558mQ1DEOff/75HIkht+IYOnSoFilSRA3j6oumPvnkE926daseOnRIIyMj9fLly/rxxx9rgQIF9KWXXnJJDFaKI7X0ztN/+ukntdls2rt37xyJIbfisEp7WCWO1G7n9UL16t1P9rfNVqpUSfv27auzZ8/WjRs36u7du/X48eP61ltvqZ+fn7766qv5NobMmjt3rnp6emqvXr1u6xhyE8k3mOzPMrh06VKa55qcP39e161bp+vWrdP9+/drdHS0S2KwQhIwvRPOG8X2+uuvq2EYumXLFqfFYKU4MrJu3Tp99dVXtW7duuazldzd3bVdu3a6fPnyTCUC8kMMNzJkyBA1DEP//PPPfBdDRuvh6tWr9ZVXXsmRNrFCDDeKI6Nt2BVtYoUYbmTbtm368ccf6+OPP64NGzbUypUra9GiRfWZZ57RP//806lv/rJyDDcyevRodXNzy9X9hatjsCf5IiMjdcyYMVqrVi0z+eXh4aGNGzfWBx54QCtWrGj2MnHmG/KsEkdKSkqGPQRST2NfJwcOHOiS47tV4rDvp86dO6c//fSTPvzww+rv76+GYai7u7tWq1ZNa9WqZSY+2rZtqwcPHnRqDFaII73Hi6Q3jb097C9TccV6YYU47MfqM2fO6I8//phr60Vux5F6O83oOJVT64UV4ki9/KSkJF27dq2++uqrWrVqVXVzc1M3NzctXry4FipUyLxe7Ny5sx45ciRfxnAr5y6uuFa0Qgx5iaGqKrhtqaosXLhQvv32W/n777/lwoULUrNmTalZs6bUrl1batSoIRUrVhQ/P78ci+nYsWNSqlQpuXz5siQmJkpAQIA57sKFC7J9+3YRESlVqpQUKFBAihcv7rIYEhISJCkpSXx9fdOdTlVl0aJFMnv2bJk6dWq+jSP1clRVbDabOezKlSuyb98+8fHxkUKFCom3t7dL1xcrxJBZ69evl6VLl8qwYcPyZQz79u2TYsWKyblz58Tb29thW7x06ZLs27dP/Pz8XNomVoghdRznz58XHx8fueOOOzKc1lVtYoUYrpeSkuKwrSYkJMiJEyekYMGC4uHhIV5eXmIYRr6PITN27NghGzdulJdffvm2iSE+Pl6WLl0qv/76q+zcuVPi4uLk/Pnz4unpKU899ZS8+OKLUrp06dsmjuvXVRGRqKgoeeKJJ+TIkSNy8OBBl8dghTj+r717j4uqzv84/vkOqAQoMVwUCK9oiCmaN8QuXjIrRS0V19Uka9PNSz+vq918VO5aprZ2c7tvWW6Zte5jxVtr6MPyApWaYgImKkggoIhACMPM+/eHj5llGDR77Iy8OXxf/+zDmbHzfKxnzpz5nDPnWCwW2b9/v6SkpMiRI0fk3Llzkp+fLzfeeKNMmDBBHn74YQkICPCogclRX0VFRTJt2jQ5duyYZGRkNIjhejuqq6tlz549smvXLjl69GiD/XuwOOp7nzbEesHgsFqtkp6eLt9++61kZGRIfn6+nDhxQtq2bSv33XefTJ48Wby9vQ1vuFolJSUyf/58+e677+Tw4cNN1tDQ6eFbE2/JkiWycuVK8fX1lcjISLFYLFJdXS25ubkCQGJjY2XcuHHy4IMPSps2bTzmYBgCXs1w6623Sq9evaRTp07SokULAeCxL2ssDntWq1VMJpPLcqxWqyilXD5wjWq4muN61tCGqqoq2bBhg6xZs0YOHjwoJpNJOnfuLFFRUXLrrbdKXFyc9OrVSwIDAw1t+DVH7969ZeDAgdKzZ0+nAwhGNNgDIFarVby8vFzWT5vNJkopl8fdvQ1jMPya43rFYKhdYWGhFBUVSVBQkJSWlkpwcLDTgLikpER+/vlnx5CrVatWHnEzOGobysvLJTg4WG688cZ6X2t/j/v4+Mi4ceMM6bBX38G1iooKKS8vl9atW0tVVZW0aNHCI8tmdFwti8UiX331lXh7e8tdd91lKIfVapXjx49LSUmJABCbzSYdO3aU8PBwx2vKysqkvLxcwsLCPPbvweCobbDXsWPHK5544Kn1gsVRX3U/w6urq8VkMom3t7fjM9DTMRh+LavVKgcPHhQA0rdv3yZraOj08K0Jd+rUKenWrZsMGjRIVq1aJdHR0VJcXCy5ubly4sQJ2b17t2zfvl2OHz8usbGxsmzZMrn33nvrPcLxv8YwBLxWw5QpU5w+bNy9UWVx5ObmSmRkpOPPNptNANS7DE8NARkMv9VRu5qaGrcd5WIwiIjMnz9fXnnlFWnXrp107txZmjVrJhcuXJD09HQpLS2VyMhIGTlypEydOlX69OnjtuWyGX6L4+GHH5bevXs7/p4736sMBhGREydOSKdOnRx/ttlsYrPZrutRXgYDi4PBYC8/P1+eeuop+c9//iN5eXnSsmVL6dChg0RHR0u/fv0kPj5eevTo4Tiz21PbcgbH1QxxcXFy2223Sffu3T0+2Gloh/3/26utl3WH5fa/485/FwbHtRiuRyyOzMxMeeKJJ2TLli1SXV0tLVq0kMDAQGnXrp3ExcXJ3XffLbfddpu0bNlSROo/68oojqsZ4uPj5Z577pH4+HiP/9KDxfFr1f038MQ2ozEYdOS56/erusbX888/D7PZjB07dgCAy3U/SktLsXfvXsyZMwdKKbRp0wYHDx50u+PkyZPw9fXFfffdh2PHjgG4fCeyAwcOYMOGDZg9eza6dOkCpRR69uyJLVu2ALjytYwaq4HNoZTC8OHD8cEHH6C4uNjp+ZqaGscy7b/zt9/4wUgGFgeDAQCys7Ph4+OD8ePHo7CwEMDli5bn5OQgNTUVK1asQHx8PJo1a4b27dvjww8/dDIZxcDiYDAAwE8//QSlFLp27YoVK1YgPz/f6fmamhrHRf/tyy4vL0dBQcGvXm+qMRlYHAwGe/n5+YiLi3NcB2n8+PGYMGEC4uLiHNfB6datG5577jnk5eW5ddlsjt9isN+pGbi26281NkdpaSlOnz7t9Fjt9fJ6xeBgMLA48vLy0L17d5hMJiQlJWH+/PlYtGgRRo4ciYCAAMedMx9++GHs37/f0I7fYkhNTXX8vd96/a3G4jh//jx27dqFS5cuue2/2RgNLA4GQ2NND9+acFOmTEFYWJjj5gn2jWR9G8tPP/0UAQEBiIuLc7uDYQjIYGByLFu2zOmOkcHBwUhKSsLmzZtdTPYhz5tvvomhQ4ciMzPTMAYWB4MBAP7yl7/AbDbjq6++AuB6F0WLxYLs7GysXr0aISEhUEph27Ztbls+i4HFwWAAgOXLlzutn6rWnSPr3tyi9vrZr18/HDhwwDAGFgeDwd6SJUsQEBCA1atXOx4rKSlBbm4udu/ejaeffhoxMTEwmUwYMGAAvvnmGwDuHxAzOBgMLI558+ZBKYXbb78d77//vstNsywWi8ugLz8/H2fPnjWcg8HA4nj66acRGBiId9991/FYVVUVqqurkZOTg7feegsDBw6EyWRCTEwMkpOTAbj/PcLgYDAwORYsWOC4y+zSpUuRnp5+xdfal52VlYVDhw657SZbDAYWB4OhsaaHb024lStXQimFDRs2OB6r+8Fae+M5depUBAcHIyMjw60OhiEgg4HJMXLkSLRs2RLvvvsukpKSHEfDlVKIiorCggULXO6G98ADD0AphfLycsMYWBwMBgCYMWMGbrzxRuTm5gK4+s7Vl19+ibCwMNx8881uPTLGYGBxMBgAYOzYsbjhhhvwj3/8A0uWLEFMTIzTnSN/97vfOQaE9ty9fjIYWBwMBnsxMTEYOXKk48zMuuvopUuX8MMPPzi++EdHR+Ps2bNuNbA4GAwsju7du7sMiO+//35s3rzZ6XV228WLFzFp0iQMHz7crWdnMjgYDCyO2NhY3HPPPY71rb7PtKKiIrz22mswm81o2bIlfvzxR7csm83BYGBy9OzZEyaTCWaz2bF+Dh48GG+99RbOnDnj8vry8nJMnDgRcXFxbhv2MBhYHAyGxpoevjXhdu/eDX9/f0RHR7vc7rf2zwvs/7ts2TL4+fm5fMn/X2MYAjIYWByFhYXo168fIiIiHI9VVlZi3bp1GDp0qNOOWd++ffHqq6/is88+Q1hYGBISEgxjYHEwGOy99957UErhjTfecLrF+pWGPk888QT8/f3dejYNg4HFwWAoKipCfHw82rRp43isqqoKW7duxSOPPIKwsDDH+hkSEoLFixfj448/duv6yWBgcTAY7BUUFKBr164YNmzYr77WYrHg1VdfhVIKixYtMpyDwcDiOHHiBEJCQnDnnXdi9+7deOyxx9C2bVvHehkYGIgZM2Y4bacOHjyIwMBA3HnnnYZyMBhYHMXFxejTp881HVC2WCz49NNPoZTC9OnT3bJ8JgeDgclx8uRJhIeHIy4uDocOHcLSpUtxxx13wMfHB0optGzZEomJidi4cSPOnTsHAEhLS4PZbMbgwYMNY2BxMBgac3r41kSzfzl755134OXlBaUUpk2bhh07duDixYsur//ll18wceJEBAUFud3CMARkMLA4cnJycPvtt2PEiBEAXK8d9vPPP2PlypVOR0ntG9y6R0gbs4HFwWCwd+TIEURERMBsNmPTpk1Oz9lsNsfPHu3r58svvwwfHx/s3bvXUAYWB4OhoKAA99xzD4YNGwaLxeJyRLOoqAhr167FqFGj4Ofn5zQsdtf6yWBgcTAYgP9+Xo0bNw6tWrVyXAuo9npZX927d8eQIUNQVlZmGAeDgcnx5ZdfQimF+fPnOx67cOEC1q9fj/HjxzuuI6WUQqdOnfDiiy9i0aJFUEo5ftJmFAeDgcFh/07y6KOPQimFTZs2OQ4kXe2suoEDB6Jv376OL/hGcDAYmBwAkJKSApPJhMcff9zxWFlZGbZv3465c+eiR48ejvUzIiICc+bMwfTp0936PmEwsDgYDI05PXxr4pWXl+Nvf/sbQkNDoZRCaGgoRo8ejWXLlmHHjh04f/48UlNTMX36dDRv3tzpg9kdMQwBGQxMjurqaqSkpGDv3r1OF/GvfVF/e5mZmZg5cyaUUjCbzYYysDgYDPZlAsDWrVtx0003QanLN4D47LPPcP78eZfXl5eXIzEx0SPv1YY0sDgYDPaOHz+O9PR0l/Wz7hl4OTk5eP755+Hr64vAwEDDGVgcDAZ7b7/9NpS6fB2puteEsVqtTq7S0lLcd999uOWWWwzpYDAwOPbu3YvIyEi8/fbbAFyvbXv69Gm89tprGDRokNNw2N3rKIODwcDk2LJlC5RS6NKlC7Zv3+70nP3mD/Z188KFCxgzZgy6dOniVgOLg8HA4jh06BA6d+6MV1991bHc2uXn5+OTTz5BUlISOnTo4JH1k8HA4mAwNOb08K2JVncnvLy8HKtXr8aAAQPg7e3teKOYTCY0b94cSilMnTq13t9xu6OGHgKyGJgcV7qrmf2ol31jm5aWBl9fX0ybNs2QBhYHgwG4vFP++eefOx3Zio2NxcyZM/HFF1/g2LFj+Oc//4kJEybAy8sLixcvNqSBxcFguFr2wY99/dy3b59H109WA4ujIQwvvvgiTCYTlFJISkrC9u3bUVlZ6WQCgB07diAiIgKPPvqoYR0MhoZ2VFdX4+jRo45r29qXV9/Zd1lZWZg8eTKUUpg5c6bbDCwOBgOTAwDWrVuH1q1bQ6nL15Bav36907Uo7evm5s2bER4e7rH3CIODwcDiuHjxosuBxfr2i/Py8jBr1iwopTBjxgzDGVgcDIbGmh6+6ZwqKirCnj17sGrVKowZMwYJCQmYP3++011u3BnDEJDBwOSw72z92k9R7Nk3qt99952hDCwOBsOV2rhxI0aMGOGyfiql0Lx5c8ydO9dpZ96oBhYHg+HXsp+ZeT3WT2YDi8OTBvtnWklJCVatWuU4oOTt7Y3+/ftj3rx52LRpE3bv3o1Vq1ahQ4cOCA4OxuHDhw3nYDAwOX7NWPuz7rnnnmuQ9wmDg8FwvR2XLl3CunXr0Lt3b8fnWOvWrZGYmIh33nkHa9euxZ/+9CcEBQUhPDz8qndZbOwOBgOT40rVXT+XLFnS4O/VhjCwOBgMzCkAEF2TqrCwUI4cOSJZWVlSXl4u/fr1k+joaAkODhYvLy+n11ZVVUmLFi0cfwYgSimPG4uLiyUrK0v2798vX3/9tVitVunSpYt07dpVHnnkEY8vn8XA5KivixcvyvTp02Xnzp1SUFDQZA0sjuthACA2m81pW1FQUCA7d+6UPXv2SLNmzSQ8PFyio6MlISHBsAYWB4PhWquoqJCZM2fKli1bpLCwsMkaWByeNtTdX7h06ZJ8+OGHsnbtWtm3b5/L62NiYuSJJ56QSZMmGc7BYGBx2Gw2MZlMYrVaXfY56zqzsrIkISFBampq5MSJE24zsDgYDEyOusvbtGmTvP322/Lll19KTU2N0/MDBgyQp59+Wu69916PGVgcDAYmx9XKzs6WMWPGSFlZmZw8ebLJGlgcDAa29PCtibV161b585//7LKTZTabZejQoTJhwgRJSEiQZs2aOZ6zfyi7O4YhIIOhMTiCgoLE29tbRMRl56yqqkoKCwslMjLSMAYWB4NB5LdtA+p63LV+MhhYHAyG3+qo3cWLF6VVq1aGMbA4GAzXWk5OjuzYsUPS09OlTZs2EhoaKrfddptERUU1OQeDgclRu8zMTBkzZowkJCTISy+91KQdDIbr4cDlX2U5bctKS0tl165dkp2dLeHh4eLv7y99+/aV0NBQty+fycFgYHJcSydPnpTp06fLnXfeKU899VSTNbA4GAxs6eFbEyo3N1cGDRokFRUV8tBDD8ngwYMlOztbDh48KD/88IMcPnxYqqqqJCYmRp588kkZN26cNG/e3CNnuzEMARkMjcVx1113ORz2oY8nYjCwOBgM9XWldc9qtYrJZBKllNTU1HjUxWBgcTAYruaoXU1NjSilrnhmhREMLI6GNmzbtk3S09Pl0KFD0rp1a+nTp49ERUVJZGSkBAUFOX2eeTIGB4OBxVHbEBoaKn379pWoqChp166dBAUFiZeXV737nO7ehjE4GAwsjiudcWe1WkUp5ZETAFgdDIbG4PDU32M1sDgYDI0+D/2cVUfYU089hcDAQHzxxRcuz+Xm5mL9+vWYNGmS4/f8y5cv94gjJycHHTt2ROvWrbFo0SJs27YNa9aswaOPPop+/frBx8cHSil069YN69atQ1VVFQDXa6I1dkNjdNxyyy1OjivdBKCxGlgcDAYAKCgowLx587Bt2zaUlJQ4PWez2dy+HrIaWBwMBhYHg4HFwWCwV1JSgj/96U+O64jZ9yeUUggKCsKoUaPw97//HefOnXNxGs3BYGBxXKuh7vp7Ldc5bWwOBgOLo+4+i81mq3c/pvbj9ptMuTMGB4OhMTrqZt8fNoqBxcFgMEp6+NaE6t+/PwYNGoSioiIAcLpDYu1SUlLQq1cvtGjRAu+9957bHQxDQAaDdvAZWBwMBuC/F0nt0KEDRowYgRUrViAtLQ2XLl1yep3VanVsS3bu3ImtW7caysDiYDCwOBgMLA4Gg72XXnoJvr6+uP/++7Fz505kZmbi008/xXPPPYeRI0ciJCQESinceuut2Lhxo9uXz+RgMLA4GAwsDgYDi2PNmjVITExEcnIyysrKnJ6zWq1uP6DI7GAwaAefgcXBYDBKevjWRCorK8Ndd92F6OhoVFRUAHCeYtedYB84cACBgYEYNWqU43l3xTAEZDBoB5+BxcFgAICePXuiefPmiIuLc9xht3379pg0aRLeffddHDt2zOn1FRUVGDVqFEwmEyorKw1jYHEwGFgcDAYWB4PBXrt27TBixAgUFxe7PJeXl4fk5GRMmzbNcabNO++849blMzkYDCwOBgOLg8HA4mjfvj2UUvDx8UH//v3xzDPPYN++fS7fOexnVVVUVOCvf/0rUlJSDOdgMGgHn4HFwWAwSnr41oRatGgRlFL1fkmv/eaxD+FGjx6NLl264NSpU24zMAwBGQzawWdgcTAYgMs/fW3fvj169+6N6upq7Nu3D8888wxiY2OhlIKXlxd69OiBWbNm4bPPPkNpaSnS0tLQpk0bJCQkGMbA4mAwsDgYDCwOBoO9Y8eOwd/fH08++aTjsfqOiFdVVWHz5s3o2LEjzGYz9u7dazgHg4HFwWBgcTAYWBzp6elQSqFPnz4YNmyY40x+f39/DB8+HK+88orLgYOvv/4aSikMHDjQUA4Gg3bwGVgcDAYjpYdvTagzZ86ge/fuUEph9uzZ+P77712Oetsn1qWlpRg/fjzatm3rdgfDEJDBoB18BhYHgyE1NRVmsxlJSUkALl/nxWq14uzZs9i6dSv++Mc/ol27dlBKwdfXF3fccQeGDh0KpRQ2bdpkGAOLg8HA4mAwsDgYDPZ+/PFH3HTTTZgwYQKAy/sTdQ8c1N5+/etf//LIz+YZHAwGFgeDgcXBYGBxfPLJJ1BK4eWXXwYAZGZmYvny5ejZs6fjy31YWBgmTpyItWvX4vz581i1ahWUUkhOTjaUg8GgHXwGFgeDwUjp4VsTa+PGjejQoYNjgr106VLs3LkTp06dchrEffzxxwgJCcH06dPdbmAYAjIYtIPPwOJgMBw/fhwPPPAA1q1bV+/z1dXVOHXqFD766CMkJibCbDZDKYXAwEBDGVgcDAYWB4OBxcFgqF3//v3RsmVLbNmyxeU5+5d5+5f8c+fOoUOHDhg3bpwhHQwGFgeDgcXBYGBwvPXWW1BK1bv8tLQ0zJ07F5GRkY4v9126dEGbNm0QEBDgNgOLg8GgHXwGFgeDwUjp4VsTqO7P0M6dO4cFCxagbdu2UEohNDQUQ4YMweTJkzFt2jQ8+OCDaNGiBaKjo5GRkeERE8MQkMGgHXwGFgeD4cKFC/VeD6Z29p3zN998E0opzJgxw3AGFgeDgcXBYGBxMBjs+xmpqamIiIiAUgpz5sxBamqqy4ED+40g9u7di/DwcDz++OOGcjAYWBwMBhYHg4HFYbPZsG/fPsydOxc//fSTi81eZWUlkpOTkZSUhICAACilMGvWLLcYWBwMBu3gM7A4GAxGSw/fmkj2N0lubq5jJ/zIkSN44YUXMHz4cMcgTikFs9mMIUOGID093SMGew0xBGQwaAefgcXBYKjPAfz352xXauHChVBK4fvvvzeMgcXBYGBxMBhYHAyG+pb/wQcfICwsDEopdOvWDXPnzsWGDRtw9OhRh+3MmTOYOHEivL29PWJhcDAYWBwMBhYHg4HFUVZWhqqqqnqfq7t9mzlzJpRSOHjwoFsNLA4Gg3bwGVgcDAajpIdvBs9isWDXrl2YMmUK4uLiMGDAAAwdOhSLFy/GgQMHAFx+05w+fRoZGRnYsmULsrOzHT9pc+ddTmv/9xiGgA1p0A4+A4uDwVDbkZ+f7/JlvqamxmnbkJubix49eiA4ONhwBhYHg4HFwWBgcTAY6quwsBBLlixBdHQ0TCYT/P39cfPNN6N3794YNmwYIiMj4ePjg8cee8zwDgYDi4PBwOJgMDA56su+/frpp5/Qu3dvREVFXXcDi4PBoB18BhYHg6GxpABAdIZt5cqVsnTpUikrK5OoqCjx8vKSzMxMx/MxMTEyY8YMGTdunISGhnrMUVNTI3v27JH3339fsrKyRCklvr6+0rdvX0lMTJRevXoJAMnNzZXKykrJzs6W6OhoiYyMFG9vbwEgSqlGb9AOPgOLg8FQn8NkMskNN9wgsbGxMnbsWImPj3f5O8XFxfLRRx9JeHi4TJgwwRAGFgeDgcXBYGBxMBjqC4DYbDbx8vKSyspKOX78uHz77beyZ88eSU1NlYyMDAkJCZHIyEj5wx/+IJMnTxY/Pz9DOhgMLA4GA4uDwcDkuJaSk5Nl1KhRsnDhQlm+fHmDGFgcDAbt4DOwOBgM9F2/OZ/uepednQ0/Pz/cfvvtyM7OxpkzZ2CxWJCbm4s1a9Zg8ODBjjNohgwZgm+//dZjlhUrVqBVq1ZQSqFz586Ijo52LNt+uvsbb7yBs2fPGtqgHXwGFgeD4VocXbt2xcsvv4z8/Hynv1dVVXXVn7s1NgOLg8HA4mAwsDgYDNea1WpFRUUFLBYLiouLPXKmbmNxMBhYHAwGFgeDoSEc1/rrmoKCAnzwwQc4d+6cYR0MBu3gM7A4GAxGSQ/fDNwzzzyD0NBQ7Nixw/FY3TfP4cOHMWXKFPj4+ODmm2/Gd99953YHwxCQwaAdfAYWB4PhtzqGDh3qkevQMBhYHAwGFgeDgcXBYLD3yy+/ICMjA7/88ovLc1ar1Wmfo+7+hzuHgAwOBgOLg8HA4mAwsDiuZvi1ampq3GJgcTAYtIPPwOJgMBg1PXwzcA888AA6duyI06dPA4DTddzqvjFWr14NpRQeeughtzsYhoAMBu3gM7A4GAz/q8Nd14dkMLA4GAwsDgYDi4PBYO+FF15Anz59sGzZMqSkpCAvL89l/8Jmszktt7Cw0LE/YiQHg4HFwWBgcTAYWBzXYqhbQ/1/4WkHg0E7+AwsDgaDUdPDNwO3dOlSKKVw9OjRK76m9ofs2LFj0bZtW5w4ccKtDoYhIINBO/gMLA4GA4uDwcDiYDCwOBgMLA4Gg72IiAgopeDt7Y2goCAkJCTgtddeQ1paGoqLi11eX15ejgULFmDq1KluPauHwcFgYHEwGFgcDAYWx/9icOfZNAwOBoN28BlYHAwGo6aHbwbum2++gVIKPXv2xFdffVXvLYJr76w/+eST8PX1xQ8//OBWB8MQkMGgHXwGFgeDgcXBYGBxMBhYHAwGFgeDAQAyMzPh7++P+Ph4vP766xg9ejRCQ0OhlEK7du2QlJSEjz76COnp6SgpKQEA7N+/HwEBARg9erShHAwGFgeDgcXBYGBxMBhYHAwG7eAzsDgYDEZOD98MXE1NDebPn++4+PLrr7+OgoKCel97/vx5TJkyBSEhIW53MAwBGQzawWdgcTAYWBwMBhYHg4HFwWBgcTAYAGDTpk3w9vbGs88+CwA4deoUtm/fjmeffRZ33HEH/P394e3tjR49emDOnDnYtm0bFi5cCKUUkpOTDeVgMLA4GAwsDgYDi4PBwOJgMGgHn4HFwWAwcnr41gR688030alTJyilEBERgVmzZmHz5s04fPgwjh49iry8PCxevBg+Pj6YN2+e25fPMARkMGgHn4HFwWBgcTAYWBwMBhYHg4HFwWAAgA0bNkAphfXr1zs9Xl1djePHj+Pzzz/H//3f/yE2NhbNmzeHn58ffH19ERgYaDgHg4HFwWBgcTAYWBwMBhYHg0E7+AwsDgaDkdPDtyaQzWZDVlYWFi5ciMjISCh1+S5orVu3xk033QQvLy8opfD73/8eubm5HnM09BCQxaAdfAYWB4OBxcFgYHEwGFgcDAYWR0MbbDYbfvzxR2RnZzv+XLfy8nIcOHAAn3zyCe6++24opTB79mzDORgMLA4GA4uDwcDiYDCwOBgM2sFnYHEwGIycHr41scrLy5GSkoI5c+YgMTERgwYNwqhRo/Dxxx+jsrLSo8tmGAIyGLSDz8DiYDCwOBgMLA4GA4uDwcDiYDBczVa32bNnQymFAwcONCkHg4HFwWBgcTAYWBwMBhYHg0E7+AwsDgZDY08BgOiaZBaLRZo1a9Ygy66oqJC0tDT597//LT///LMUFhZKq1atJDExUcaOHSs+Pj5NwqAdfAYWB4OBxcFgYHEwGFgcDAYWB4Ohvmw2m5hMJjl16pSMHj1aSkpKJCcnp0k6GAwsDgYDi4PBwOJgMLA4GAzawWdgcTAYGmveDQ3QNVwNNXgTEfHz85PBgwfL4MGDG2wIyGDQDj4Di4PBwOJgMLA4GAwsDgYDi4PBUF8mk0lERPLy8sRisciMGTOarIPBwOJgMLA4GAwsDgYDi4PBoB18BhYHg6Gxps980+l0Op1Op9N5LABy5swZMZvN4ufn16QdDAYWB4OBxcFgYHEwGFgcDAbt4DOwOBgMjS09fNPpdDqdTqfT6XQ6nU6n0+k8lKmhATqdTqfT6XQ6nU6n0+l0Op1R08M3nU6n0+l0Op1Op9PpdDqdzkPp4ZtOp9PpdDqdTqfT6XQ6nU7nofTwTafT6XQ6nU6n0+l0Op1Op/NQevim0+l0Op1Op9PpdDqdTqfTeSg9fNPpdDqdTqfT6XQ6nU6n0+k8lB6+6XQ6nU6n0+l0Op1Op9PpdB5KD990Op1Op9PpdDqdTqfT6XQ6D6WHbzqdTqfT6XQ6nU6n0+l0Op2H+n/EM54vLeGDYgAAAABJRU5ErkJggg==", - "text/plain": [ - "
" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "plot_distribution(samp_dist.binary_probabilities(), figsize=(15, 5))" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "b2dd6e37", - "metadata": {}, - "source": [ - "The most probable bit-strings, up to finite-sampling deviations, encode the solution. Here we see that `00001` and `11110` are found, and are indeed correct. There are two solutions because the labeling of the two partitions with `'0'` or `'1'` is arbitrary." - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Reverse 11110 to convert quantum result to classical solution\n", - "solution = [0, 1, 1, 1, 1]\n", - "\n", - "mpl_draw(\n", - " G,\n", - " pos=rx.bipartite_layout(G, {0}),\n", - " with_labels=True,\n", - " node_color=[\"#EE5396\" if kk else \"#0F62FE\" for kk in solution],\n", - " font_color=\"#F4F4F4\",\n", - ")" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "071d7e49", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.14.1'" - ] - }, - "execution_count": 20, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit_ibm_runtime\n", - "\n", - "qiskit_ibm_runtime.version.get_version_info()" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "f3f06a12", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.45.0'" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit\n", - "\n", - "qiskit.version.get_version_info()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/docs/tutorials/quantum_approximate_optimization_algorithm/qaoa_with_primitives.ipynb b/docs/tutorials/quantum_approximate_optimization_algorithm/qaoa_with_primitives.ipynb new file mode 100644 index 000000000..c421cf399 --- /dev/null +++ b/docs/tutorials/quantum_approximate_optimization_algorithm/qaoa_with_primitives.ipynb @@ -0,0 +1,617 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "f028436d", + "metadata": {}, + "source": [ + "## Background\n", + "\n", + "The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid iterative method for solving combinatorial optimization problems. In this tutorial, we demonstrate how to implement the QAOA algorithm using Qiskit Runtime for solving a simple max-cut problem.\n", + "\n", + "In a max-cut problem, we want to partition nodes of a graph in a way that maximizes the number of edges between nodes in differing groups. The desired max-cut partition for the following graph is clear: the 0th-node on the left should be separated from the rest of the nodes on the right by a cut. We will find this answer by applying QAOA by using Qiskit Runtime primitives and sessions." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "e291b6c0", + "metadata": {}, + "source": [ + "## Setup" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "4a7d432c", + "metadata": {}, + "outputs": [], + "source": [ + "# General imports\n", + "import numpy as np\n", + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "# Pre-defined ansatz circuit, operator class and visualization tools\n", + "from qiskit.circuit.library import QAOAAnsatz\n", + "from qiskit.quantum_info import SparsePauliOp\n", + "from qiskit.visualization import plot_distribution\n", + "\n", + "# Qiskit Runtime\n", + "from qiskit_ibm_runtime import QiskitRuntimeService\n", + "from qiskit_ibm_runtime import Estimator, Sampler, Session, Options\n", + "\n", + "# SciPy minimizer routine\n", + "from scipy.optimize import minimize\n", + "\n", + "# rustworkx graph library\n", + "import rustworkx as rx\n", + "from rustworkx.visualization import mpl_draw" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ibm_osaka'" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", + "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", + "backend = service.least_busy(operational=True, simulator=False)\n", + "backend.name" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 1: Map classical inputs to a quantum problem\n", + "\n", + "To demonstrate max-cut, we'll create a graph using the [rustworkx library](https://github.com/Qiskit/rustworkx), and create Pauli Hamiltonian that encodes the cost in a manner such that the minimum expectation value of the operator corresponds to the maximum number of edges between the nodes in two different groups." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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JG4CBSNzkUVppe1i1DRPRvPzSaL5zUzQvv7TSYzLCoARgAN7FTd5kNSTpzbu8AejLu7jJk3GnbQbjQglATxI3eeIimW8GJQDnkbjJC0OyGCRvAM4icZMH0naxuFACEBESN/ngIllMBiUAEjeZMySLTfIGqDiJmyxJ2+XgQglQURI3WXKRLBeDEqCCJG6yYkiWk+QNUDESN1mQtsvNhRKgIiRusuAiWQ0GJUAFSNyMmyFZLZI3QMlJ3IyTtF1NLpQAJSVxM04uktVmUAKU0OuJe9++fbF3716Jm5ExJImQvAFKZ3ni/vKXv+wqyUhI2yznQglQEhI34+AiSS8GJUAJSNyMmiFJP5I3QMFJ3IyStM0gXCgBCkriZpRcJBmGQQlQQBI3o2JIshaSN0DBSNyMgrRNEi6UAAUhcTMKLpKkwaAEKACJm7QZkqRJ8gbIOYmbNEnbjIILJUBOSdykyUWSUTIoAXJI4iYthiTjIHkD5IzETRqkbcbJhRIgJyRu0uAiSRYMSoAckLhJypAkS5I3QMYkbpKQtskDF0qAjEjcJOEiSZ4YlAAZkLhZK0OSPJK8AcZM4mYtpG3yzIUSYEwkbtbCRZIiMCgBxkDiZliGJEUieQOMmMTNMKRtisiFEmBEJG6G4SJJkRmUACMgcTMoQ5IykLwBUiZxMwhpmzJxoQRIicTNIFwkKSODEiAFEjerMSQpM8kbICGJm36kbarAhRJgjSRu+nGRpEoMSoA1kLhZiSFJFUneAEOSuOlF2qbKXCgBBiRx04uLJBiUAAORuDmXIQk/JHkDrELiZjlpG87nQgmwAomb5VwkYWUGJUAPEjevMyRhdZI3wDkkbiKkbRiGCyXAGRI3ES6SsBYGJUBI3BiSkITkDVSexF1t0jYk50IJVJbEXW0ukpAegxKoJIm7ugxJSJ/kDVSOxF1N0jaMjgslUBkSdzW5SMLoGZRAJUjc1WNIwvhI3kDpSdzVIm3D+LlQAqUlcVeLiyRkx6AESknirg5DErIneQOlI3FXg7QN+eFCCZSGxF0NLpKQPwYlUAoSd/kZkpBfkjdQeBJ3uUnbkH8ulEBhSdzl5iIJxWFQAoUkcZeXIQnFI3kDhSNxl5O0DcXlQgkUhsRdTi6SUHwGJVAIEnf5GJJQHpI3kHsSd7lI21A+LpRAbknc5eIiCeVlUAK5JHGXhyEJ5Sd5A7kjcZeDtA3V4UIJ5IbEXQ4uklA9BiWQCxJ38RmSUF2SN5A5ibvYpG3AhRLIjMRdbC6SwOsMSiATEndxGZLAuSRvYOwk7mKStoGVuFACYyNxF5OLJLAagxIYC4m7eAxJYFCSNzByEnexSNvAsFwogZGRuIvFRRJYK4MSGAmJuzgMSSApyRtIncRdDNI2kBYXSiA1EncxuEgCaTMogVRI3PlnSAKjInkDib2euCMiDh8+HLt37874FbGctA2MmgslsGa9ErcxmR8uksC4GJTAmvRK3Js3b876ZRGGJDB+kjcwNIk7n6RtICsulMDAJO58cpEEsmZQAgORuPPHkATyQvIGViVx54u0DeSNCyWwIok7X1wkgbwyKIGeJO78MCSBvJO8gfNI3PkgbQNF4UIJvEHizgcXSaBoDEogIiTuPDAkgaKSvAGJO2PSNlB0LpRQYRJ3tlwkobi684vRevaFaH3zZLSefSG684tZv6RMuVBCRc3OzsaHP/zheOihh2Lv3r3x8Y9/PBqNRtYvqxJcJKGY2sdPxcKhmVh84lh0Ts6d93h903RMXLctJm/dHo3LLsngFWan1u12u1m/CGC8lifugwcPukqOiSEJxdQ+ORen9x+J1tETEfVaRKfPdDrzePPqrTF1165obJoe3wvNkOQNFSJxZ0PahuJaODwTcx+7P1pPPbf0hX5jctnjraeei7m774+FwzMjfoX54EIJFSFxj5+LJBTb/Bcej1fvezTx86zfszM23H59Cq8ov/wMJVSAd3GPlyEJxbdweCaVMRkR8ep9j0b9oqmYvPmKVJ4vjwxKKLF2ux333HNP7Nu3L3bv3h2f//zn/W7JETIkoRzaJ+fi9IFHej5Wu/zNUb/h7VG7YnPULn1TxA9ei84zfxPt//lkxMlXVnzO0wf+LJo7tpT2Zyr9DCWUlF9UPj5+RhLK5fT+IxHtTs/HGj+zI+o/8aPRffp70b73sWg//M2ov3NTTHzyg1HbctHKT9rqLD1vSblQQglJ3OPhIgnl0z5+aund3Cs9/icz0f2Pf3vW4Oz8xXdj4p6fjfoHd0R7f+/LZnS60Tp6ItonXozG1ovTftmZc6GEEvEu7vFwkYTyWjg0s/Srf1bQ/fbfnH+9PPlKdJ9/KWo/srH/k9drsfDA0ym8yvwxKKEkJO7RMySh/BafOLb6rwbqoTa9PuKVhf5/qNONxSePrfGV5ZvkDSUgcY+WtA3V0J1/recn4Kym/tOXR+2SN0X7D/7fqn+2MzsX3fnFqG2YWMtLzC0XSigwiXu0XCShWtqzw4/J+PvT0fjIP4jOt74fnUeeGfD7vDz898k5gxIKSuIenXOH5Pve9z5DEqpgsT3cn9+4PiZ+9eaI+cVo/YcjEYN+Vsyw36cAJG8oIIl7NKRtqLiJIT49bMNENP/VLRFT62Lxt/8k4qX50XyfgnChhAKRuEdD2gaOHz8e/+PIF6MbA1wZJ+rRvHt31DZfGK1/9+WI54dL2I3Nq7wbvIBcKKEgfBZ3+lwkobqOHz8eR44ciYcffjgefvjheOaZpZ9//MsPfSq2rOsz+Gq1aP6LXVF7+1ui9TsPRfeZF4b6vvXN06V7Q06EQQmFIHGny5CE6llpQF511VXxgQ98IG666aZ43/veF1N/+I1YeOCpFX91UGPP9VG/7rLoPHk8ahesi9pPX37W450/f3blF1GvxcS121L7z5QnBiXkmM/iTpchCdUx6IC89NJLz/p77Vu3x8IX/3LF56396CUREVG/9rKoX3vZeY+/1m9QdroxeduVa/hPk38GJeSUxJ0eQxLKb60D8lyNyy6J5tVbo/XUcz2vlK1PH1rbC6zXorljSyk/djEiotbtDvoed2BclifugwcPStxrZEhCefUbkDfddNPAA7KX9sm5mLv7/ojXUvz1PusaMf2ZO6KxaTq958wRgxJyROJOhyEJ5TPKAdnLwuGZOP2fjqTyXBERU//8ppi8+YrUni9vJG/ICYk7OUMSyiOthL1Wk7dsj87L8/HqfY8mfq71e3aWekxGuFBCLkjcyRiSUHzjvkAOauHwTJw+8EhEu7PiO797qtcimvWYuvPG0o/JCIMSMiVxJ2NIQnHldUD20j45F6f3H4nW0RNLQ7HfsDzzePPqrTF1167S/szkuQxKyIjEvXaGJBRPkQbkStrHT8XCoZlYfPJYdGbnznu8vnk6Jq7dFpO3XVnad3OvxKCEDEjca2NIQnGUYUD2051fjPbsyxGL7YiJRjQ2byzlJ+AMyqCEMZK418aQhPwr+4CkP4MSxkTiHp4hCfllQLKcXxsEY+CzuIdjSEL+ZP1rfMg3F0oYIYl7OIYk5IcLJMMwKGFEJO7BGZKQPQOSJCRvGAGJezCGJGRHwiZNLpSQIol7MIYkjJ8LJKNkUEJKJO7VGZIwPgYk4yR5Qwok7v4MSRg9CZssuVBCAhJ3f4YkjI4LJHliUMIaSdwrMyQhfQYkeSZ5wxpI3L0ZkpAeCZsicaGEIUjcvRmSkJwLJEVmUMKAJO7zGZKwdgYkZSJ5wwAk7rMZkjA8CZsyc6GEPiTusxmSMDgXSKrEoIQVSNw/ZEjC6gxIqkzyhh4k7iWGJKxMwoYfcqGEZSTuJYYknM8FElZmUMIZErchCcsZkDA4yRtC4jYkQcKGJFwoqbSqJ25DkipzgYT0GJRUVpUTtyFJFRmQMDqSN5VU1cRtSFIlEjaMjwsllVLVxG1IUgUukJAdg5LKqGLiNiQpMwMS8kPyphKqlrgNScpIwob8cqGk1KqWuA1JysQFEorDoKS0qpS4DUnKwICE4pK8KaWqJG5DkiKTsKE8XCgplaokbkOSInKBhPIyKCmNKiRuQ5IiMSChOiRvSqHsiduQpAgkbKguF0oKreyJ25Akz1wggdcZlBRWmRO3IUkeGZDASiRvCqmsiduQJE8kbGBQLpQUSlkTtyFJHrhAAmtlUFIYZUzchiRZMiCBtEjeFELZErchSRYkbGBUXCjJtbIlbkOScXKBBMbFoCS3ypS4DUnGwYAEsiJ5k0tlSdyGJKMkYQN54UJJrpQlcRuSjIILJJBXBiW5UYbEbUiSJgMSKArJm1woeuI2JEmDhA0UlQslmSp64jYkScIFEigLg5LMFDlxG5KshQEJlJXkTSaKmrgNSYYhYQNV4ULJWBU1cRuSDMIFEqgqg5KxKWLiNiTpx4AEWCJ5MxZFS9yGJL1I2AC9uVAyUkVL3IYky7lAAgzGoGRkipS4DUkiDEiAtZK8GYmiJG5DstokbIB0uFCSqqIkbkOymlwgAUbDoCQ1RUjchmS1GJAA4yF5k4q8J25DshokbIBsuFCSSN4TtyFZbi6QAPlgULJmeU7chmQ5GZAA+SR5syZ5TdyGZLlI2ADF4ELJUPKauA3JcnCBBCgmg5KB5TFxG5LFZkAClIPkzUDylrgNyWKSsAHKyYWSvvKWuA3JYnGBBKgGg5IV5SlxG5LFYEACVJPkTU95SdyGZL5J2ABEuFByjrwkbkMyn1wgAejFoOQNeUjchmS+GJAADELyJiKyT9yGZD5I2ACshQtlxWWduA3JbLlAApAGg7LCskzchmQ2DEgARkHyrqisErchOV4SNgDj4EJZMVklbkNyPFwgAciCQVkhWSRuQ3K0DEgA8kDyrohxJ25DcjQkbADyyIWy5MaduA3JdLlAAlAEBmWJjTNxG5LpMCABKCLJu6TGlbgNyWQkbADKwIWyZMaVuA3JtXGBBKCMDMoSGUfiNiSHY0ACUAWSd0mMOnEbkoORsAGoIhfKght14jYk+3OBBACDstBGmbgNyd4MSAA4n+RdUKNK3Ibk2SRsAFidC2XBjCpxG5JLXCABYHgGZYGMInFXfUgakACQnORdEGkn7qoOSQkbANLnQplzaSfuqg1JF0gAGD2DMsfSTNxVGZIGJACMn+SdU2kl7rIPSQkbALLnQpkzaSXusg5JF0gAyB+DMkfSSNxlG5IGJADkn+SdE0kTd1mGpIQNAMXjQpmxpIm76EPSBRIAis+gzFCSxF3UIWlAAkD5SN4ZWWviLtqQlLABoPxcKMdsrYm7KEPSBRIAqsegHKO1JO68D0kDEgCQvMdk2MSd1yEpYQMA53KhHLFhE3fehqQLJACwGoNyhIZJ3HkZkgYkADAsyXtEBk3cWQ9JCRsASMqFMmWDJu6shqQLJACQNoMyRYMk7nEPSQMSABg1yTslqyXucQ1JCRsAGLfKXyi784vRnn05YrEdMdGIxuaNUdswMfDfXy1xj3pIukACwPgl3Q9lU8lB2T5+KhYOzcTiE8eic3LuvMfrm6Zj4rptMXnr9mhcdsmKz9MvcY9qSBqQAJCNtPZDGVVqULZPzsXp/UeidfRERL0W0enzH/3M482rt8bUXbuisWn6rIeXJ+6DBw++kbjTHpIGJABkK839UFaVGZQLh2fi9IFHItqd/v8QzlWvRTTrMfXRG2Lylu0rJu60hqQBCQD5kdZ+KLtKDMr5Lzwer973aOLnaX1we9zxuU+elbhbrVaiIWlAAkA+pbUf1u/ZGRtuvz6FV5RfpX+X98LhmVT+MURENP9oJt79wrr4+OHD8d73vjf2798/9JD0LmwAyL8098Or9z0a9YumYvLmK1J5vjwq9YWyfXIu5j52/9I7sM7VrEfj56+J+k+/LeJN66J7/MVof+Fr0X36eys+Xze6Ec1G/J/3tOMTnx1sSLpAAkCx9N0PERGTzWh84Mqove3Spf+5YDJa//kr0XnkmZWfdF0jpj9zR2l/prLUF8rT+48s/cxDD41/9t6o/8S26Bz6enRPzkX9hrdH81dvjtanD0X3W9/v+XdqUYvW4mJc+L++Gbt27eo5JF0gAaDY+u2HiIi4cDIaP/fj0X3hB9E9/mLUrjj/E/HO0+rE6f1H4sLf+lB6LzRHSjso28dPLb0bq4fa294cjZ+8PFr3fzU6X5yJiIjOV56Jid/+2Wj8k+uidc+frPi8zVoj3r/pivhHn74jGlsvNiABoET67Yc3vDQfr/3L/x7x8qtRe+ubo77vZ1Z/4k43WkdPRPvEi9HYenE6LzZHSjsoFw7NrPjW/vpPbItuuxOdh771wy8udqL9p9+O5j++LuKSqYhTp1d87k4t4o9//d/H3Y9+zoAEgBLptx/e0OpEvPzq8E9er8XCA0/H1J03rP0F5lRpB+XiE8dW/MdQ23ZJxOxcxKuLZ329+50Xlh7/0Uui22dQ1rsRb/3BOgMSAEqm335IrNONxSePRYRBWQjd+dd6/gb7N1y0IbovzZ//9858rXbRhljtn9LWdRfF7/zrX6v0xywBQJmsuh9S0Jmdi+78Yun2QykHZXu2/z+G2rpmdFs93rn1+ru51g32X8v//a/3xysXlfK/QgConAtfasV7x/B92rMvR/PycpXNcq6hld7mf0b3tVZEs3H+AxNnvvZaa6Bvs/fjvxWPv/jdIV8cAJBH11/81vjS7l8f/TdaZacUUTkH5USPsbjcS/NRu3jqvC/XLtoQEdEzh/fy0CN/GvVt1frwdwAoq86xU9H6rT8a/TdabacUUCkHZWPzxr6Pd//6zO+MWj9x1htzam+79Mzjpwb6Phdcvrl0PwMBAFXVvXxdvDSG77PaTimietYvYBRqGyai3uc30XceOxa1Rj3q7/+xH36xWY/Gje+Izrf/pu+vDHpdffO0MQkAJbLafkhDWfdDKS+UERET122LhQee6vnW/+53Xoj2o9+Nxi9cF7UL10f3+69E/Ya3R1x6QbT/y5+v/uT1Wkxcu20ErxoAyFK//bBc/ZZ3RUyti9pFSz9CV79m69LvsY6Izpe+ETG/2OMvlXc/lHZQTt66PRa++JcrPt7+vUcifv7aqL/3bRFTk9E98WK0PvNgdP+q98cunqXTjcnbrkzx1QIAebDafnhd4x9eGbW3XPDG/15/z7aov2dpLL7259/pPShLvB9KOygbl10Szau3Ruup53r/fxmLnWj//uPR/v3Hh3viei2aO7aU8mOTAKDqVt0PZyz+2h8M98Ql3w+l/BnK103dtSuimfJ/xGZ96XkBgFKyH4ZX6kHZ2DQdUx9N9+ONpu68MRoj/oFdACA79sPwSj0oIyImb9ke6/fsTOW51u/ZGZM3X5HKcwEA+WU/DKfW7XZH9Ano+bJweCZOH3gkot0Z7kPf67WlM/WdN5b+HwMAcDb7YTCVGZQREe2Tc3F6/5FoHT2x9H/ofv8wzjzevHprTN21q9RnagBgZfbD6io1KF/XPn4qFg7NxOKTx6IzO3fe4/XN0zFx7baYvO3K0r4bCwAYjv2wskoOyuW684vRnn156YPaJxrR2LyxlL/BHgBIj/1wtsoPSgAAkin9u7wBABgtgxIAgEQMSgAAEjEoAQBIxKAEACARgxIAgEQMSgAAEjEoAQBIxKAEACARgxIAgEQMSgAAEjEoAQBIxKAEACARgxIAgEQMSgAAEjEoAQBIxKAEACARgxIAgEQMSgAAEjEoAQBIxKAEACARgxIAgEQMSgAAEjEoAQBIxKAEACARgxIAgEQMSgAAEjEoAQBIxKAEACARgxIAgEQMSgAAEjEoAQBIxKAEACARgxIAgEQMSgAAEjEoAQBIxKAEACCR/w/bFE6ItSFS8AAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "num_nodes = 5\n", + "# The edge syntax is (start, end, weight)\n", + "edges = [(0, 1, 1), (0, 2, 1), (0, 3, 1), (0, 4, 1)]\n", + "\n", + "G = rx.PyGraph()\n", + "G.add_nodes_from(range(num_nodes))\n", + "G.add_edges_from(edges)\n", + "mpl_draw(\n", + " G, pos=rx.bipartite_layout(G, {0}), with_labels=True, node_color=\"#EE5396\", font_color=\"#F4F4F4\"\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "987e72fd", + "metadata": {}, + "source": [ + "For this simple example, the operator is a linear combination of terms with `Z` operators on nodes connected by an edge (recall that the 0th qubit is farthest right): $IIIZZ + IIZIZ + IZIIZ + ZIIIZ$. Once the operator is constructed, the ansatz for the QAOA algorithm can easily be built by using the [`QAOAAnsatz`](https://docs.quantum-computing.ibm.com/api/qiskit/qiskit.circuit.library.QAOAAnsatz#qaoaansatz) circuit from the Qiskit circuit library." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "b6dabf56", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Problem to Hamiltonian operator\n", + "hamiltonian = SparsePauliOp.from_list([(\"IIIZZ\", 1), (\"IIZIZ\", 1), (\"IZIIZ\", 1), (\"ZIIIZ\", 1)])\n", + "# QAOA ansatz circuit\n", + "ansatz = QAOAAnsatz(hamiltonian, reps=2)\n", + "\n", + "ansatz.decompose(reps=3).draw(output=\"mpl\", style=\"iqp\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "da92068c", + "metadata": {}, + "source": [ + "The previous image illustrates the ansatz in basic gates for clarity. However, it can be expressed in multiple levels of decomposition by changing the `reps` argument or by drawing the circuit without the `decompose` method. For example, the following representation directly shows the QAOA structure with the default `reps` value, which is `reps=1`. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "8fbe14ff", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ansatz.decompose().draw(output=\"mpl\", style=\"iqp\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Optimize problem for quantum execution.\n", + "\n", + "We can schedule a series of [qiskit.transpiler](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler) passes to optimize our circuit for a selected backend. This includes a few components:\n", + "\n", + "- [`optimization_level`](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler_preset#preset-pass-manager-generation): The lowest optimization level does the bare minimum needed to get the circuit running on the device; it maps the circuit qubits to the device qubits and adds swap gates to allow all 2-qubit operations. The highest optimization level is much smarter and uses lots of tricks to reduce the overall gate count. Since multi-qubit gates have high error rates and qubits decohere over time, the shorter circuits should give better results.\n", + "- [Dynamical Decoupling](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_provider.transpiler.passes.scheduling.PadDynamicalDecoupling): We can apply a sequence of gates to idling qubits. This cancels out some unwanted interactions with the environment." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.transpiler import PassManager\n", + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "from qiskit_ibm_runtime.transpiler.passes.scheduling import (\n", + " ALAPScheduleAnalysis,\n", + " PadDynamicalDecoupling,\n", + ")\n", + "from qiskit.circuit.library import XGate\n", + "\n", + "target = backend.target\n", + "pm = generate_preset_pass_manager(target=target, optimization_level=3)\n", + "pm.scheduling = PassManager(\n", + " [\n", + " ALAPScheduleAnalysis(durations=target.durations()),\n", + " PadDynamicalDecoupling(\n", + " durations=target.durations(),\n", + " dd_sequences=[XGate(), XGate()],\n", + " pulse_alignment=target.pulse_alignment,\n", + " ),\n", + " ]\n", + ")\n", + "\n", + "ansatz_ibm = pm.run(ansatz)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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9CyMjI7i4uKBLly7IzMzEtWvXEBUVhS+//BLHjx9Ht27d1B80ERFRE6zaEYUTF9M02sfqL6MwIMAJQ/vp51KKj5Rl3AEASCz0795+tZHLFZj63lkkpas/efdIRYUCUxadRfRPY9DG0Vxj/WhDcxwD+sDt8Z5IPn5Z6DBIB3AOCofzUHdwHhARERGpn1joAKh+9vb2GD58OJYuXYpffvkFs2bNalC9F154AadOnUJBQQHu3buH8PBwJCYmIioqCp07d0ZWVhaee+45DUdPRESkmqsx2Vj9VaRKdcJDRyH5xESEh45Sqd5Ly87hQUG5SnWEJC8rhuxhNqQPslCScB1Jn7+GkrtXYeYVCJM23kKHpzbbf7yl8tWXjRkDDwrKMXPleSgUClVDFExLGQP6wKqdEwoSMoQOg7SMc1C3cB4Kg/OAiIiISDt4BZ4eWLx4cZXHf/31V4PqTZ06tcbt/v7++Oqrr9C7d2/ExMQgJiYGPj4+TY6TiIioqRQKBV5efh4ymWoJFSd7M7g24iqqlPtFWPLpFWx+p6/KdYWQHroU6aFLq2yz7jsG7jM/FSgi9cvMKcFbGy6pXK+xY+Don8k4cCIB455oq3JdIbSEMaAPJGYmkBaWCh0GCYBzUHdwHgqH84CIiIhIO/QmgZednY2PPvoIP/30E1JSUuDg4IAxY8Zg9erVmDt3Lnbu3IktW7Zg9uzZQocKoPIDSJFIJHQYtfp3wq64uFjASIiIiP5xITITV25ma7XPnQfjsHJ2AKwsjLTab2PYD50Bm8eehaJCipLE68j4aS3Ks1MgMjRRlimIDkP8imHV6ipk5VDIKxDwc4U2Q1bZzoOxKCqRabXPzXui9SaB1xLGgD5wGdgFqWejhA6DBMA5qDs4D4XDeUBERESkHXqxhGZkZCT8/f3x8ccfIyMjA76+vpBKpfjkk08wYcIExMTEAIBG7+UWHBwMkUiEhISEesteu3YN3bt3R3x8vMbiaarz588DAMzNzdGxY0eBoyEiIqr06Q83td5nYbEU3x7R3ffsfzN29oJVtyFoFTAMTmMWosN7v6A4PhxJn72iLGPpF4Tuewur/Phti4XE0h4uz60UMPr6VVTI8fmPt7Te77mr93EtNlfr/TZGcx8D+qJ1r07ICr9dZVuPd5/D9PT96DBxUI11njywHM8nhMK6o5s2QiQN4RzUHZyHwuE8ICIiItIOnU/gZWdn46mnnkJGRgYWLFiA9PR0REREICMjA2vXrsXRo0cRHh4OkUiELl26CB0uAODrr79GVFQUQkJCcPfuXaHDUZLL5UhPT8fu3bsxffp0AMDq1athYWEhbGBEREQAiktk2H8iQZC+dx/WjwTef1n4PAbb4OeRd24vCmMu1FhGLi3D3Q/HwMK3P5yfXaTlCFUTFnEfiWmFgvS9+3CcIP02VXMbA3pBJAJEgEIur7I5ct0+5MUkInDZNJg521bZ5ztjJJwe80Pkur3Iv52szWhJwzgHBcJ5qFM4D4iIiIg0Q+cTeHPnzkVKSgpmz56NdevWwdLSUrlv4cKF6Nq1K2QyGTw9PWFlZSVgpP9Yv349nn/+eaSkpCAkJKRBV+1p0ueffw6RSAQDAwO4uLhg2rRpcHV1xS+//IK5c+cKGhsREdEjUbE5kMrk9RfUgMjbOSiX6udSTs4T3gfEBkj7fkmN+5O2vQK5tBSe83ZpN7BGuHQ9S7C+w6O1u3SrOjWnMaAPHLp3QPbV6kl/uVSGsHlbITEzRr8Ns5Tbrdq7oMc7k5B1JRY3th3WZqikJZyD2sd5qHs4D4iIiIjUT6cTeDExMdi7dy/s7e2xZs2aGssEBAQAALp27VprO8OGDYNIJMKyZcuaHFNKSgoSEhLq/ElKSsKyZcswaNAgJCUlISQkBElJSU3uu7GcnZ3Rr18/9O7dGy4uLhCJRLh27Rq+//57PHjwQLC4iIiI/u2ygAmUcqkcN+LyBOu/KUycO8A2aCIKrp1CQXRYlX2Zv3yCB5ePoP27ByE2NhMowoa7rOX7H/7b1Vs5kMsVgvXfFM1pDOgaxz4+EBlU/ZOpTUh3pJ6JrLF87vV7uLblZ7QJ7gbvKUMgEosR9MkcAEDYvK3Vrhai5oFzULM4D/UD5wERERGR+ul0Ai80NBRyuRyTJ0+udZlHU1NTALUn8Pbt24fIyEi1xRQUFIS2bdvW+9O+fXucPn0aAJCQkIApU6aoLQZVPf300zh37hz++usvpKamIioqCn369EFoaChGjBghWFxERET/Fn0nX+D+9TOBBwBOz74HiMVVvvVecO0MUna/jXYLf4Sxo6dwwalAyNegoEiK5Axhlu9Uh+YyBnSJ56jHMOTbRXDs7VNlu6GVGaQFxbXWi9q4H7k37qHnkqnoveoFOPTwQsTaUDy8k6bpkElAnIOawXmoXzgPiIiIiNRLInQAdXmUAAsJCam1TEpKCoCaE3gPHz7E/PnzsW7dOrUl0Pz9/WFkZNSgsjk5OcrlM318fOourEX+/v44evQo2rVrh/Pnz+PkyZMYMmRIo9vz8vKCWKzTuWCiZi/d+g1A3ArpGelwdXUVOhwSQHMYA7nmYwDjmr+QEx46Ck72tX9j28neVPlv8omJdfaTkV2MXpOqL581Z/5CvPtquAoRN4zIyBSOm5p2fzVL/2AEHKr96jBTNx8E/PzPEqBl9xNw9+PxcJ3+MSz9g5vU9395e3tBUV6i1jYfyWg1HzCwqXGfNsZAYN8BMKzQ/DKejRkTQo4BTb7mQjBUiLEUgfWWSzh8AVZtneA2tBcyLkQDAMzb2KMope4xopBVIGzeVow89iE6TX8S9/+Owc0dR5sUs7eXN6QiXjX0iDqOq6rSpeOwqnRxDuvbPGxuc7Cxc4jvRURERESqc3JywuXLlxtVV6cTeImJiQAADw+PGvfLZDKcP38eQM0JvPfeew/e3t6YPHmy2hJ4hw8fhqenZ73lUlJSMHDgQADAhAkTsG3bNrX0ry6WlpYYOHAgDhw4gKioqCYl8NLT09UYGRE1imUFIAbkFRVITU0VOhoSQnMYA65FgHHNu5zszeDqaF5vExIDcYPK1eRBfi4e5Kr/dyc2NoOj2lutnbysGHfWPINWgaPQesRstbeflpYGeVntVz00iYUMMKh5lzbGQOb9+0CZ5s9rND0m1D0GNPqaC8BIZICGvgCJxy5h8K63Eb50FwDA7fGeSD5e/x9e0ofFkJfLYGBkiJRTEYCiacuzpqWnoVyhn/fp1ARtH1dVpenjsKp0cQ7r2zxsbnNQG3OI70VERERETafTCbyioiIAQElJzd+y2rt3L7Kzs2FpaYm2bdtW2Xf58mV88cUXuHLlisbj/K/U1FSEhITg7t27GDduHL777jsYGNTyaZSAZDIZAKCioml/iDg7O/MKPCKBpRsYQA5AbGAA5zZthA6HBNAcxkC+qSGKatmXkV33BzZO9qaQGIghq5AjI7vub2fX1pZNK3OYmar/dycyMlV7m3XJu3AAJfeiUJoai7xze6vt99t6E0YO7o1u38XFRWPfgL8vlkNWyz5tjAHH1jaQyDV/TqPpMaHuMaDJ11wIhgox0MALaR7EpgAKwNrbFfmxKbBs64SCXffrrddv02sQG0qQH5uMLvPHIuHwBRQk1l+vNi7OLs3q6p+m0vZxVVWaPg6rShfnsL7Nw+Y2B7Uxh/heRERERFTJycmp0XV1OoHn5OSEvLw8REREoG/fvlX2paen46233gIAdOnSBSKRSLmvoqICM2fOxOzZs+Hn56fVmAFg+fLliI+Px+jRoxEaGgqJRPd+zbm5uTh79iwAoFu3bk1qKy4uDubmjfumOxGph+uQUKRmFsPZyRkpN1KEDocE0BzGwNbQm5iz5mKN+2pa7vDfkk9MhKujOTKyS+D2+A+N6v/U0d3o7mPfqLp1KZEBQb+qvdla2YU8D7uQ5zXWfmxsHEw1dGoz4a3T2Pf7vRr3aXoMWJobIi3yBsRiUf2Fm0jTY0LdY0CTr7kQpMWl2NO+4atzJJ+4DLehvVCYkg1pYf0fHvu8OBzO/TrjyprvkfzbJTx1/GP02zgLv41Z2uiYY+NiYWhm0uj6zY22j6uq0vRxWFW6OIf1bR42tzmojTnE9yIiIiKiptPpy6YeLeu4du1axMbGKreHh4cjJCQE2dnZAKonoLZu3Yr79+9j2bJlaotl4MCBGDt2bIMSVZs3b8by5cuxd+9ewZJ3ly9fxpIlSxAfH19t39WrVzFs2DDk5+fD398fgwcPFiBCIiKiqgJ87QTr28hQDL8ONd97jbQnQAMJ1Ibq4WOnleQd6Z/k45fh9kRPuAR3Rdqf1+osa9nWCT0WPYesq3G4sfUg8mNTELl+H5z6+sHnxeFaipio+eE8JCIiIqKWSKcTeAsXLoSdnR2Sk5Ph5+cHf39/eHl5ITAwEO3atcOgQYMAVL3/XXZ2Nt5//30sWbIEMpkM+fn5yM/PBwCUlpYiPz8fcrnqS18sX74c+/fvh4ODQ71lTU1NsWTJEhgaGqrcT03Onz8Pe3t75c+GDRsAAD/88EOV7Y/uBwgAhYWFWLlyJby8vODo6IiePXuid+/eaNOmDXr06IFLly7B29sbBw8e1MnlPYmIqOXp6m0HI0NhTk26d7KDkSHfD4XWu0v951maEthZuL5Jt93/OwZW7ZzhMSwQWeG3ay8oEqH/ptkQi8U4N28rFP/7m+PGp4eQHRmPHoueg6WHLt+5jUh3cR4SERERUUuk0wk8V1dXhIWFYcSIETAxMUFCQgJsbW2xfft2HD16VHlV3r8TeCkpKSgoKMDMmTNhY2Oj/AEqr+SzsbFBUlKSIM+nsaRSKXJycpQ/j+4JWFZWVmW7VCpV1unatSs2b96MZ555BlZWVoiNjcXVq1dRUVGBIUOG4NNPP0VUVBTatWsn1NMiIiKqwsxUgmefaFt/QQ2YNspLkH6pqv7dHeHpYiFI38+P7CBIv6T7FBVypP4RVfn/Or4I6PfKU3AM7ISrH+/Fg7jUf+rL5Tg3byvEBgbot3GWxuMlao44D4mIiIioJdL5FcR9fHxw5MiRatsLCwuRkJAAsViMzp07K7d36NABZ86cqVY+JCQE06ZNw/Tp05t000AhBAcHQ6FQqFTHxsYGc+fOxdy5czUUFRERkfrNmuCDPUfvaLVPS3NDTBnZXqt9Us0MDMR4ZXwnvLPpslb7DerhCH9vW632Sfol6dgloI7z8VZebdBj4URkXr6N6M9/qbb/0RJ+AYsmw+fF4Yj5Sodv4EakozgPiYiIiKil0fkEXm2io6OhUCjg7e0NMzMz5XYLCwsEBwfXWMfT07PWfURERCS8vl1bI7CzAy7dyNJany+O9oaluZHW+qO6vTi6I1Z9EYWCImn9hdVk/pTO9ReiFi3xyMU69z+IS8W3bZ+rs8z1LT/j+paf1RkWUYvCeUhERERELY1OL6FZl+vXrwOounwmERER6TeRSIQdS/tBIhFppT93Z3Msn9VDK339m7y8FPGrn8GNV71xc15XxC55HKXp8TWWzQ8/ghuzOuHGK164s2YMKoofAoDy6vyEzdOrPK7LladFiJ7rjweXK686KIoLx62FjyHiWTPEr36mStncsL2Ifs0Xkc9ZN+5JNpK9jQnWLQjUWn+jgt0xerCH1vrTtLzz+5H42asqjTEifafKeC9Ni8OthY/hxqveiFnQCyVJ0QD+OYamhS5D2f2EKsfUB5d/RfRrvrg5vxtuLeyL0tRY5b7/HleTdszF9Zc9ceVpEYrvRlbp+/Z7IYicbIv7hzep8dkTad71lz1x49WOuDm/G27O74bcsL0Nqsf3JCIiIqKmaTEJPIVCgWXLlmkwIiIiIlKHrh3t8P6M7irVycguRsr9ImRkF6tU76vlQbCyEObqO4cnZsBv2234bo6Cde+nkbj1pWplKkoKkbjlRXRYdBCdP4+Doa0L0veuBACk712BzKOfQlEhQ+7Z75G8Y06D+u24Ogyteg4HABjaOMPtpU1we3FjtXK2QRPQYYkwy4u9PLYjHu/rolKdxowBGysjfP5+P4hE2kkYa0P+Xz/DuvczABo2xoiai4aO96RtM2E/dAY6fxYLpzFvK78EkX/hAFK+eRsVRfkoiruEhI3PQ/Ywp7LO9tfg9vJm+G6KhGXXIcg69lmVNv99XLXpNw4d15yDUevqXwzouOoMrANHNej53H4vGGX3Exr47Ik0r91be+G7KRK+myJhGzShQXX4nkRERETUNC0mgUdERET6490Xu2JYf9cGl+816TDcHv8BvSYdbnCdpa90x5A+bRoTXpOJjUzQqudwZeLI3LsPyjMTqpV7GHEMZu26w8S1EwDAYdgs5IaFAgBcJi6FSCxG7tk9KE64BveZW5H56zbcfL0HpHkZyjbubXwemUe21BiHkb0rzL0DITI0VvMzbBqRSIRdKwfA08WiwXVUHQMSiQh71gTD2cGs/sI6RFaYj2svuCJyih1uzu+G6Nd8EDHWGAlbXoJCJkXhrfOw6jKowWOMqDlo6HiX5meiKP4y7IKnAACsHxuL8uxklKbHw6bfONg8Ng7ZJ3ci69hn8Jj9JSRWdgCA8qxEmHXoiYrSIhTfuQJjp3a1xmLpNwBG9g1//2qKuo4HRNrA9yQiIiIizdLbBN7p06ehUCgwYsQIoUMhIiIiNTM0FGP/+sEY0ke1q7Aa6q3p/lj6qmpX+WlS5pHNsA58utr28qykKldxGDt6QpqXDkWFDOl7V0Ihr4DtwMkw9fBH8hfz0Hr4LNj0HYP7hyuvqJPm38eDK8dgN2ia1p6Luri0NsepL4fBQ4UkXkMZSsT4YW0IhgW5qb1tTZNYWMN2wHNwfGo+fDdFwvXFTTDv2Aeec75EwfUzMO/0GEQSw2r1ahtjRM1RrcfU7GQY2jhDZFB5K3iRSAQjB3eUZyUh7+JPyLuwH/aD/w8Ow15F4qczlFfgQaFAYcx5XJvmiOI7EbDqPlSbT6dWdR0PiNQtYdNURM/1R8KWFyF9UHmvYr4nEREREWmW3ibwiIiIqHkzM5XgyNYn8OJob7W1aWQoxsa3emPt6710ZtnE9B9Xoyw9Hm2mrlGpntP4xWg9YjZEBhLYBU+G60ubAAB2g19A7p+hUFRUIOu3z2EbNBEGZlYaiFzz2rla4dyukXisW2u1telkb4pftz2BsY+3VVub2lZ8LxKm7SoT0MV3rsDsf//P//sgbPqMrla+sWOMSB81drxb9xkN12lrYWBhA3OvQHjO/0Z5BR4AWPj0R7fQh3B/ZRtuvxsEWWG+miMH7m2cqrzHWHH8ZcSvGK58XNtymrUdD4jUqePqP+H7yTX4boiAxMoeCZv/+WIQ35OIiIiINIcJPCIiItJZxkYG+HJ5EI5++gTatG7aUoeBnR1wdd8zmP98Z51J3mX8vA75F39ChyXHIDau/vyMHNxRnpmofFx2P0F59cij5+A5bxcAKB8b2bnA1NUHDy4fRfbvO9B6xGzNPxENcnUyx59fj8D6NwNhYmzQpLamjGyP6J/HCrZ0qrqU3ItUfkD66MNShUKBB1d/h1WPYVXK1jfGiJqTeo+p9m7Kq5iByvukl2clwcjBXXkMdZm0DMaOnjW+T4jEYtj0HQOJpS3K0mLVHn/b13cr7zFm1qEnOiz5VfnY2NGzxjo1HQ+I1M3IwR0AIJIYwvGp+SiMDlPu43sSERERkeYwgUdEREQ6b3iQG6J/Hov1bwaig7tqV5P17+6IPWuCcX73SPi2t9FQhKq7f2gD8sJC4bXiBCQW1jWWser+JIrvRqA05RYAIOvYNtgGTay3bduQqUj8bCZMXH2U98/TZwYGYrwx1R8xB8fizWn+sG3V8Hv2SSQiPPtEW5zdORzfrg5Wqa4uKs9JBSCCkV1lErIk4RpMPfxRHHsJpq4+MDD9Z8nRhowxouaiIePd0Lo1zNr3QM4f3wEA8i8cgJGdK0ycO9Tb/oPLRwFULm0szcuAcQPqaFptxwMidaooLapyxWluWKgyYcf3JCIiIiLNkggdABEREVFDtLI0whtT/TF/SmecvpSGM5fSceVmNiJicpCVVwoAEIkAD2cLBPjaI8DXHsODXNG1o109LWtfeXYKUnYugJFTO8QuDgEAiCTG8Fn3N9L2LIGhrQschr0CAzNLeLz2JeJXPwNUyGDi0Rlt531Tb/s2fUcj6bOZcBg+q85ypSm3EbtkMORlxZCXl+DaC65wGrcIreupJxTPNpb4eEEgVrzWA4fOJOJiVCauxOQg6nYuCoulACrvb9fRs9X/xoAdxg7xhEtrc4EjV5/iu1erXGFjYG6NzF+3QWJlD+vezyi31zXGiJqb+sZ7wpaXYB04Cta9R8Hj1e1I+GQ6MvavhoGpFTznft2gPrKObkH6vpUQiQ3gNmMLJJa2NZZL3DYTDy4fhTQvA3HLhsLA1BKdt8er54n+R23HA94Dj9RJln8fdz4cC8groIACxo7t4Dl/NwC+JxERERFpGhN4REREpFfEYhGG9GlTZRlEhUIBmUwBiUSkM8tj1sXI3hUBhxQ17nOZvKLKY+velR86q0JsbAaJlT2MHdvVWc7EtSO67ExRqW1dYGoiwcRh7TFxWHvlNrlcAblcAYmkeS8wYd1rJKx7jVQ+9lkfDgCInu0Hxw/OKLfXNcaImpv6xvu/E1omrh3R6aOLKvfRYelvDbpqyGPWdpXbrknHVX/UW6a24wGROhk7tYPvpqs17uN7EhEREZFmNe9POIiIiKhFEIlEMDQU60XyTkgSa0fEvjcQDy7/Wm/Z3LC9iF/1FCStHLUQWdOJxaJmn7yri9/WaBhatxY6DKIWR5Xj6u33QlBw4yzEJs3nqmCimvA9iYiIiEg9eAUeERERUTPk/0VCtW1dv8locH3boAmwDZqgxoiIiPRTXVcOqXJc7bjqTP2FiIiIiIiI/qflfk2ZiIiIiIiIiIiIiIiISAcxgUdERERERERERERERESkQ5jAIyIiIiIiIiIiIiIiItIhvAceERERkQaZGABhw4WOQn1MDISOQP/p25hobq+5xNQYk+98J3QYKpGYGgsdgk7RtzkkNF2cw/o2D5vbHNTHOaSL45iIiIhI05jAIyIiItIgkQgw5RkX/QvHhLBEIhEMzUyEDoOagHNI/3EeCotziIiIiEg/cAlNIiIiIiIiIiIiIiIiIh3CBB4RERERERERERERERGRDmECj4iIiIiIiIiIiIiIiEiHMIFHREREREREREREREREpEOYwCMiIiIiIiIiIiIiIiLSIUzgEREREREREREREREREekQJvCIiIiIiIiIiIiIiIiIdAgTeEREREREREREREREREQ6hAk8IiIiIiIiIiIiIiIiIh3CBB4RERERERERERERERGRDmECj4iIiIiIiIiIiIiIiEiHMIFHREREREREREREREREpEOYwCMiIiIiIiIiIiIiIiLSIUzgEREREREREREREREREekQJvCIiIiIiIiIiIiIiIiIdAgTeEREREREREREREREREQ6hAk8IiIiIiIiIiIiIiIiIh0iEToAIiJq3hQKoLRC6CjUx8QAEImEjkL3KRQKyErKhA5D4ySmxhCpOCAUCgWKS2QaikgzzEwlKj3PlvL6Ay1jDKj6+usCjkGqiz6emzS38w99m6O6OM/0cRwLRRfnT0ufA/o4fnVxHBERUfPHBB4REWlUaQUQ9KvQUahP2HDAlO+e9ZKVlGFP+ylCh6Fxk+98B0MzE5XqFJfIYNFnt4Yi0ozCv6bC3MywweVbyusPtIwxoOrrrws4Bqku+nhu0tzOP/RtjuriPNPHcSwUXZw/LX0O6OP41cVxREREzR+X0CQiIiIiIiIiIiIiIiLSIUzgEREREREREREREREREekQJvCIiIiIiIiIiIiIiIiIdAgTeEREREREREREREREREQ6hAk8IiIiIiIiIiIiIiIiIh0iEToAIiJSnVQqR/SdPFy5mY3I27nIfVAGAMh7WIYPdlxFgI89Anzt0drOVOBISVMKi6WIvJWDKzezEX0nv8oY2PTtDQT42qO7jx0szAwFjpSIiIiIiIiIiIhUxQQeEZEeiU14gM/2xWDXoTjkF5RX219cWoH3t0YoH/fv7ohZE3ww9nFPGBkaaDNU0gCFQoGwKxnYti8GB04mQCZTVCtTXFqB1z/+GwAgkYgwZrAnZk3wwYAAJ4hEIm2HrFVOff3w5E/LcW7eVsTv+0PocEgAHAMkNI5BIiIiIiIiUhcm8IiI9EBGdjFmr76IAycTVKp37up9nLt6H07rTLHxrd6Y8GQ7vUziFFz/A7GLQ6psE5uYw9jFG3bBz6P1yDkQGTTvt7SIm9l4efk5RMTkNLiOTKbAvt/vYd/v99Ctky2+XBaEAF97DUZZt0cfbD8ir6iAtKAExRm5yLl2F/cOnkPqmUjB4iPN4xggoXEMUmPxXISI84CExzFIREQtDd/ViIh03PdH72DOhxeVSyQ2RkZ2CSa9/Qd+PJ6AbYsfg6OeLq1pM2ASWgUMBxQKSPMykPPHbqTsfAOlKTHweG2H0OFpRLm0Aiu3R2LNV1GoqKh+xV1DRd7KRe/Jh/HOC13w/szuMDYS7orMuz+FIeV0BCASwdDcFK06uMD9yUB0GB+MtLNR+GPGepQ/LBYsPtI8jgESGscgNVZLPBch+i/OAxIaxyAREbUUTOAREekohUKBdzdfxtqd19TW5k+nEnAlJhsntj8JL49WamtXW8za9YBd8BTlY4fhsxA9qxOyT3wJlymrYNjKQcDo1K+oWIrRr5/EiYtpammvokKBVV9E4a9rWTi4eYhg98fLuX4Pdw+EVdkWvvQbBLw/BZ1fGYUBn72Ok5NXCRIbaQfHAAmNY5Aaq6WdixDVhPOAhMYxSERELQUTeEREOuqdTeH46Ovram83Ma0QA1/4Fee/GYm2rpZqb1+bDEzMYd6xD/Iv7EdZxp1m9YdaaZkMT805gTPh6Wpv+9TfaRg5+ziObRsKUxPdOBVQyOW4vHw3HLp7wXVQd7QO7ITMS7cAAIaWZugydww8RvSGuYs9pIXFSPvzOiI+/B6FSZl1NywSocvc0XAJ7oZW7ZxhZG2Bkqx8pJyMwNW1oSjLKwQAmNhZ4dmI7Ug48hfCXttcrZneq19Cp2lP4EDv11CYkqX2508cAyQ8jkFqjOZ8LqIvpqfvV1tbu5zHqa2tloTzQFicAxyDRETUfOnGp3ZUr4SEBJw6dQrh4eEIDw/H9evXIZVKMW3aNOzatavWetOnT8c333xTZ9sxMTHo1KmTmiMmoqbY+XOsRpJ3j6RnFWP4a78jYu8zOpPAaayyjDsAAImFrcCRqNerH1zQSPLukbOXMzBjxTl8uzpYY300Rtz3p+DY2weuQ3og89ItGFqaYfgvq2DRxh5xP5xG/u1kmLa2QafpQzHy1zX45cm3UZSSXWt7BkYSdH71aSQc/QvJv4VDVlIGu67t4TVpEBwDO+GXoW9DLpWhNOchko9fhsewQPxtZVZl6TwDY0O0G90faWHX+aG5FnAMkNA4BklVzfVcRB+Yt7HHpaW7cHPHEaFDafE4D4TBOfAPjkEiImqO9PtT2xZk06ZN2Ly5+jdxG8rLywutW7eucZ+ZmVmj2yUi9UtKL8T8j/5SqU546Cg42ZshI7sYvSYdblCdW/ce4P2tV7Duzd6NCVMQ8rJiyB5mQ6FQQJaXgazfPkfJ3asw8wqESRtvocNTm1/+SMKuQ3Eq1WnMGPjuyB2Me7wtng7xaEyYGpEbkwgAsGrnAgDovnACLN1b4+jIRci7magsF7/vDJ4+vQHd35yAc/M/rbW9ijIp9nZ7GRWl5VW2Z12+jX4bZsH9yV5I+OUiACD2u5PwHNkXbUcH4fY3vyvLeozoA2NrC8TtOam250m14xggoXEMUl1ayrmIvnB7vCeSj18WOowWh/NAd7TUOcAxSERELQUTeHrC3t4ew4cPR69evdCzZ08cO3YM27Zta3D9RYsWYfr06ZoLkIjUQqFQ4OXl51BQJFWpnpO9GVwdzVXub8O3NzD2cU/07eqocl0hpIcuRXro0irbrPuOgfvM2j841Tf5D8swc+V5les1dgzMXHEeAwKcYGNlrHJdTZAWlAAAjCxMAQDtxgTh/t8xKM7IhbHtP0u+yorLkBURB5eBXett89GH5iKxGIYWJhBJDJB+7gYAwL6Hl/KD87SzUShIvA+v5wZV+eDca9IglOY+RNJv4ep5klQnjgESGscg1aUlnIvoE6t2Tri1K0PoMFoczgPd0VLnAMcgERG1FEzg6YnFixdXefzXX6pdnUNE+uHva1k4fiFVa/0pFMCqL6JwZOsTWuuzKeyHzoDNY89CUSFFSeJ1ZPy0FuXZKRAZmijLFESHIX7FsGp1FbJyKOQVCPi5Qpshq+yLA7eRnlVcf0E1uZ9Tgh37b+HtF+r/AFobDC0rPzAvLyyBiZ0VTGyt0Ca4GyZFf11jeXlF/a+n51N94ffKKNh29oSBkWGVfcatLKo8jv3+FALefQ62fp7IjU6AhXtrOD3mh5tf/gq5VNbIZ6UZq+YGYNFL3fDCkj/x9cHqV2ye+Wo4+nZtjYCJhxAdnydAhI3DMdBwzXUMCI1jkOrSEs5F9IXEzATSwlKhw2iROA90Q0ueAxyDRETUUuhVAi87OxsfffQRfvrpJ6SkpMDBwQFjxozB6tWrMXfuXOzcuRNbtmzB7NmzhQ4VQOWVNCKRSOgwiEiPbNsbo/U+fw1Lxr2UArR1tay/sMCMnb1g1W0IAKBVwDBY+PTH7Xf7I+mzV9DurR8AAJZ+Qei+t7BKvfKcNNxa0BMOI3Tj/aE2crkCn/94S+v9fr7vFt6c5g8DA7HW+/4vW5/K5Twf3kkD/vcemnY2Ctc/Pdio9tyH90bwjgXIiojDpfe/RlFaDirKyiEyEOOJ0PchEld9n44PPY3ub46H16RB+HvxTnhNGgSRWKyTy9Yt23YVTw10x4Y3e+P4xVSk3v8n8Tt/ih+CeznjnU3hepe44RhouOY6BoTGMUh1ae7nIvrEZWAXpJ6NEjqMFonzQDe05DnAMUhERC2F8J/UNVBkZCT8/f3x8ccfIyMjA76+vpBKpfjkk08wYcIExMRUfujdrVs3jcUQHBwMkUiEhISEesteu3YN3bt3R3x8vMbiUcX+/fvxzDPPYNCgQRg/fjw2bNiArKwsocMion/Je1iGfcfvab1fhQLYcUD7SSN1sPB5DLbBzyPv3F4UxlyosYxcWoa7H46BhW9/OD+7SMsRqubkX6m4m1Kg9X4T0gq1euVnXbyeGwwASDl5BaU5D1GWXwhDSzOkh12v9acu7ccNgKykDL+NW4rbu48j5eQVpIddR1FKze+BJVn5SD5xBe3GBEFiaowO40OQdSUW+bEpan+uTSWVyTFt8Z8wNzXEV8uClNu9PVth1Zye+OtaJj7eVffvRxdxDDRccx0DQuMYJFU0t3MRfdK6Vydkhd+usq3Hu89hevp+dJg4qMY6Tx5YjucTQmHd0U0bIbYYnAfC4Bz4B8cgERE1V3qRwMvOzsZTTz2FjIwMLFiwAOnp6YiIiEBGRgbWrl2Lo0ePIjw8HCKRCF26dBE6XADA119/jaioKISEhODu3btCh4OjR4/i0KFDOHPmDH788UcsWLAAbdu2xXfffSd0aET0PxejMlFWLswyHn+EpwvSrzo4T3gfEBsg7fslNe5P2vYK5NJSeM7bpd3AGuGMgK/DH5eFHQMisRg9l0yFY28fJJ+8gszw24BCgbs/hcGhhxc8RvSpsZ6JnVWd7Soq5JXti6qe8nSZP67WOrF7TsLYxhJ9P5oBcxc7xH5/SsVnoz1XY3Kw5qsoDO3nipfHdoRYLMLuVQMgEgHTFv8JuVwhdIgNxjHQOM1pDAiNY5Aaqzmdi+gNkQgQAQq5vMrmyHX7kBeTiMBl02DmbFtln++MkXB6zA+R6/Yi/3ayNqNtETgPtIxzoBqOQSIiao70YgnNuXPnIiUlBbNnz8a6deuq7Fu4cCG+//57REVFoW3btrCyqvsPaG1Zv349cnJy8O233yIkJARnz56Fp6en1uPw9vbGxo0bERISAk9PTxgaGuLKlSv44IMPcPz4cUydOhU2NjYYMWKE1mMjoqqu3MwWrO+o2FzIZHJIJHrxvY4qTJw7wDZoInLP7kFBdBgs/f65CiXzl0/w4PIRdFoXDrGxmYBRNoyQY+DKzRyt9WXn3xbtxla+TobmpmjVwQXuTwbCwq01Uv+IxJ+zNivLRnwYita9OiF4xxtIOHwRWRGxqCiXwcLVAa6DuyPn2l2cm1/7zeoTj/wFz5F9MXT/Utz58SzEhhK4P9kLElPjWuuknolEYXIm2o8bCGlhCe4dPK++J68BK3dcxahgd6xbEIhunezQ27813vj4b8QmPBA6tFpxDKiXPo4BoXEMkjo1p3MRfeHQvQOyr1Zf7UYulSFs3laMPLoG/TbMwolJHwAArNq7oMc7k5B1JRY3th3WdrgtAueBdnEOVMcxSEREzZHOJ/BiYmKwd+9e2NvbY82aNTWWCQgIQFRUFLp27arcFhYWhuXLlyM6Ohq5ublwcHBAv379sGzZMvj4+DQpppSUhi1fs2zZMqSmpuL06dPKJJ67u3uT+lbVokXVlwUICgrCb7/9htGjR+PQoUOYP38+hg8fzvv1EQksIkZ7CZT/KimtwK17+ejsZVt/YR3k9Ox7yA0LRdr3S9Bx1RkAQMG1M0jZ/Ta8lhyDsaOnsAE2kJBjQJvJw3ZjgtBuTBDkFRWQFZWiKD0XGRdv4t7bO5B6JrJKWWlBMX59+j34vTIKbZ/qC7ehPaGokKMoPQeZl24hdk/dV6XcO3QeEgtT+M0YgV5LpqLsQRGST1zGlVV78FzMrporKRSIDT2NHgsn4t7hC5AVl6rniWuITKbAtMV/Ijx0FGZN8EFYRAY2fXdD6LDqxDGgXvo4BoTGMUjq1lzORXSRYx8fZIbfVl7NCgBtQrojeseRGsvnXr+Ha1t+Rrc3noX3lCGI+/40gj6ZAwAIm7e12hVLpD6cB5rBOdBwHINERNTc6HwCLzQ0FHK5HJMnT4aFhUWNZUxNTQGgSgIvLy8P/v7+mDlzJlq3bo2UlBSsWbMGffv2xY0bN+Dq6tromIKCguov9B8JCQmYMmUK/vzzz0b3q04ikQhr167FoUOHEB8fj+vXrzd6+VEvLy+Ixfp31Q6RrsmyfAEw9KhxX3joKDjZ1/5NQSd7U+W/yScm1tlPRnYxek2q/q3LkMdHwViW0PCAG0hkZArHTXFNasPSPxgBh2pfBs7UzQcBP/+z/GjZ/QTc/Xg8XKd/DEv/4Cb1/V/e3l5QlJeotU0AUECEHNtlte5X1xio7fXPLyhHG1d3iKCeP+gNFWIsRWDVvi9GY5dz7UvG1aaipBzXNu7HtY376yxXW/txe04ibs/JatvrikVeJq2sW8+ydd5e3pCKVPudyWEI2C5WqU59HhSWo6y8AkaGBvg1LBkKNa+a6OXtDTGkDS5f0+sPcAwo29azMaDq668LOAapLo05NxH6XERT5x9CqW2O/pfnqMfQb/2rODXtQ2RciP6nvpUZpAXFtdaL2rgf7k/0RM8lU2Hr5wmHHl64tGwXHt5Ja1S8ujjP1HGOrSqh50Fj6eL8aelzoLHjV8gxqIvjiIiI9IOTkxMuX77cqLo6n8A7ffo0ACAkJKTWMo+uiPt3Am/UqFEYNWpUlXK9evVCx44dceDAAcybN6/RMfn7+8PIyKhBZXNycpCQkAAATb7yT906duwIW1tb5ObmIi4urtEJvPR0/b13FpFOaV8BGNa8y8neDK6O5vU2ITEQN6hcTbJz8oDC1EbVrYvY2AyOam+1dvKyYtxZ8wxaBY5C6xGz1d5+Wloa5GW1/7HcaCIDoI4LILUxBtLSMgCFej6kNxIZQKsvvBqJDMTwfv5x5N5MRNaV2DrLpqWnoVyh4r0rRUZ1vtaN8fWKIBgZGuDmnTwsntEN+36/h7spBWprPz0tDVCUN7i8Pr/+AMfAf6n6+usCjkGqi6bPTTRxLqKx8w+BNHSOJhy+AKu2TnAb2kuZvDBvY4+ilKw66ylkFZXLCB77EJ2mP4n7f8fg5o6jjY5XF+eZts+xVaXpc3JV6OL8aelzQBvjV91jUBfHERERNX86n8BLTEwEAHh41HxVikwmw/nzlfeE+HcCryZ2dnYAAImkaU/78OHDDbqfXUpKCgYOHAgAmDBhArZt29akfjXB0LAyWyCTyVSqZ2Zmhm7duuH+/fsQiURcfpNIDbIMxajt49GM7Lr/UHCyN4XEQAxZhRwZ2XV/K7C2tuztrGHcqk1DQlWJyMhU7W3WJe/CAZTci0Jpaizyzu2ttt9v600YOTR+OWMXFxcNXYEHpCnkgKjmK5rVNQbqasfFxREiqOeyHUOFGGq6mE9rLNxaw6GnN9yH9oKVpxPOvrKx3jouzi6NuvpKnV99mfOcL0ICXbDok8s4dCYREXufwc4VQQh+4Ve19eHs4qLyFXj69voDHAO1UfX11wUcg1QXTZ+baOJcRFPnH0JRZY4mHruEwbveRvjSXQAAt8d7Ivl4/d9glj4shrxcBgMjQ6ScikBTLk3WxXmm7XNsVWn6nFwVujh/Wvoc0Mb4VfcY1MVxRERE+sHJyanRdXU+gVdUVAQAKCmp+U1y7969yM7OhqWlJdq2bVttf0VFBeRyORITE/Huu+/CyckJ48eP12jMAJCamoqQkBDcvXsX48aNw3fffQcDAwON96uKrKwsZGZmAoDKS4qKRCJcvXpVE2ERtVjPL/oD3x25U+O+mpY8/LfkExPh6miOjOwSuD3+Q6P6Dz//GzzbWDaqbl1KZECQ+vII9bILeR52Ic9rrP3Y2DiYaujd0/PJvUhMK6xxn6bHgJuTOZKuJatcrzbS4lLsaT9Fbe1pg1NfX/TfPBulOQ8QuX4f7h06X2+d2LhYGJqZqNRPUbEUFn12NzbMKjq4W2HNvJ64dD0La3deg1yuwLLPIrBmXi/Mec4XW76/qZZ+4mJjYW5WyyXCNdDH1x/gGKiNqq+/LuAYpLpo+txEE+cimjz/EIIqc/RBbAqgAKy9XZEfmwLLtk4o2HW/3nr9Nr0GsaEE+bHJ6DJ/LBIOX0BBYv31aqKL80zb59iq0vQ5uSp0cf609DmgjfGr7jGoi+OIiIiaP52/cdmj7GRERES1fenp6XjrrbcAAF26dKnxKrCBAwfCyMgIXl5eiIyMxOnTp+Hg4KDZoAEsX74c8fHxGD16NEJDQ5t81Z8mrF+/HgqFAq1atUKvXr2EDoeoxQvwsResb9tWxvBwqfk+o6Q9Qo6BAF/h+tYV8fv+wC7ncfih84uIXLdP6HDqJRIBu1YOgIFYhGmLz0Iur/xW9UdfX0f4jSysmdcT7VzVn5RvzjgGSGj6NgaJtCX5xGW4De0FiZkJpIX1XwHj8+JwOPfrjMgNP+KPl9dDbGCAfhtnaSFSIs3gHCAiImqZdD6BN2TIEADA2rVrERv7z/0fwsPDERISguzsbABAt27daqz/1Vdf4a+//kJoaCisrKzwxBNPICkpqVGxDBw4EGPHjoW5ef33Ftq8eTOWL1+OvXv3Cpa8O3HiBN555x3cuVP1ip7i4mKsWLECH330EQDg3XffbfA9/YhIc4RMoAT42nEpXB0Q4GvXIvumxlkwzR/9ujtiybYI3Lr3QLldLldg+vt/QmIgxs4VQQJGSJrGMUBELUXy8ctwe6InXIK7Iu3Pa3WWtWzrhB6LnkPW1Tjc2HoQ+bEpiFy/D059/eDz4nAtRUykXpwDRERELZPOJ/AWLlwIOzs7JCcnw8/PD/7+/vDy8kJgYCDatWuHQYMGAaj9/ncdO3ZE7969MXHiRJw6dQoFBQXKxJWqli9fjv379zfoCj5TU1MsWbJEeY+5pjp//jzs7e2VPxs2bAAA/PDDD1W2P7ofIFC5/OjatWvRoUMHuLi4oFevXggICIC9vT2WLl0KhUKBGTNmYOHChWqJkYiaJtDfAQ42wizNM3KAdu4/QXV7aqBwrwPHgH7p1LYVVr7WAxejMrH+mxvV9t+8k49ln0VgYE9nzHnOV4AISdM4BoioJbn/dwys2jnDY1ggssJv115QJEL/TbMhFotxbt5WKOSV9+y68ekhZEfGo8ei52Dp4ailqInUh3OAiIioZdL5BJ6rqyvCwsIwYsQImJiYICEhAba2tti+fTuOHj2qvCqvtgTev1lbW6NDhw6Ij4/XdNhqJ5VKkZOTo/x5dE/AsrKyKtulUqmyTkBAABYvXozBgwfDyMgIN2/eRHR0NBwcHDBhwgScPHkS27dv51U3RDrC2MgAL47x1nq/ZiYSTBvlpfV+qTp/b1v06679P6j7dm2Nbp14BZ4+uXXvAUx7fYPHnv9FuWzif3341TWIunyltvvgkW7hGCCilkRRIUfqH1GV//9fQqImfq88BcfATrj68V48iEv9p75cjnPztnIZQdJbnANEREQtk+7dmK0GPj4+OHLkSLXthYWFSEhIgFgsRufOnettJzMzE7dv30bv3r01EaZGBQcHQ6Go+cOZ2ri5uWHlypUaioiINGHmuE5Yu/MaVJzuTTJ5RHu0suQyurpi1ngfnL/auJvLN9ar4ztptT8iIiIiVSUdu4S6TpJbebVBj4UTkXn5NqI//6Xa/kfLCAYsmgyfF4cj5qtfNRkukdpxDhAREbU8epHAq010dDQUCgW8vb1hZmZWZd+UKVPQoUMHdOvWDdbW1oiLi8PGjRshkUjw+uuvCxQxEVHdPNtYYt5kP2z6Llor/bWyNMLSV7prpa9/k5eX4u66iShNvgmxkSkkrVrD/dXPYOLcoVrZ/PAjSPn6TUBeAVMPf3jO2wUDMysoFAqIRCIkbJ4Oz3m7lI/rcuVpEUw8OsN16lq06jkcRXHhSP5iHorvRcKq+xPosOigsmxu2F6k/7Ac0rw0dPs+X82/gdqNH9oWm/dE49KNLK3016uzPSYNa6+VvoiIiIgaK/HIxTr3P4hLxbdtn6uzzPUtP+P6lp/VGZZOUOXcujQtDgmbpkFWkA0Ds1bwnLcLpu5+ynPptNBlsBs0HUatPZTn1g8u/4qUr9+EyNAIYiNTeM77BiZtKlcO+e/5ddKOuXgQfhjlmYnw2XgVZu26Kfu+/V4IShKi4DxhCRxHzdfGr6ZZ4RwgIiJqefQ6gXf9+nUANS+f2adPH+zevRubN29GaWkp3NzcEBISgkWLFsHDw0PboRIRNdiqOT1xNCwZcYkPNd7XpoW90cbRXOP91MThiRmwChgGkUiEzKNbkbj1JXRc9UeVMhUlhUjc8iI6rj4LE9dOSNo+G+l7V8L1/z5G+t4VkFjaQ1EhQ+7Z71F46wLcZ26tt9+Oq8MgsbAGABjaOMPtpU0ovnsVDyKOVSlnGzQB5t69EfN6NzU944aRSMTY9cEAdB9/EGXlFRrty8hQjK9XDIBEor0VtQNXvgD3oT1h4dYah4e8idzoBADA4z+8D1MHa0Auh7SoFH8v3oncG/cAAGIjCXotnYY2wd1QUVaO3JuJCJv9CQDAsq0TgjbPgbGtJaQFxTg3byvyY1MAANPT9yMvJhGXP/gOqaevVoul0/89Cfuu7XFu/qew9fNEqw5tcO/QP/eSHbp/GWx9PRC1cT9ufnFUs7+YFsTA2BADP38drbxcUVFajtLsB7j4zhcoSMjAiKNrYGBUeXoqkhjAppM7Dg1agLyYRPR49zl4DO+NijIp5LIKRHz4PdL+t5QURCL0Xvl/aDO4B6BQ4OYXR3Hr698AAP03vQbnAV2QcuIKLr69o1o8EjMTTLnzHXY5jwMAdFswHte3/oyKssplyX1njESn6UMhKyrF4cff0sJviDSNxyHSpLzz+/Hw2im4vbixwQkVInVoyLk1ACRtmwn7oTNgP3g68s7vR8Lm6fBZH478CwdQFB8OhbQMRXGXkLZnMdxe2gyJlR2Str8Gj9d2wKrb40jd8z6yjn0Gt5c2Ktv89/m1Tb9xcBqzELff7V+t746rziBh8/QGPZ/b7wXDc+4uGDt6NuK3Qc3N9Zc9IZIYQ2xsCgBwGvsubIMm1FuPx2QiItJ3zTaBN3v2bMyePVvbIRERNZmZqQTffDAAwS/8inJp7fc3+LeM7OIq/zbE6MEegt37TmxkglY9hysfm3v3wf2D66qVexhxDGbtusPEtXKJR4dhsxC37Am4/t/HcJm4FFnHPkPu2T0wtHOF+8ytyPx1G7JPfAmvJb/C0MYJAHBv4/Mw9wpE65FzqrVvZO8KI3tXlCTr1v2hfNpZ46PXe2He2r8aXKcxY2DNvJ7w62CjcnxNkXj0Im5sO4jhhz6osv3sjPUof1gZu/uwQPTf9BoOD3kTABDw3hRAocBP/SpfQ1MHa2W9xz6aidjvTiB+3x/wGNEH/TfPxpFh7yj3H3vmfWW7dbH184T7sMAqH5z/Pm4Z+m96rdHPlWp3+9sTymRGp/97Ev3Wv4rfxi7F0RHvKst4jOiDbgueRV5MIgDg/t8xiNq4HxWl5bDx9cCwn1dgX7cZkJWUof24AWjl7Yaf+82FoZUZRp34GBnnbyiTKNGfHW5w8qPbm+Nx84sjygTezR1HkHv9HgJXTFfjb4CExOMQaVL+Xz/DNmQqgIYnVIiaqqHn1tL8TBTFX4bX8uMAAOvHxiJpx2yUpsfDpt84GLX2QOz7g1F8LwpeS49BbGQCACjPSoRZh56oKC1C8Z0raNVjWK2xWPoNUPOzq52sMB8353aGvLwERvZuUEjLUJZxF7bBz8Nzzpdai4O0o91be6tc0dkQPCYTEZG+a7YJPCIifda3qyP2rRuEcQtOQSar/4Z4vSYdVqn94F7O2LMmuN4lJ7Ul88hmWAc+XW17eVYSjFr/c9W0saMnpHnpUFTIkLF/DQwsbGA7cDJMPfyR/MU8uL28GRWFubh/eCNcp62FNP8+Hlw5BveZn2rz6ajF3Ml+SM8uxodfXWtQeVXHwFvT/fH68/XfP1bd7v8VU+P2f3+4bWRppry/h8TUGF6TBuHHHjOV+0uy8gEAJnZWsOvaHscnVt7vNfHoX+iz+kVYejqhICGjWh8ScxP0W/8qbP08UZr7EPm3k5XtdFs4AUaWlYmfrIi4Gq/UIvWoKJNWuRIpKyIOnV8dVa2c13ODERd6Wvn433XyYpIAkQgmdlYoTMmC56jHELfnJBRyOcrzC3Hv0Hm0Hd0fV9f+UGMM3s8/js6vjIK0qBSJx/5Wbu+7dgYAYNjBlVBUyHF84kqU5mj+amjSLh6HqCnqShh4vPoZCm+dh+e8XRBJDBuUUCHShFrPrbOTYWjjDJHB/652F4lg5OCO8qwklCRcQ1Hs37Af/H8w9+mHxE9nwO3FjZBY2QEKBQpjzuPeuokQm1jA7cVNWn5GNZNYWMN2wHMwMLWE84T38SDid2TsX83kXQvCYzIRETV3ep3AO336dP2FiIj01NMhHji4aQjGv3kGxaUytbU7coAb9q0bBFMT3XgLSP9xNcrS4+Gx8pRK9ZzGL668B178ZdgFT4btwMr7PdgNfgG3FvZBmymrkfXb57ANmggDMytNhK5xq+f2hJmJBEs+jVBru0tf6Y6lr3bXmQTuI/0/mQPnx/wAACemrAYAWHo6oTy/EF3mjoHzgC6oKC1H5Lp9SD93HeZt7FFyPw+Kin+uVC1MzYZ5G/saPzjv9sazqCiX4eegeTC0NMOIo6uRHRGH0pyHiPxoL9yHBeL0/32knSdLSr4vDUfS7+FVtpm52MGpry/C5nxSYx2viSEoTLyPwpTKe0VatLFX/h8ACpOz4BDgXWNd645u6P7meBx+/C2UZOajx7v/3Cvm4ts70HHqEw2+YoqaHx6HqD51JQweXj0O806PQSQxrFavtoQKkbo19tzaus9o2PQdg7TQZTD3CoRNv2ernCta+PRHt9CHyP/7IG6/GwS/bbeVy2aqy72NU1GSWPnltbL0eMSvGA6RoREAoP27B2tcTrP4XiRaj5xb+f87V2DWTvv39ybtSNg0FQooYO4ViDZTP4RhKwcek4mIqNnT3k1viIhIZSMGuOPagdEYEODU5LbMTSX4dFFfHPrkcZ1J3mX8vA75F39ChyXHIDY2q7bfyMEd5ZmJysdl9xOU3xp+9IGC57xdAKB8bGTnAlNXHzy4fBTZv+9A6xH6u5yySCTC+zO749QXw+DpYtHk9jxcLHByxzAsm9VD55J3AHBu7hb82PMVRKwNRc/FUwAAIokYFm6tkR+XgiNPvo2/F+/EwO2vw8S+lcrtOwf5Iy608sMsaUEx7v58Tq3xk+r8546BpacTrqzeU2V7hwkhSD5xBWW5BdXqOPf3R9cFz+KPVzZW29cQzv39kXL6Kkoy8wEAt775vVHtUPPE4xA1RPG9SJj+L0nw74RB/t8HYdNndLXyjxIqbaau0Wqc1PLUe25t76ZczQIAFApF5YoXDu7Kc0OXSctg7OhZ47miSCyGTd8xkFjaoiwtVu3xt319N3w3RcJ3UyTMOvREhyW/Kh/Xdi+8knuRyjnIBF7z1XH1n/D95Bp8N0RAYmWPhM3TlPt4TCYiouaMCTwiIh3X3s0KZ74ajk8X9YVHI5I4BgYijHvcE9cPjMGsib4Qi3UjcXP/0AbkhYXCa8WJWr+9a9X9SRTfjUBpyi0AQNaxbbANmlhv27YhU5H42UyYuPoo75+nzwb1dsH1n8bgzWn+sLKo/g3S+lhZGOKNqZ1x/cBoDO7jooEI1evOj2fh9JgfjG0sUJSaDXlFBe4eCAMA5N64h8KkTNj4uKMoNRumjjYQGfxzOmPRxh5FqdkN60hR//K0pDl+r4yCx/DeODl5FSpKyqvs85oQokxy/JtjX1/02zQLp6Z+iId30pTbC1OzYeHqoHxs4eaAotSsavVrxHFANeBxiOpSU8JAoVDgwdXfYfWfe4PVl1AhUpeGnFsbWreGWfseyPnjOwBA/oUDMLJzhYlzh3rbf3C58l6y5VlJkOZlwLgBdTStPCcVgAhGdm0AACUJ12Dq4S9sUKQRRg7uAACRxBCOT81HYXSYch+PyURE1JwxgUdEpAfEYhFmTfTFnaPP4pctj+Opge6wsTKqs7xfe2ssfaU7En+bgB/XD0ZbV0stRly38uwUpOxcAFlRPmIXh+Dm/G6IebM3ACBtzxJkHfscAGBgZgmP175E/OpncGNmB5TnpMB5/Pv1tm/TdzTkJQVwGD6rznKlKbdx7QVXpOx8Aw+v/o5rL7gi89dtTX+CGmBhZoiPFwQi7eQk7FjSD/26O8LE2KDW8ibGBujX3RHbl/RD6slJWP9mb1ia1z5mhGRkZQZTRxvlY/cne6Esr7DyJ7cA6eduwCW48n63Fm6tYeHeGg/iUlGa8xC51++h/dgBAACPEX1QlJ5b47J1AJD25zV4TQgBABhamKLtM/2V+8oLS2BoyT/itcV35ki0Hd0PxyesqLZUpXN/f4gkYqSdrXr/R8c+PgjaMgenp3+EvJuJVfYl/nIRXpOHQCQWw8jaAm2f7od7hy7U2Hf6uetoE9Idpg7WAICOU5+osr+8oBiGVhwLLQ2PQ9RQtSUMimMvwdTVBwam/3zZqiEJFSJ1qOvcGgAStryE/L8r75fs8ep2ZP++HTde9UbGgQ/hOffrBvWRdXQLbszqhLjlw+A2YwsklrY1lkvcNhPXXnBFeXYK4pYNxY2Zmkv0Fd+9WuWKOwNza509l6fGqygtgqwwX/k4NyxU+brzmExERM2dbqyhRkREDWJgIMbIge4YOdAdCoUCCamFiLydg7yH5ZBVyGFqbID2blbo6m0LczPVr9TSFiN7VwQcqvmqA5fJK6o8tu49Cta9R6nUvtjYDBIrexg7tquznIlrR3TZmaJS20IzNzPEy+M64eVxnSCTyRFzNx834vNQXCqDQlG5VKpfBxv4trOGRKJ739Pp+9EMuA4OgGlrazweuhjSwhL8Pn45gncsgMTECAq5AqU5D3HqX0vaXFy4Hf02zELPxVOgkCtwceF2FGfkAgAuLNyO/pteg//cMZAWluDc/E9r7Ttq4370W/8qRodtRmnuQ2ReioGBUeU8SQ+7js6vjMKoU+uRdfk2Lr69Q7O/iBbMzNkWgcum42FCBp7cvwwAUFEuw9ER7wIAvCYNQvwPZ6pdmdRv/SwYGBmi/8Z/EvN/ztmC/FtJuLP/T9h164AxF7ZAoVAgevsvyL+VVGP/+beTEbl+H4YdXAlpUSkSj/1dZX/057/giR+WoKKkDMcnrkRpzkM1PnvSBTwOUVPUljCQWNnDuvczyu2PEipGTu0Qu7gyaSuSGMNn3d//bZKoyeo6twYAzzlfKv9v4toRnT66qHIfHZb+1qCkh8es7Sq3XZOOq/6ot4x1r5Gw7jVS+dhnfXgdpUlfyfLv486HYwF5BRRQwNixHTzn7wbAYzIRETV/TOAREekpkUiEtq6WOnVlna6TWDsi9r2BaPP8GrTqObzOsrlhe5H+4weQtHLUUnSqk0jE8Pe2hb93zd+A1kUXF9b8gfTR4e/WWqcwKRO/j1tW476Hd9Lw61PvNahvWVEpztZy3zRpQTF+HdWwdqhpitNzsct5XK37/3xtc43bf+o3p9Y6Crkcfy/6Eg39CCb22xOI/faE8vG1jfuV/4/a8COiNvzYwJZIH/E4RE1RW8IgerYfHD84o9xeX0KFqLlQ5fz69nshKM9MgLlPPy1FR82BsVM7+G66WuM+HpOJiKi5YwKPiIiaJf8vEqpt6/pNzUua1cQ2aAJsgyaoMSLStpLMPDz50wpcWb0Hqadr/qO/LkP3L4OFmwPuh9/WQHSkLeUFxeg4bShadWjTqCuafGeMhPfkwSjOyNNAdNTc8TjUcvhtjRY6BCKNqSvxocr5dcdVZ+ovRKQGPCYTEVFzwQQeERERNUt7u77cpPq1XW1D+uXS+18DaNj9fWpyc8cR3NxxRH0BUYvC4xARERERERE1lu7dHIeIiIiIiIiIiIiIiIioBWMCj4iIiIiIiIiIiIiIiEiHiBQKBe/iSkREGqNQAKUVQkehPiYGgEgkdBS6T6FQQFZSJnQYGicxNYZIxQGhUChQXCLTUESaYWYqUel5tpTXH2gZY0DV118XcAxSXfTx3KS5nX/o2xzVxXmmj+NYKLo4f1r6HNDH8auL44iIiJo/JvCIiIiIiIiIiIiIiIiIdAiX0CQiIiIiIiIiIiIiIiLSIUzgEREREREREREREREREekQJvCIiIiIiIiIiIiIiIiIdAgTeEREREREREREREREREQ6hAk8IiIiIiIiIiIiIiIiIh3CBB4RERERERERERERERGRDmECj4iIiIiIiIiIiIiIiEiHMIFHREREREREREREREREpEOYwCMiIiIiIiIiIiIiIiLSIUzgEREREREREREREREREekQJvCIiIiIiIiIiIiIiIiIdAgTeEREREREREREREREREQ6hAk8IiIiIiIiIiIiIiIiIh3CBB4RERERERERERERERGRDmECj4iIiIiIiIiIiIiIiEiHMIFHREREREREREREREREpEOYwCMiIiIiIiIiIiIiIiLSIUzgEREREREREREREREREekQJvCIiIiIiIiIiIiIiIiIdAgTeEREREREREREREREREQ6hAk8IiIiIiIiIiIiIiIiIh3CBB4RERERERERERERERGRDmECj4iIiIiIiIiIiIiIiEiHMIFHREREREREREREREREpEOYwCMiIiIiIiIiIiIiIiLSIf8PERJ3sB0dXK4AAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ansatz_ibm.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also use `apply_layout` to transform our virtual observable to physical" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "SparsePauliOp(['IIIIIIIIIIIIIIZIIIIZIIIIIII', 'IIIIIIIIIIIIIIZIZIIIIIIIIII', 'IIIIIIIIIIIZIIZIIIIIIIIIIII', 'IIIIIIIIIIIIIZZIIIIIIIIIIII'],\n", + " coeffs=[1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hamiltonian_ibm = hamiltonian.apply_layout(ansatz_ibm.layout)\n", + "hamiltonian_ibm" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "b58c33dc", + "metadata": {}, + "source": [ + "## Step 3: Execute using Qiskit Primitives." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "fe36b13c", + "metadata": {}, + "source": [ + "As with an iterative optimization procedure, we now need to define our cost function over which to minimize. We proceed in an identical manner to the [Variational Quantum Eigensolver tutorial](https://learning.quantum-computing.ibm.com/tutorial/variational-quantum-eigensolver), computing the expectation value of our Hamiltonian with respect to the parameterized ansatz circuit using the [Qiskit Runtime `Estimator`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator#estimator) primitive:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "2f3e4de4", + "metadata": {}, + "outputs": [], + "source": [ + "def cost_func(params, ansatz, hamiltonian, estimator):\n", + " \"\"\"Return estimate of energy from estimator\n", + "\n", + " Parameters:\n", + " params (ndarray): Array of ansatz parameters\n", + " ansatz (QuantumCircuit): Parameterized ansatz circuit\n", + " hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n", + " estimator (Estimator): Estimator primitive instance\n", + "\n", + " Returns:\n", + " float: Energy estimate\n", + " \"\"\"\n", + " cost = estimator.run(ansatz, hamiltonian, parameter_values=params).result().values[0]\n", + " return cost" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "32035dc8", + "metadata": {}, + "source": [ + "Any classical optimizer can be used to minimize the cost function. On a real quantum system, an optimizer designed for non-smooth cost function landscapes usually does better. Here we use the [COBYLA routine from SciPy through the minimize function](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html).\n", + "\n", + "Because we are iteratively executing many calls to Runtime, we use a [`Session`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Session) to execute all calls within a single block. Moreover, for QAOA, the solution is encoded in the output distribution of the ansatz circuit bound with the optimal parameters from the minimization. Therefore, we will need a [`Sampler`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Sampler) primitive as well, and will instantiate it with the same [`Session`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Session).\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "f2fffe34", + "metadata": {}, + "outputs": [], + "source": [ + "# To run on local simulator:\n", + "# 1. Use the Estimator from qiskit.primitives instead.\n", + "# 2. Remove the Session context manager below.\n", + "\n", + "options = Options()\n", + "options.transpilation.skip_transpilation = True\n", + "options.execution.shots = 10000\n", + "\n", + "session = Session(backend=backend)\n", + "\n", + "estimator = Estimator(session=session, options={\"shots\": int(1e4)})\n", + "sampler = Sampler(session=session, options={\"shots\": int(1e4)})" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "b0b5aa51", + "metadata": {}, + "source": [ + "We can set an initial set of random parameters:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "1631f250", + "metadata": {}, + "outputs": [], + "source": [ + "x0 = 2 * np.pi * np.random.rand(ansatz_ibm.num_parameters)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "43520f43", + "metadata": {}, + "source": [ + "We can run our minimization routine:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "0076beb6", + "metadata": {}, + "outputs": [], + "source": [ + "res = minimize(cost_func, x0, args=(ansatz_ibm, hamiltonian_ibm, estimator), method=\"COBYLA\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "95404ae5", + "metadata": {}, + "source": [ + "In the end, we have a result in the standard [SciPy `OptimizeResult`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.OptimizeResult.html) format." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "7a299ed5", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + " message: Optimization terminated successfully.\n", + " success: True\n", + " status: 1\n", + " fun: -2.5309634084695976\n", + " x: [ 1.982e+00 6.601e+00 5.917e+00 2.669e+00]\n", + " nfev: 51\n", + " maxcv: 0.0" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "d162e690", + "metadata": {}, + "source": [ + "## Step 4: Post-process, return result in classical format." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "677cf16b", + "metadata": {}, + "source": [ + "The solution vector of parameter angles (`x`), when plugged into the `ansatz` circuit, yields the graph partitioning that we were looking for." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "29cff98d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Assign solution parameters to ansatz\n", + "qc = ansatz.assign_parameters(res.x)\n", + "# Add measurements to our circuit\n", + "qc.measure_all()\n", + "qc_ibm = pm.run(qc)\n", + "qc_ibm.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "554563ff", + "metadata": {}, + "outputs": [], + "source": [ + "# Sample ansatz at optimal parameters\n", + "samp_dist = sampler.run(qc_ibm).result().quasi_dists[0]\n", + "# Close the session since we are now done with it\n", + "session.close()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "38c59bdc", + "metadata": {}, + "source": [ + "For small problem instances, the solution can be visually obtained:" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "9c61fa56", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "plot_distribution(samp_dist.binary_probabilities(), figsize=(15, 5))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "b2dd6e37", + "metadata": {}, + "source": [ + "The most probable bit-strings, up to finite-sampling deviations, encode the solution. Here we see that `00001` and `11110` are found, and are indeed correct. There are two solutions because the labeling of the two partitions with `'0'` or `'1'` is arbitrary." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Reverse 11110 to convert quantum result to classical solution\n", + "solution = [0, 1, 1, 1, 1]\n", + "\n", + "mpl_draw(\n", + " G,\n", + " pos=rx.bipartite_layout(G, {0}),\n", + " with_labels=True,\n", + " node_color=[\"#EE5396\" if kk else \"#0F62FE\" for kk in solution],\n", + " font_color=\"#F4F4F4\",\n", + ")" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "071d7e49", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'0.19.1'" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit_ibm_runtime\n", + "\n", + "qiskit_ibm_runtime.version.get_version_info()" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "f3f06a12", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.0.0rc1'" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit\n", + "\n", + "qiskit.version.get_version_info()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/tutorials/submitting_transpiled_circuits/user-transpiled-circuits.ipynb b/docs/tutorials/submitting_transpiled_circuits/user-transpiled-circuits.ipynb new file mode 100644 index 000000000..419b8affe --- /dev/null +++ b/docs/tutorials/submitting_transpiled_circuits/user-transpiled-circuits.ipynb @@ -0,0 +1,377 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Submit pre-transpiled circuits\n", + "\n", + "## Background\n", + "\n", + "To get the best performance from your circuits, the Qiskit Runtime service will pass all circuits through Qiskit's transpiler before running them. While this is usually a good thing, we might sometimes want to disable this by passing the argument `skip_transpilation=True` to the primitive we're using.\n", + "\n", + "For example, we may know better than the transpiler in some cases, or want to target a specific subset of qubits on a specific device. In this tutorial, we'll disable automatic transpilation to test the performance of different transpiler settings. This example will take you through the full process of creating, transpiling, and submitting circuits.\n", + "\n", + "## Setup\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# General\n", + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "# Create circuit to test transpiler on\n", + "from qiskit import QuantumCircuit, transpile\n", + "from qiskit.circuit.library import GroverOperator, Diagonal\n", + "\n", + "# Use Statevector object to calculate the ideal output\n", + "from qiskit.quantum_info import Statevector\n", + "from qiskit.visualization import plot_histogram\n", + "\n", + "# Qiskit Runtime\n", + "from qiskit_ibm_runtime import QiskitRuntimeService, Batch, Sampler" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ibmq_mumbai'" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", + "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", + "backend = service.least_busy(operational=True, simulator=False)\n", + "backend.name" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 1: Map classical inputs to a quantum problem\n", + "\n", + "In the following code cell, we create a small circuit that our transpiler will try to optimize. In this example, we create a circuit that carries out Grover's algorithm, with an oracle that marks the state `111`. We then simulate the ideal distribution (what we'd expect to measure if we ran this on a perfect quantum computer, an infinite number of times) for comparison later.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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hhuS100YIDSVo8wZfT9FzoaG+nmDIUsSDlMViAQ/eeE78l06nRQyniEUMp4hFDKeIRQyniEUMp4hFDKeIRQyniEUMp4hFDKeIRQyniEUMp4hFDKeIRQyniEUMp4hFDKeIRQyniEUMpzt7DFIulwtaWnw9Rs+Fhl6+G4l4nSIerFpaaH/kSV9P0WNBmzfodkI+otNpEcMpYhHDKWIRwyliEcMpYhHDKWIRwyliEcMpYhHDKWIRwyliEcMpYhHDKWIRwyliEcMpYhHDDYmInU4ndrud1NRUwsLCGDVqFEuWLKGhoYEFCxZgsVhYt26dr8ccEMXOs4Rs28zPKo5dc5uQbZt5aP8eL07Vf9HJI8ku/A9mbn+BeX//NQUnfscDf36JzCXfICg81NfjeZXff5748OHD5Ofn43A4GDZsGOnp6dTU1LB27VoqKiqoq6sDIDs727eDSq+kzZvK2P+8j8/eO0jFH/bgau/AOjmDO555jDGzJ7Nj1rN0NLf6ekyv8OuInU4ns2fPxuFwsHTpUpYvX05UVBQAq1evZtmyZQQFBWGxWMjMzPTxtNIblTv28ckv3qTtUuPVZcd/+x4XT9WS9d25pD06lWO/eceHE3qPX59OL168mKqqKhYtWsSaNWuuBgxgt9vJysqivb2dMWPGEB0d7cNJpbfOHanoEvAVp/70IQDDx4729kg+47cRl5WVUVRURGxsLCtXrnS7zcSJEwHIysq6umzLli3MmTOHxMREIiIiGDt2LM899xz19fVemXugNHZ04GxpcfvHnwyLHwFA0+cXfDuIF/nt6fSmTZvo7OykoKCAyMhIt9uEh4cDXSNes2YNo0eP5oUXXiAhIYHDhw+zYsUKiouL2b17NwEBZn7fe/54Cc8fL/H1GAPKEhBA1nfn0tnWzqdvfuDrcbzGbyPetWsXAHl5edfcpqqqCuga8bZt24iLi7v693vvvZe4uDgKCgr44IMPmDJlSq9nmTRpEg6Ho1ePCQ8IoDQ7t9fPdS1Pj05mTvwot+vy9xX3e/82m42mzs5+7+eKYFcAy8np1WNynn+KW+68jY9feI2LFTUem6WnbGk22ix9ew2sVisHDx7s02P9NuLTp08DkJiY6HZ9e3s7e/fuBbpG/K8BXzFp0iQAqqur+zSLw+Ho9WMjAgMhu09P51ZqZCTT4m713A6/pKamhsaODo/tL8QSCL0Y93b7PMYtuJ/jv3uPo79402Nz9EZNbQ2tLs+9Bj3ltxE3NDQA0NTU5HZ9UVERTqeTqKgokpKSrruv999/H4Bx48b1aRar1drrx4QbdtoeHx/v8SMxPdxd9tJHyPreXE5s2sVH9pc9NkNvxY+M79eRuK/8NmKr1cr58+c5dOgQubldT0tra2spLCwEIDMz87o3Pa+urubHP/4x9913X59/l9yX0yRXc7NR950uLy/H4sH7Trc1NvNayuM33C576SNk/+ARTha9z96lv/TY8/dF+YlygiO8f+9ts77d98L06dMBWLVqFeXl5VeXHzhwgLy8PJxOJ3D9izzq6+t58MEHCQkJ4ZVXXhnQeaX3sr4393LArxfzwff+B1wuX4/kE357JLbb7WzcuJEzZ86QkZHB2LFjaW5u5uTJk+Tn5zNmzBjefffdLu+H/1VTUxOzZ8/m1KlT7Nmzh5EjR3r5K5DrGfvUfdxun0d91efU7vmE5G/c02V90+dfULv7Ex9N511+G3FCQgJ79uyhsLCQ4uJiKisrSU9PZ/369SxcuJCUlBQAtxG3tbUxd+5cDh48yM6dO0lPT/f2+HIDsdmX//0iE+L46trvdFvv+LBkyERscbmG3jlIfX090dHRWCwWLl26RERExNV1nZ2dzJs3j61bt/LWW28xdepUn8xo2nvioM0bfPKeeDApqPi9T94T++2R+HpKSkpwuVzYbLYuAQN8+9vf5vXXX+eZZ54hIiKCffv2XV2XkpLi9ldQIr7ktz/Yup6jR48C7k+l3377bQBefPFFcnNzu/zZsWOHV+cU6YkheSS+XsSVlZVenkakf3QkFjHckDwSX7muWsQfDMkjsYg/UcQihlPEIoZTxCKGU8QihlPEIoZTxCKGU8QihlPEIoZTxCKGG5KfJzaBy+UCk27sHhp63XuV9ZbL5aK9yaCvHwgK9+xr0FOKWMRwOp0WMZwiFjGcIhYxnCIWMZwiFjGcIhYxnCIWMZwiFjGcIhYxnCIWMZwiFjGcIhYxnCIWMZwiFjGcIhYxnCIWMZwiFjGcIhYxnCIWMZwiFjGcIhYxnCIWMZwiFjGcIhYxnCIWMdz/AUbRO+GrcA4uAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "oracle = Diagonal([1] * 7 + [-1])\n", + "qc = QuantumCircuit(3)\n", + "qc.h([0, 1, 2])\n", + "qc = qc.compose(GroverOperator(oracle))\n", + "\n", + "qc.draw(output=\"mpl\", style=\"iqp\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ideal_distribution = Statevector.from_instruction(qc).probabilities_dict()\n", + "\n", + "plot_histogram(ideal_distribution)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Optimize problem for quantum execution.\n", + "\n", + "Next, we transpile the circuits for our backend. We're going to compare the performance of the transpiler with `optimization_level` set to `0` (lowest) against `3` (highest). The lowest optimization level just does the bare minimum needed to get the circuit running on the device; it maps the circuit qubits to the device qubits, and adds swaps gates to allow all 2-qubit operations. The highest optimization level is much smarter and uses lots of tricks to reduce the overall gate count. Since multi-qubit gates have high error rates, and qubits decohere over time, the shorter circuits should give better results.\n", + "\n", + "In the following cell, we transpile `qc` for both values of `optimization_level`, print the number of CNOT gates, and add the transpiled circuits to a list. Some of the transpiler's algorithms are randomized, so we set a seed for reproducibility.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "CNOTs (optimization_level=0): 27\n", + "CNOTs (optimization_level=3): 14\n" + ] + } + ], + "source": [ + "# Need to add measurements to the circuit\n", + "qc.measure_all()\n", + "\n", + "circuits = []\n", + "for optimization_level in [0, 3]:\n", + " t_qc = transpile(qc, backend, optimization_level=optimization_level, seed_transpiler=0)\n", + " print(f\"CNOTs (optimization_level={optimization_level}): \", t_qc.count_ops()[\"cx\"])\n", + " circuits.append(t_qc)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since CNOTs usually have a high error rate, the circuit transpiled with `optimization_level=3` should perform much better.\n", + "\n", + "Another way we can improve performance is through [dynamic decoupling](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-provider/qiskit_ibm_provider.transpiler.passes.scheduling.PadDynamicalDecoupling#paddynamicaldecoupling), where we apply a sequence of gates to idling qubits. This cancels out some unwanted interactions with the environment. In the following cell, we add dynamic decoupling to the circuit transpiled with `optimization_level=3`, and add it to our list.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.transpiler import PassManager\n", + "from qiskit_ibm_runtime.transpiler.passes.scheduling import (\n", + " ASAPScheduleAnalysis,\n", + " PadDynamicalDecoupling,\n", + ")\n", + "from qiskit.circuit.library import XGate\n", + "\n", + "# Get gate durations so the transpiler knows how long each operation takes\n", + "durations = backend.target.durations()\n", + "\n", + "# This is the sequence we'll apply to idling qubits\n", + "dd_sequence = [XGate(), XGate()]\n", + "\n", + "# Run scheduling and dynamic decoupling passes on circuit\n", + "pm = PassManager([ASAPScheduleAnalysis(durations), PadDynamicalDecoupling(durations, dd_sequence)])\n", + "circ_dd = pm.run(circuits[1])\n", + "\n", + "# Add this new circuit to our list\n", + "circuits.append(circ_dd)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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zmXU2KTRf6tXPdutCRq7ee/IKlyu2uVsOlMXdxkISOVCa8PBwTZ8+XeHh4c4OBTZCoQ12FVgnVFumzdWBOSucHYpTefoFKrDFFUrdtFjZiTFudSAhBwpU1hw4nZypAff/avMi20U7IpN17SOrtPqzYS79jIbK2v6AVHD1uq2LbJd64KWNqlndTzdc3dBu+3CEytoPmEwm3fH0XzYvsl10Pi1XQyas1Ob516lp/RC77MNRKmsOmIPxYOVu/237z+im/9q+yHbRot+OqkYVP334TC+7bB/l98n3B21eZLvUY29sVs1q/ho9vInd9lEeJxLTNOiB32xeZLto485TGvnfP/XL7MEuN43kpSpzP/j7pjiNe9b2RbaLPlhwQLWq++nZ+zvZZfuOUplzoCyMhQq4cw78W5UqVTR06FBnhwEbct2zlnAJ9QZ21Ynftzk7jAohOzFGkuQVVN3JkTgWOfA/lS0HTCaTJry8yaKpUbYuvE4nVt2urQuvM3udDTtP6Y0v7XcS31EqW/sDkrQ36qyeeteyPt7SfsBkku59YYNOJ9unoO9IlbEf+PyHKIuni7Q0B86ey9Zdz9nv5JUjVcYcMAfjwQKVsf2zsvP+/+5j84ts1owHZy+K1M/rjlsTIuws+tg5PfbGPxatY00OTHhlo+JsMCWjrZlMJt0zbb1OWTBOsebzr9x00upnYVcklbEfTDmfrfHPrVd+vvnjFGtyYNrsndq674w1IVYolTEHzMFY6H/cNQf+LSUlRd9//71SUlKcHQpshEJbOSQlJWnKlClq2rSp/Pz8VK9ePU2aNEnp6em65557ZDAYNGvWLGeH6VQhjcN0ITbR2WE4nDE7Q3nnk5R77owyY/fq+McPKfPITgU06y6/Os2dHZ5DkQOVNwe+W3lUP/wZa9E6YaEBqls7UGGhARatN/3jndobddaidZzJHdofyM01avxz65SbZ7RoPWv6geTUbE18ZZNMtngAnIO4Qz9wPCFN/5252eL1rMmBDTtP6YMF+y3elzO5Qw6Yyx3Hg+7S/tNm79DBo+csWsfa8eD9L25Uynn73DEE6+TnG3XX8+uVlW3Z3YzW5MD5tFzdN31DhRsLfLbkkFb9bdld3dZ+B556b6tNnontKO7SD0567R8lnMmwaB1rcsBoNGn8c+uUlZ1naYhO4y45YA53HAtJ5EBpTp06pTfffFOnTp1ydiiwEaaOtNKuXbs0dOhQJSYmKjAwUK1bt1Z8fLzef/99xcTE6OzZghPCHTt2dG6gTuQV4KfctCxnh+EUCQunKWHhtCKvVe15k+o/8KGTInIOcqDy5kBurtGqk6tW7y/PqMff3qKVHw9x2D7Lo7K3PyBJXy2P1o7IZIftb8kfsVq3PVFXdnWNOezdoR949oPtupCe67D9PfPBdo2/vrmqBPs4bJ/l4Q45YA53HQ+6Q/sfi7+gmV/tc9j+4k9n6PUv9ui1x7o5bJ+2ZDKZ9OfmeP2+6aTOpeUowM9LV7SvpRuvaSAfb09nh2eV71Ye1cadjjtB+NvGOP26IU7D+tZz2D5Lk5GZpyff3eqw/WVm5eupd7dq8dvXOGyf5eEO/eDWfWf09YrDDtvfgZhUffL9wQr/zMKL3CEHzOGuYyGJHIB7odBmhaSkJF177bVKTEzU5MmTNW3aNAUHB0uS3njjDT355JPy8vKSwWBQ+/btnRyt80Rc2V4n1+52dhhOETr4flXrdYtM+bnKPLZXiT+8rpykOBm8/QqXubB/vQ6/ePlcvKa8HJmM+eqy1D7POHAkcqDy5sCyNccUf9qyq/bK6/dNJxUVe07NG1Zx6H6tUdnbHzCZTPpwkeOnL/rw20iXKbRV9n4gKSVLi1Yeceg+0zPzNO+naD0yuo1D92utyp4D5nLX8aA7tP/H3x90+JSuny+N0gsTOsnP17VOZXz1Y7Re/Wy3oo79++6//apdw18Pj2qlp+/pIE9P15p06MNFkY7f57cHKkyh7dvfjijlfI5D97lszTHFJaarbligQ/drDXfoB2c74Tswe9FBPXpHGxkMFf95fe6QA+Zw17GQRA7AvbjWKK6CePTRRxUXF6eHH35YM2fOLCyySdKUKVPUoUMH5eXlqWHDhgoJce2HtpdHrW4tdWbroSKvdX56tMYnLFbT268udp0hS6ZrbOxCVW1RMQbO1vINb6aQjgNUpctQhd00RU2f+UkZh7fq+EcPFi4T3KavOi1KK/Jfm9lR8goOVcTol5wYve2QA5U3B5zxB4Ukffy9c/Zrqcre/sA/e05r10HHT+e6dHWs4k9XvOezFKey9wNfLI1STq5l04bawuxFkRVu2rCSVPYcMJe7jgcre/tn5+Trsx+iHL7fpJQsLV4V6/D9lscz72/T+OfWFVNkK3AqOVPPzdqhkf/9U7lO6FettftQskPvZrvo1w1xOhLn/OkTTSaTPvzW8Rcd5eeb9OmSQ2UvWAFU9n4wOTVL3/7m2IuOJCnq2Dmt3pzg8P1ao7LngLncdSwkkQNwLxTaLBQZGalFixYpNDRUM2bMKHaZLl26SJI6dOhQ+NrFwlz37t3l6+tb4pUn5i5X4RkMkkEyGYv+obBr5ndKiTym7i+MU0B40Ydetr5/hMJ6tdGumYuUeuiEI6O1u6BWvVT9qrFK2bBIaZGbil3GmJutI6/dpKDWfRR+y1QHR2gH5EARlSkHUs5n66+tzhnYL/3zmFP2W16Vqf0ByXnfxbw8k35e55rHh8rWDyxdHeuU/R48ek6HYi17HlRFUdlywCyMBwtVtvbfuPOUklKcMw2WK40HP/4uUq9+Zt5dDD+uOa5HX/vbzhHZzrLVzmkHk0lavua4U/Z9qbhT6Q6dQvtSzjoGl1dl6wdXbjxp8fMJbYUccCGMhYpwyxwoQUBAgHr06KGAAMue14mKi0KbhRYuXCij0ag77rhDQUFBxS7j7+8vqWih7fDhw1qyZInCwsLUrVvJc8qbu1xFV7NTUyXtvHyeamNuntZPmiWvAF/1fnti4eshTSLU+alROrM9SvtmL3dkqA4Tfttzkoen4hc8X+z7x2c/KGNulhpOmuvYwOyEHLhcZcmBHQec8welJMXGpyk51TXnNq8s7Q9I0vYDSc7bt5NOatlCZekH8vKM2h3l+DsaL3Jm/pVXZckBczEeLKoytb9zjwOu0Qfk5ho1/eOdFq0zZ8khnUhMs1NEtrXdiX8TVIQccOZ34MCRVGVm5Tlt/+VRqfpBJ+YhYyHXwVjocu6WAyWpX7++PvjgA9WvX9/ZocBGKLRZaPXq1ZKk/v37l7hMXFycpKKFtn79+ikhIUHLly/XgAEDSlzX3OUqktpXtJLhX3PJ1+nfSSfX7Cp2+bN7j2rPB0tV56qOaj5mgAweHur7/iOSpPWTZl12lUdl4RfeVNX73q4Le/7Uhf3ri7x3+qf3dW7bCjV5epk8fF3vSgZywDyVJQecPah31pWj5VVZ2h8wmUxO/R46uw8qj8rSD0QeSVVmlvOelUAOVEyMB8tWmdrfmSeYj7nIhVfL1hxTYlKmResYjSbNWewa0wI6t8jg/L8HnBlDfr5Juw8574KX8qhU/aATxyO7o84qL881j5OVKQf+jbGQeSpzDlgiPz9faWlpys/nGXSVBYU2Cx07VjA9QoMGDYp9Py8vTxs3bpRUtNDm4WHer9rc5SqKhtf10oCvp6p2j1ZFXvcOCVDuhYwS19v9zmKd3XdUXZ+/Uz1euVs1OzfTjtcX6nxMvL1DdqqwW56RPDyKXLVxYc8axc17Uo2nfC/f2g2dF5yVyAHLVIYcOHryglP3fyTOufsvj8rQ/kDK+RylXshx2v6d3QeVV2XoB444uQ2OnnSNuz1KUhly4N8YD5qvsrT/0Tjnfg9dYTz44xrrplZc+mesbQOxg5zcfMWfLvm7bW8Vof2dHYMrj4cqSz/ozBzIzMq3uJBfkVSWHLgUYyHLVMYcsFR0dLSuvvpqRUdHOzsU2IjB5CpPE68gqlevrpSUFG3atEk9e/a87P358+drzJgxCg4O1rlz54p9xtoLL7yg6dOnl/kgd3OXK0l6enrh9Jbh4eEWFfG8TR6aZuxu1rLtJ90k3+oh2jptriQpsE6oGgzroQOf/lzqetVaN9CIX1+Tp4+3Tm2O1K83Pl8w4bqVpntsUa7B8qs9DD7+qv2uczq17FOxOvh4N4XfPk21hj9s8+2feqyZTDnWDb7cKQeK46i8sGUOlKe9LZESeIMyfDsV+97WhdcpLLTkq47CQv3l5emhvHxjmX8YJCZlqNuoy6dKqJL+q4Ky/7EsaCs4Igds3Qc4Kgfg3vINQUqs9kSJ79uqHyipDzCYchSR8oplQVuB40DJMnzaKCXo1mLfK6v9pfLngG9OtELTvrEsaCuQA643HrTlWFBiLFDqfkImKM8rrNj3HDEeDD3/hXzzKvaz2pKC7lC2T3OL1/Mwnld46lt2iMh2jPJVQvWSn5tj77GAJEWcnSZnPtE+Oeg2Zfm0LvY9R3wHqqYtU2COZVOTWoN+sGQJVZ+Q0aP4R8o44jtQO/U9eRntf2ejq+WAu4+FJM6NOeu8yM0332zR8qdPn9bChQs1atQo1apVy6x1Fi9ebE1oFcqNdz2mwKAQpaed19Iv373sZ2cwGo1KSEiQJHXs2FE7d1p3fPWyZVDuICwsTCkpKdqxY8dlhbaEhAQ98UTBiaf27dsXW2RzlovJYi4fg6dU27xlj/26RdfMfbLwQFJvYFed+H1bmevlns+QMSdPnj7eivtzR7kOIpIUnxCvHJPlt9t6+AaY+1FtypidoZgZN6hK9+vsUmSTpPj4eBmzrbvS0J1yoDiOyAtb50B52tsidS5IvsW/FRYaoLq1A8vchJenh1nLFedcarLOnT1p1bqWsHcO2KMPcFgOwL15BknVSn7b3v2AyZinkyddvw+QXPg4EFJbKv68ktntL1mfA9lZGeRACWydA642HrTlWFBiLFAq/+wSzyY4YjyYdCZRyrB/P1Au9dMkH8tXM+ZmOaSPKxeDj1S95LftngOmPMU7+3dUL73E9nXEdyA1JUmpqa5/LHTpfjA4r8R5whyRA6cS46Vc+09h6mo54O5jIYlzY846L5Kenm7R8pmZmYX/N3fdCj8+MIPx/6fKNObn6+TJk5f97GynTp2yel0KbRYaMGCAIiMj9frrr2vgwIFq3rzgCrWtW7dq7NixSkoqmKO5Y8eOTozyctbc0SYzL344FxUnmaSqzesqNSpOwY3CdGFu2UnZ+92H5OHtpdSoE2r/2EjFLt+kC8esT+aI8Air72hzhpRNS5R5dLeyTkYpZcOiy95vM+uAfGqW74GYERER5bqjzV1yoDiOyAtb50B52tsS5/wNKmmyoMSk0gczll69WZxqVXwV4F/HnFDLxd45YI8+wFE5APdmkqfiTfmSwbPY923VD5S0HU9lKayO6/cBkuseB7K9/FXSU0nKan+p/Dng72tSdXKgWLbOAVcbD9pyLCgxFihNkleuskt4zxHjwVo1guRdzf79QHmc9z4nayaW8zMkqYYD+rjyMMmgBFOOTIbiK032Hgt4mLIU7uTfUaqfSSWdFnXEd6BGVT/5Bbr+sdCV+8FThmzllfCevb8DkhReu4o8TH7mhFourpYD7j4Wkjg35qzzIoGBlhXNLxbX/P39zV63TgUfH5jDw9Oz8P916tS57GdnuPSOttq1rS8tM3WkheLi4tSxY0clJyfLy8tLLVu2VFZWlg4fPqyhQ4fKaDRq5cqVmjNnju67775it+GMqSPT0tIs+sLnZmRpfpMxZi/f7YVxyko+r8jPf1Xbh67Xrjcv7xgv1eqeYerx8t3aPmOBTvy2Rdf+/qbO7IjSbzdNM3uf/3ZHzDfyDrB8kJGZJ/X9xerdVmjrh0n+VpbT3SkHiuOKeVGe9rbEt7/GaNSTf1m17olVt6tu7UDFnUpXvYHfWrWNgz+OVItGVa1a1xLkAFCy9iN/0N7oFKvWLW8/cNM1DbXknWus2rcl6ANKlnI+W9X7WD91Y3lz4J0neuixsW2t3r+5yAHXGw/aciwokQOlmfL2Fr05d69V65a3DwgK8FbqxjHy9KzYzzePS0xXw6GLlJ9v2d/zv38yRAN7VvwTaT3HLNc/e85YtW55c2Bwrzr67eMhVu3bVj5dfFD3v7jRqnVt8TfRyT9uV0Qt6+6EsgT9YMnunLpWX684bNW65c2BJvWCdfjn4qfxtjVXywF3HwtJnBtz1nmRrVu3WrT8wYMHdeedd2revHlq2bKlWet069bNmtAqlFc/nK/zaekKCQrU1IfuuOxnZyhPDeVSFXtkWgHVrVtX69ev1/Dhw+Xn56fY2FhVr15dn3zyiX7++WdFRUVJkjp06ODkSB3rxO/bVG9QV0Vc1UHx6/aUumxwozB1njpaZ3ZGa9+sZUqNitOut75TWM82anXPMAdFDFsjB9xHl9ahTtt3cKC3mjWo4rT9AyjgzH6gS+saTts3ClQL8VWTesFO278z8w+lYzzoPpz5PezUsnqFL7JJUt2wQN10TUOL1mnZqIqu6RFhn4BszLljAecfB5wZQ1iov0OKbCidM8ekFeE7gOIxFoK5mjZtqpUrV6pp06bODgU2UvFHpxVQq1attGLFCl24cEEXLlzQ5s2bdf/99ys9PV2xsbHy8PBQ27b2v8q2Ijm1OVIhjcPVYGh3ndl6qOQFDQb1efdheXh4aMOkWTIZC25l3vfhj0radVidp45WcANnPDEN5UUOuI8m9UIUXrPkBzvbU++OteXhUXGefwm4q35dwpy2776dnbdv/I+zciDAz0udW1FsragYD7qP3h1ry1mPJHel48DsZ3qpuZkXiVUJ8tHit65xmbGuu48F2jarpqrBVjyEzwYqwucH3wEUj7EQzOXl5aVq1arJy4tpiSoLCm02tH//fplMJjVr1kwBAZefhF68eLEWL16sAwcOFPl527ZtVi1XkZjyjTr51+6CfxtLnge4zYPXqnb3ltr55iKdi/7fAw5NRqM2TJolD09P9X5not3jhe2RA+7Dw8Og+25q4ZR9P3CLc/YLoKhbBzVSSJC3w/fbqnFV9enMH5wVwf0jzZvexNbGjGiiwADH5x7Mw3jQfdQNC9TwvvUcvl+DQbrXSeNQa4RW89O6ucPVo13NUperHx6o9XOHq03Tag6KrPyu799ANavZ//lQ/9YwIkgDezr/rj8fb0/ddUMzp+z7gZudcwxGUZ1ahaprG8ffWebv56kxw5s4fL8wD2MhmCsuLk6TJ09WXFycs0OBjVBos6G9ewvmqC9p2shbbrlFt9xyi77//vsiP8+aNcuq5Sqa479u0fHfSp6PtkqzOuo85Xad3nZI+z/+6bL3uUXa9ZED7uO+kS3k6enYq23r1g7UiH6WPQgbgH0EBnhr/HWOP7k08bZWMjjrFgoU0aN9TXVq6fg7yybc2srh+4RlGA+6j4m3Of77OKxvPTWq67ypa61Ru4a//v7mWv0xZ6huuqahAi95cIyPt4cWvdlf0StuUbvm1Z0YpeV8fTydUvR88NaWFWbq0Advcfx3oEXDKrq6R7jD94viOaMfvGNYE1UN8XX4fmE+xkIwR1pamtavX6+0tDRnhwIb4d5EGyqr0GYymfcQZHOXq2iOrfi71PfPRZ/U141Gl7rM3g+Wau8HS20ZFhyIHHAfdcMCNf66Zvp8aZTD9vnUPe3l5VUx/qgGID02pq0++yFKGVl5DtlfnVoBuvNa5q+vKAwGg565r4NunrzaYfsc3q+eOjqhuAfLMB50H4N711WX1qHafiDJYft86u72DtuXLRkMBl1zRYSuuaLgTqw61yxQ/JlM1azmp1sHN3ZydNZ7eFQrfbjogM6n5TpkfzWr+VWoOxqbN6yiWwc30ncrjzpsn1Pv7cBFRxXI7UMa66VPdunoyQsO2Z+Pt4cmj2vnkH3BeoyFAPfEGUsbKqvQhsonKz5aB6f00r4JzRU5uZsyj+8v13JJf3yp7dcblPrPMklS3vlkHXisY+F/+yY01/YbvZR34awkKWraIB14tL0OPNZRh57uq4wjO+3yOWFbKRsX69hHE4q89u+2dwUzJ3dXnVqOeVZbvy5hleYuhsrS/kCjusGaMamrw/b36bQ+CglyzrNQHOHffYMr9AsjBzbSzQMbOmRfVYJ99PGzvR2yL2tZOy7juICLUjYuVux7d+nwqzdo34TmOjCpg6KeH6ishMPODq1YHh4GffliX3k76EKoR0e3Vp9K8lyiylIoiagVqLcf7+Gw/c1+ppdqVHX8dJWl+eCpngp10BSaw/rW1dhKftGRq42H/P289MWLfR22v+kTO6tlo6oO2589XWxrY06Wyxz34BiuNh4CLqLQZkOrV6+WyWTS8OHDnR0KHOT47AcUOvh+tf0oSmE3PanY98ZbvVz2qVgl/f6pAltcUfiaV0gNtX53V+F/oYPuV5UuQ+UVXDCtSOMnvlPr9/eo9bu7VOu6/5a4f1Qsqf8sVdUeNxT+XFzbu4KqIb76dFofi9ZJTMpQ3Kl0JSZlmL1OwP//8eIqD4YvS2Vpf0CSHh7V2uIHwVvTD9x1QzMNdcKzgBzp0r7BlfqFD6f2svgZPdbkwDtP9FDdsEBLw3Moa8dlHBdwUeo/S1X1ihtUc9D9ajP7kFq/t1tVe1yvY7PudXZoJWrXvLpemNDJonWs6QOa1AvWq4867uIOmO/uG5trSO+6Fq1jTQ7cOriRbh7UyNLw7K5WDX99OLWnRetY8/mrBPtozvN9Kk2RtiSuOB66qlu4Hhnd2qJ1rMmBbm1D9Xglupvt0rZ2peMe7M8Vx0OAxNSRgNVyU08r/fA2NZv+uySpaq+ROj7nYWUlHJZfeFOLljMZjTo2617Vu/8DxX05ucR9Jv/xueqMnVH4s1dQ1cJ/52ecK3g6OJwuLy1VBx5tK2NOpnxC68mUm63sxCOqftVYNZjwkdIOblTDSXMlmd/2FdXQvvU0c3J3Pf7WFrOW7zZquUXb9/by0JK3r1GTeiHWhOcU7tT+gIeHQd/PvFr97vpZh2LPmbWOpf3AlV3D9OHUXtaEV2GU1i80fOQzmfJyC/sGV+sXatXw108fDNQ19/2q9EzzphG1NAceH9dO4693/DMBLVXSuIzjAiTL+gGDl3fheoHNr9CpZTOdGHnZnrqngyKPpuqbFTFmLW9pH1Czmp9+njVIgQHeZS8MhzMYDFrw+lW68q6ftTc6xax1LM2BHu1q6vPpjrtryFK3Dm6sAzGpmv6xeXcyW/r5/Xw9tfy9AapTu2JfcFKWyjwemjm5u6KPnddvG+PMWt7SHGhUJ1jL3h3gUo9SMHf8Y/DyVpWu/3sOmSsc92C9yjweslTNmjU1adIk1axZ09mhwEYotAFWykk6Ie9q4TJ4FnyNDAaDfGrWV86Z40UKbeYsd+rHtxXUqrcCm3YpcX9pkZuUl5aiKt1GFHn96Dt36sLeNZKkZs//YtPPCOt4BVVV9X6j5ekfrPDbntO5HSuVuPhVNXzkM53f+bsCW/YqHDCY0/YV3eRx7WQySU+8bV6xzVx+vp76fubVGtLHsitknc3d2h+oVcNfqz8bqkEP/Kb9Mak23fbV3cO17L0B8vdz7SFraf2CJF3Yu6awb0hcOtPl+oUe7Wtp5cdDNPzh33XuQo5Nt/34uHZ647/dXOYK/uLGZRwXIFnWD1zq9Ir3VLX79c4I2WwFU0j2k4fBoHk/2XZap/CaAVr1yRC1qCRTpVVW1UJ89eenQzVkwkrtiEy26bZ7d6qtFR8MVFAFL7ROm9BJJpP04ie2fZxDoL+Xlr8/UP26htt0u85QmcdDPt6e+uGda3Tz5D/1y3rzim3matYgRKs+GaKIWq5VaLVk/HMpVzjuwXqVeTxkqRo1auiOO+5wdhiwIdc+awHY0cEpPZUVH13se63fsd3gOfPYPqX+vUQtXl1X6nJJf3yuGv3vLCzYXdToP/MkScmrv1LcvCcptlUQGUd3qdaIRwv+HbNdAY0LptRJ3bxM1a6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+ "text/plain": [ + "
" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "circ_dd.draw(output=\"mpl\", style=\"iqp\", idle_wires=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 3: Execute using Qiskit Primitives.\n", + "\n", + "At this point, we have a list of circuits transpiled for our system. In the following cell, we create an instance of the sampler primitive, and start a batched job using the context manager (`with ...:`), which automatically opens and closes the Batch for us. This is where we pass the `skip_transpilation=True` argument.\n", + "\n", + "Within the context manager, we sample the circuits and store the results to `result`.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "with Batch(service=service, backend=backend):\n", + " sampler = Sampler()\n", + " job = sampler.run(\n", + " circuits=circuits, # sample all three circuits\n", + " skip_transpilation=True,\n", + " shots=8000,\n", + " )\n", + " result = job.result()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 4: Post-process, return result in classical format.\n", + "\n", + "Finally, we can plot the results from the device runs against the ideal distribution. You can see the results with `optimization_level=3` are closer to the ideal distribution due to the lower gate count, and `optimization_level=3 + dd` is even closer due to the dynamic decoupling we applied.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "binary_prob = [quasi_dist.binary_probabilities() for quasi_dist in result.quasi_dists]\n", + "plot_histogram(\n", + " binary_prob + [ideal_distribution],\n", + " bar_labels=False,\n", + " legend=[\n", + " \"optimization_level=0\",\n", + " \"optimization_level=3\",\n", + " \"optimization_level=3 + dd\",\n", + " \"ideal distribution\",\n", + " ],\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can confirm this by computing the [Hellinger fidelity](https://docs.quantum-computing.ibm.com/api/qiskit/quantum_info) between each set of results and the ideal distribution (higher is better, and 1 is perfect fidelity).\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.873\n", + "0.983\n", + "0.981\n" + ] + } + ], + "source": [ + "from qiskit.quantum_info import hellinger_fidelity\n", + "\n", + "for counts in result.quasi_dists:\n", + " print(f\"{hellinger_fidelity(counts.binary_probabilities(), ideal_distribution):.3f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'0.19.1'" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit_ibm_runtime\n", + "\n", + "qiskit_ibm_runtime.version.get_version_info()" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.0.0rc1'" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit\n", + "\n", + "qiskit.version.get_version_info()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "env", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/docs/tutorials/user-transpiled-circuits.ipynb b/docs/tutorials/user-transpiled-circuits.ipynb deleted file mode 100644 index fe78ab888..000000000 --- a/docs/tutorials/user-transpiled-circuits.ipynb +++ /dev/null @@ -1,372 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Submit pre-transpiled circuits\n", - "\n", - "## Background\n", - "\n", - "To get the best performance from your circuits, the Qiskit Runtime service will pass all circuits through Qiskit's transpiler before running them. While this is usually a good thing, we might sometimes want to disable this by passing the argument `skip_transpilation=True` to the primitive we're using.\n", - "\n", - "For example, we may know better than the transpiler in some cases, or want to target a specific subset of qubits on a specific device. In this tutorial, we'll disable automatic transpilation to test the performance of different transpiler settings. This example will take you through the full process of creating, transpiling, and submitting circuits.\n", - "\n", - "## Setup\n" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "metadata": {}, - "outputs": [], - "source": [ - "# Create circuit to test transpiler on\n", - "from qiskit import QuantumCircuit, transpile\n", - "from qiskit.circuit.library import GroverOperator, Diagonal\n", - "\n", - "# Use Statevector object to calculate the ideal output\n", - "from qiskit.quantum_info import Statevector\n", - "from qiskit.visualization import plot_histogram\n", - "\n", - "# Qiskit Runtime\n", - "from qiskit_ibm_runtime import QiskitRuntimeService, Batch, Sampler" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'ibm_hanoi'" - ] - }, - "execution_count": 43, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", - "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", - "backend = service.least_busy(operational=True, simulator=False)\n", - "backend.name" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 1: Map classical inputs to a quantum problem\n", - "\n", - "In the following code cell, we create a small circuit that our transpiler will try to optimize. In this example, we create a circuit that carries out Grover's algorithm, with an oracle that marks the state `111`. We then simulate the ideal distribution (what we'd expect to measure if we ran this on a perfect quantum computer, an infinite number of times) for comparison later.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 48, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 48, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "oracle = Diagonal([1] * 7 + [-1])\n", - "qc = QuantumCircuit(3)\n", - "qc.h([0, 1, 2])\n", - "qc = qc.compose(GroverOperator(oracle))\n", - "\n", - "qc.draw(output=\"mpl\", style=\"iqp\")" - ] - }, - { - "cell_type": "code", - "execution_count": 49, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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TNWnSJN1yyy0aMWKEbrrpJlmWle/tJiQkSMr8WjUnAQEBznVyEx8fr/T0dJ04cULPP/+8XnnlFd1zzz1KTU3V+++/r//+97/q27ev9u7dK19f3xy3MXXqVD333HPZ2leuXKny5ctLkurUqaPWrVtr165dioyMdK7TqFEjNW7cWFu2bFFsbKyzvVWrVgoJCdHGjRt1+vRpZ3v79u1VrVo1rVy50uUH17VrV5UrV05Lly51qaF37946e/as1q1b52zz9vZWnz59FBcXp7CwMGe7v7+/unXrpqioKO3cudPZXrVqVXXo0EHh4eHat2+fs50+0Sf6RJ/oE32yR59ulacV9c9p27Zt+aqjUC+ASE5O1tdff63Zs2c7vwqtWbOm7r//fj3wwAOqWbPmRbfRq1cvrVq1SuHh4apfv3625TVr1lRSUlKege7o0aPO13rsscc0ffp0l+WDBg3SggUL9Nlnn+nuu+/OtS8XHpmrXbu24uLinCchXh6ffOgTfaJP9Ik+0aeS16eHZ3j+yNz7/y7an1N8fLyqVKly0QsgCvUqgLJlyyo0NFTR0dHat2+foqOjdfjwYT333HOaMmWKHnjgAb366qvOI1s5yToil1tYS0xMVKVKlfKs4/yjev369cu2vF+/flqwYIF++eWXXMNc2bJlVbZs2WztPj4+8vFx3YG8vLzk5eWVbd3cLrLIrf3C7brT7nA45HBkPxUyt/bcaqdP9Kmg7fSJPkn0KbcaC9pOnwreJ0/w1M8p2+vla618WLlypQYOHKhatWrpySeflGVZeuaZZ/Tnn39qwYIFuuaaa/Tee+/pkUceyXM7WefK5XReXExMjJKSknI8n+58fn5+ziNzFStWzLY8q+3s2bP56BkAAEDJdUlh7siRI3rhhRdUr1493XzzzVq4cKG6du2qhQsX6tChQ3ruuedUr1493XHHHQoLC1Pv3r31v//9L89tdu7cWVJmOLzQihUrXNbJS7du3SRJf/zxR7ZlWW1169a96HYAAABKMrfD3C233KK6detq8uTJOnv2rJ588klFRERo2bJluu2223I8XNihQ4eLXrzQvXt31atXT1988YXLyYMJCQmaMmWKypQpo6FDhzrbo6OjtXfv3mzbffDBByVJL730kk6dOuVsj4mJ0ZtvvimHw6H+/fu70XMAAICSw+1z5pYuXapu3bpp1KhRuv322/P1vW7fvn1Vo0aNvAvy9tasWbMUGhqqTp06uUzndejQIU2bNs3liNqECRM0Z84cffzxxxo+fLizvUOHDho7dqxef/11tWjRQn379lVqaqr+97//6fjx45oyZYoaNmzobvcBAABKBLfD3P79+3O82jQvV199ta6++uqLrte1a1f9+OOPmjx5subPn6/U1FQ1b95cL7/8sgYNGpTv13vttdfUvHlzzZgxQ5988oksy1Lr1q313nvv6fbbby9Q7QAAACWR27cmue+++3TbbbfleLVolsWLF+ubb77RRx995HaBJQVzswIAUHIwN+s/3D5n7pNPPnE5py0nv/76a77mUQUAAIB7Cu3WJDk5d+4cE9oDAAAUoUtKWrlN02WMUVRUlJYtW3bRCx4AAADgvgIdmcuaXiLrtiPPPvus8/H5/7y9vXXllVdq+/btGjx4cJEUDgAAgAIemevUqZPzaNzGjRtVp06dHG+86+XlpcqVK6tbt24aMWJEoRQKAACA7AoU5tavX+/8f4fDoXvvvVeTJk0q7JoAAACQT26fM5eRkVGYdQAAAMANRXo1KwAAAIpWvo/M3XfffbIsS1OmTFFQUJDuu+++fD3PsizNnj3b7QIBAACQu3zPAOFwOGRZlvbs2aOGDRvK4cjfQT3LspSenn5JRZYEzAABAEDJwQwQ/8j3kbm//vpLklSzZk2XxwAAAPCcfIe5kJCQPB8DAACg+HEBBAAAgI3l+8hcZGSk2y9Sp04dt58LAACA3OU7zNWtWzfXuVjzYlmW0tLSCvw8AAAAXFy+w9zQoUPdCnMAAAAoOvkOc5988kkRlgEAAAB3cAEEAACAjRHmAAAAbIzpvAAAAGyM6bzyiem8AAAoOZjO6x9M5wUAAGBjTOcFAABgY1wAAQAAYGOXHOa+/fZb3XrrrapTp44CAwNVp04d3Xbbbfruu+8KoTwAAADkJd9fs14oLS1Nd911lxYuXChjjLy9vVWlShXFxMTo+++/16JFi9S/f3998cUX8vZ2+2UAAACQB7ePzE2dOlVff/21brzxRv3www86d+6coqOjde7cOW3cuFEdO3bUwoUL9dJLLxVmvQAAADhPvm9NcqF69erJ19dXu3btyvHIW2pqqlq0aKHk5GQdOHDgkgv1NG5NAgBAycGtSf7h9pG56Oho9e3bN9evUH18fNS3b19FR0e7+xIAAAC4CLfDXO3atZWUlJTnOmfOnFGdOnXcfQkAAABchNth7oEHHtCCBQtyPfJ25MgRzZ8/Xw888IDbxQEAACBv+b7MNDIy0uXxwIED9dNPP6l169YaM2aMOnbsqKCgIB07dkw//PCD3nzzTXXs2FEDBgwo9KIBAACQqcBzs17IGJNre9bz0tLSLrFMz+MCCAAASg4ugPhHvo/MDR06NMfQBgAAAM/Jd5j75JNPirAMAAAAuIO5WQEAAGyMMAcAAGBjlzRp6unTp/XOO+9o9erVOnr0qJKTk7OtY1mWIiIiLuVlAAAAkAu3w1xsbKw6dOigiIgIBQQEOK+4SElJ0dmzZyVJNWrUkI+PT6EVCwAAAFduf8367LPPKiIiQp9++qlOnjwpSXr88cd15swZbd68WW3btlXdunX1+++/F1qxAAAAcOV2mFu6dKm6d++uu+++O9stS6677jotW7ZMBw8e1HPPPXfJRQIAACBnboe56OhotW7d2vnYy8vL+fWqJFWqVEk333yzFixYcGkVAgAAIFduh7nAwEClpqY6H1eqVEmHDx92WScgIEDHjh1zvzoAAADkye0wV69ePR08eND5uHXr1lq1apVOnDghSTp79qwWLVqkOnXqXHKRAAAAyJnbYa5Xr15as2aN/v77b0nSqFGjdPz4cbVs2VIDBgzQ1VdfrYiICA0fPrywagUAAMAF3A5zDz74oD788ENnmPvXv/6lV199VWfOnNHChQsVExOjsWPHavz48YVWLAAAAFxZxhhTmBtMT09XXFycqlWrlu0qVzvLuo9eQkKCAgICPF0OAACXtRHTPV2B9OGYot1+frPHJc0AkRMvLy8FBQUV9mYBAACQg0sOc9HR0Zo3b5527NihhIQEBQYGqnXr1ho8eLCqV69eGDUCAAAgF5cU5mbMmKHx48crOTlZ539bO3fuXD311FOaNm2aHn744UsuEgAAADlzO8zNmzdPjz76qK644go99dRTuvHGGxUUFKRjx45p48aNevPNN53LBw4cWJg1AwAA4P9z+wKIa665RocPH9bOnTtVo0aNbMsPHz6s1q1bq06dOtq2bdslF+ppXAABAEDJwQUQ/3D71iR79uzRwIEDcwxyklSrVi0NGDBAe/bscfclAAAAcBFuh7mKFSvKz88vz3UqVKigihUruvsSAAAAuAi3w1y/fv20aNEipaWl5bg8NTVVixYt0q233up2cQAAAMib22HulVdekZ+fn3r16qVNmza5LAsLC1OvXr3k7++vl1566ZKLBAAAQM7yfTVrvXr1srWlpKRo+/btuuGGG+Tt7a0rrrhCcXFxzqN11atX1zXXXKOIiIjCqxgAAABO+Q5zGRkZ2abn8vHxUZ06dVzaLrwgIiMj4xLKAwAAQF7yHeYOHjxYhGUAAADAHW6fMwcAAADPu+S5WSUpLS1N+/btU2JiogICAtSoUSN5exfKpgEAAJCHSzoyFx8frxEjRigwMFAtWrRQx44d1aJFC1WsWFEjR47UiRMnCqtOAAAA5MDtw2fx8fFq166d/vzzT1WuXFk33nijqlevrpiYGP3yyy+aNWuWNmzYoLCwMFWuXLkwawYAAMD/5/aRuRdeeEF//vmnxo8fr0OHDmn58uX6+OOPtWzZMh06dEhPPvmkwsPD9eKLLxZmvQAAADiPZYwx7jyxXr16qlu3rtauXZvrOt26ddPBgwd14MABtwssKfI72S0AACh6I6Z7ugLpwzFFu/38Zg+3j8wdPXpU7du3z3Od9u3b6+jRo+6+BAAAAC7C7TAXGBioQ4cO5bnOoUOHFBgY6O5LAAAA4CLcDnOdO3fWV199pdWrV+e4fM2aNfrqq6/UpUsXd18CAAAAF+H21ayTJ0/WkiVLFBoaqt69e6tz584KCgrSsWPHtH79ei1btkzly5fXpEmTCrNeAAAAnMftMNesWTOtWLFCw4cP15IlS7RkyRJZlqWs6ymuuuoqffLJJ2rWrFmhFQsAAABXlzRNQ8eOHRUeHq6ffvpJO3bscM4A0bp1a91www2yLKuw6gQAAEAO3A5z9913n5o3b67HH39cHTt2VMeOHQuzLgAAAOSD2xdAfPHFFzp+/Hhh1gIAAIACcjvMXXXVVYqOji7MWgAAAFBAboe5++67T0uWLNGRI0cKsx6nrVu3qnfv3qpYsaL8/PzUrl07LViwwO3tnTx5UjVr1pRlWbrpppsKsVIAAADPcfucuf79+2vdunXq0KGD/u///k/XXXedgoKCcrzooU6dOgXa9rp16xQaGipfX18NHjxY/v7+WrhwoQYNGqSoqCiNGzeuwPWOHj1aCQkJBX4eAABASeb23KwOh8N5K5K8rlq1LEtpaWn53m5aWpoaN26sw4cPa9OmTWrVqpUkKSEhQW3bttXBgwe1f/9+hYSE5HubCxcu1B133KF33nlHo0ePVmhoqJYvX57v50vMzQoAQEnC3Kz/cPvI3NChQ4vk1iNr165VRESE7r33XmeQkzKnD5s4caKGDx+uOXPm5PtmxLGxsXrooYd0zz33qE+fPho9enSh1wwAAOApboe5Tz75pBDL+Mf69eslSb169cq2LDQ0VJK0YcOGfG/vwQcflJeXl958802+ZgUAAKXOJd00uCiEh4dLkho0aJBtWXBwsCpUqOBc52Lmzp2rb775Rt99950qVapEmAMAAKXOJYe55ORkLV26VDt27FBCQoICAwPVunVr9e7dW2XLli3w9rICV2BgYI7LAwIC8hXKjh49qn//+9+68847deuttxa4juTkZCUnJzsfJyYmSpJSU1OVmpoqKfO8QS8vL6WnpysjI8O5blZ7Wlqazj8l0cvLSw6HI9f2rO1m8fbO/PFceM5hbu0+Pj7KyMhQenq6s82yLHl7e+fanlvt9Ik+0Sf6RJ/oU8nuk488rTh+TvlxSWHu+++/18iRIxUbG+vyw7csS9WqVdMHH3ygvn37XspLuO2BBx6Qj4+P3nrrLbeeP3XqVD333HPZ2leuXKny5ctLyrxKt3Xr1tq1a5ciIyOd6zRq1EiNGzfWli1bFBsb62xv1aqVQkJCtHHjRp0+fdrZ3r59e1WrVk0rV650+cF17dpV5cqV09KlS11q6N27t86ePat169Y527y9vdWnTx/FxcUpLCzM2e7v769u3bopKipKO3fudLZXrVpVHTp0UHh4uPbt2+dsp0/0iT7RJ/pEn+zRp4IfqClsRf1z2rZtW77qcPtq1jVr1uimm26Sl5eX7rnnHt14440KCgrSsWPHtHHjRs2dO1fp6elasWKFunXrlu/tDhgwQF9//bV++eUXtWnTJttyf39/VapUyaXTF5ozZ46GDx+ur776SnfccYez/eDBg7ryyivzdTVrTkfmateurbi4OOcVJZfHJx/6RJ/oE32iT/Sp5PXp4RmePzL3/r+L9ucUHx+vKlWqXPRqVrfDXMeOHbVr1y79/PPPuvrqq7Mt37Vrl2644Qa1atVKP/zwQ763O3HiRE2dOlVffvmlBg8e7LIsJiZG1atXV7du3bRmzZpctzFmzBi9+eabF32tli1buiTnvHBrEgAASg5uTfIPt79m3bFjh+66664cg5wktWjRQgMHDtS8efMKtN3OnTtr6tSpWrlyZbYwt2LFCuc6eWnfvr2SkpKytSclJWn+/PmqVauWQkNDC3wzYwAAgJLG7TBXvnx5Va1aNc91qlWr5jy/LL+6d++uevXq6YsvvtC///1vl5sGT5kyRWXKlNHQoUOd60dHRyshIUHVq1d3XjQxaNAgDRo0KNu2Dx48qPnz56tZs2aaNWtWgeoCAAAoidyem7VHjx5avXp1nuusXr1aPXv2LNB2vb29NWvWLGVkZKhTp04aOXKkxo0bp5YtW2r//v2aMmWK6tat61x/woQJatKkib799lt3ugEAAGBrboe5adOm6fjx4xo6dKiioqJclkVFRemee+5RXFycpk2bVuBtd+3aVT/++KNuuOEGzZ8/X++++66CgoI0b948t+ZlBQAAKK3cvgCiW7duOnnypHbt2iUvLy/VqVPHeTVrZGSk0tPT1aJFC1WqVMn1BS0rz4sXSiougAAAoOTgAoh/uH3OXNa0W1LmJcgHDhzQgQMHXNb59ddfsz2vKOZzBQAAuFy5HebOvx8KAAAAPMPtc+YAAADgeYUW5iIjI7Vx48bC2hwAAADyodDC3Mcff6yuXbsW1uYAAACQD3zNCgAAYGOEOQAAABsjzAEAANhYoYW5wMBAJq4HAAAoZoUW5saMGaO//vqrsDYHAACAfOBrVgAAABvL9wwQWfeQa9u2rXx9fQt0T7lOnToVvDIAAABcVL7DXJcuXWRZlvbs2aOGDRs6H+dHenq62wUCAAAgd/kOc5MmTZJlWbriiitcHgMAAMBz8h3mnn322TwfAwAAoPhxAQQAAICNuR3mTp8+rQMHDig1NdWlff78+RoyZIjuv/9+bd++/ZILBAAAQO7y/TXrhf7v//5Pc+fO1bFjx+Tj4yNJevfddzV69GgZYyRJ8+bN07Zt29S4cePCqRYAAAAu3D4yt2HDBvXo0UPly5d3tr300kuqWbOmNm7cqAULFsgYo1dffbVQCgUAAEB2bh+Zi46O1k033eR8vGfPHkVFRemVV15Rx44dJUlff/11ge5HBwAAgIJx+8hccnKyypQp43y8YcMGWZalXr16Odvq1aunI0eOXFqFAAAAyJXbYa5WrVratWuX8/HixYtVuXJltWjRwtl24sQJVahQ4dIqBAAAQK7c/pr15ptv1owZM/TEE0/I19dXy5cv19ChQ13W2b9/v+rUqXPJRQIAACBnboe5CRMmaNGiRXr99dclSdWrV9fzzz/vXH78+HH99NNPGj169KVXCQAAgBy5HeaCg4P1+++/a82aNZKkTp06KSAgwLk8Li5Or776qkJDQy+9SgAAAOTI7TAnSeXKldMtt9yS47KmTZuqadOml7J5AAAAXATTeQEAANjYJR2ZS09P14IFC7R69WodPXpUycnJ2daxLMv5VSwAAAAKl9th7syZM+rVq5c2bdokY4wsy3JO4yXJ+diyrEIpFAAAANm5/TXrf//7X4WFhem5555TXFycjDF69tlnFR0drfnz56tevXoaMGBAjkfrAAAAUDjcDnPffPON2rVrp6efflqVK1d2tgcFBWnAgAFat26dVq9ezdysAAAARcjtMBcZGal27dr9syGHw+UoXK1atdSnTx/NmTPn0ioEAABArtwOc35+fnI4/nl6YGCgoqOjXdYJDg5WZGSk+9UBAAAgT26HuZCQEJegdvXVV2vt2rXOo3PGGK1Zs0bVq1e/9CoBAACQI7fDXPfu3bVu3TqlpaVJkoYNG6bIyEi1b99e48ePV8eOHbVz507179+/0IoFAACAK7dvTTJixAhVqVJFsbGxql69uu677z7t2LFDM2fO1M6dOyVJ/fv317PPPltIpQIAAOBCljn/5nCFIDY2VgcOHFBISIiCg4MLc9MelZiYqMDAQCUkJLjMQQsAAIrfiOmerkD6cEzRbj+/2eOSZoDISdWqVVW1atXC3iwAAABywNysAAAANub2kbl69erlaz3LshQREeHuywAAACAPboe5jIyMHOddTUhI0KlTpyRJ1atXV5kyZdwuDgAAAHlzO8wdPHgwz2Vjx47VsWPHtGrVKndfAgAAABdRJOfM1a1bV/Pnz9fJkyf11FNPFcVLAAAAQEV4AYSPj4969uypBQsWFNVLAAAAXPaK9GrWv//+W/Hx8UX5EgAAAJe1IgtzP/zwg7788ks1atSoqF4CAADgsuf2BRDdunXLsT0tLU1HjhxxXiAxadIkd18CAAAAF+F2mFu/fn2O7ZZlqVKlSurVq5fGjh2rnj17uvsSAAAAuIhLus8cAAAAPOuS52Y9fvy4jhw5ooyMDNWsWVPBwcGFURcAAADywa0LIJKTk/XKK6+oQYMGql69uq699lq1bdtWNWvW1BVXXKHHH388z5sKAwAAoHAUOMxFRUXpuuuu04QJExQREaHq1aurbdu2atu2rapXr674+Hi9+eabuvbaa7V69Wrn86Kjo7nnHAAAQCErUJhLTU1V7969tXv3bt15553as2ePDh8+rLCwMIWFhenw4cPas2ePhgwZovj4eN122206ePCgIiIi1LFjR+3du7eo+gEAAHBZKtA5c++//75+//13TZ48WZMnT85xnUaNGumzzz5Tw4YNNXnyZA0ZMkQHDx5UXFyc2rRpUyhFAwAAIFOBjswtWLBA9evXz9e9455++mk1aNBAYWFhOnfunFasWKE+ffq4XSgAAACyK1CY++OPP9SrVy9ZlnXRdS3Lcq67efNmdenSxd0aAQAAkIsChbmkpCQFBgbme/2AgAB5e3urfv36BS4MAAAAF1egMFetWjX9+eef+V4/IiJC1apVK3BRAAAAyJ8Chbn27dtr2bJliomJuei6MTExWrJkiTp27Oh2cQAAAMhbgcLcgw8+qKSkJN1+++2Ki4vLdb0TJ07o9ttv199//61Ro0ZdcpEAAADIWYFuTdK1a1eNGDFCH374oZo0aaJRo0apW7duql27tqTMGwqvWbNGH374oeLi4jRy5EgufAAAAChCBZ6bdebMmQoICNAbb7yhqVOnaurUqS7LjTFyOBx64oknsi0DAABA4SpwmPPy8tKrr76qkSNH6pNPPlFYWJjzHLrg4GB16NBBw4YNU4MGDQq9WAAAALgqcJjL0qBBA7344ouFWQsAAAAKqEAXQAAAAKBkIcwBAADYGGEOAADAxghzAAAANkaYAwAAsDHCHAAAgI0R5gAAAGyMMAcAAGBjhDkAAAAbI8wBAADYGGEOAADAxkpsmNu6dat69+6tihUrys/PT+3atdOCBQvy9VxjjJYtW6aHHnpILVq0UGBgoMqXL6+WLVtqypQpOnfuXBFXDwAAUDy8PV1ATtatW6fQ0FD5+vpq8ODB8vf318KFCzVo0CBFRUVp3LhxeT4/OTlZvXv3VtmyZdWlSxeFhobq3LlzWrFihZ566il99913Wr9+vcqXL19MPQIAACgaljHGeLqI86Wlpalx48Y6fPiwNm3apFatWkmSEhIS1LZtWx08eFD79+9XSEhIrttITU3VK6+8oocffliVKlVyae/fv78WLVqkV155RePHj893XYmJiQoMDFRCQoICAgLc7h8AALh0I6Z7ugLpwzFFu/38Zo8S9zXr2rVrFRERobvuussZ5CQpMDBQEydOVEpKiubMmZPnNnx8fPTUU0+5BLms9gkTJkiSNmzYUOi1AwAAFLcSF+bWr18vSerVq1e2ZaGhoZIuLYj5+PhIkry9S+Q3zAAAAAVS4hJNeHi4JKlBgwbZlgUHB6tChQrOddzx0UcfSco5LJ4vOTlZycnJzseJiYmSMr+qTU1NlSQ5HA55eXkpPT1dGRkZznWz2tPS0nT+t9heXl5yOBy5tmdtN0tW4ExLS8tXu4+PjzIyMpSenu5ssyxL3t7eubbnVjt9ok/0iT7RJ/pUsvvkI08rjp9TfpS4MJeQkCAp82vVnAQEBDjXKahly5bp/fffV5MmTXT//ffnue7UqVP13HPPZWtfuXKl88KJOnXqqHXr1tq1a5ciIyOd6zRq1EiNGzfWli1bFBsb62xv1aqVQkJCtHHjRp0+fdrZ3r59e1WrVk0rV650+cF17dpV5cqV09KlS11q6N27t86ePat169Y527y9vdWnTx/FxcUpLCzM2e7v769u3bopKipKO3fudLZXrVpVHTp0UHh4uPbt2+dsp0/0iT7RJ/pEn+zRp1vlaUX9c9q2bVu+6ihxF0D06tVLq1atUnh4uOrXr59tec2aNZWUlFTgQLd161Z1795d3t7e+uGHH9SsWbM818/pyFzt2rUVFxfnPAnx8vjkQ5/oE32iT/SJPpW8Pj08w/NH5t7/d9H+nOLj41WlSpWLXgBR4o7MZR2Ryy2sJSYmZruw4WJ++eUX9erVSw6HQytWrLhokJOksmXLqmzZstnafXx8nOfdZfHy8pKXl1e2dXM7Ly+39gu36067w+GQw5H9VMjc2nOrnT7Rp4K20yf6JNGn3GosaDt9KnifPMFTP6dsr5evtYpR1rlyOZ0XFxMTo6SkpBzPp8vNL7/8op49eyojI0MrVqzQddddV2i1AgAAeFqJC3OdO3eWlHlu2oVWrFjhss7FZAW59PR0LV++XNdff33hFQoAAFAClLgw1717d9WrV09ffPGFy8mDCQkJmjJlisqUKaOhQ4c626Ojo7V3795sX8tu27ZNPXv2VFpampYtW6b27dsXVxcAAACKTYk7Z87b21uzZs1SaGioOnXq5DKd16FDhzRt2jTVrVvXuf6ECRM0Z84cffzxxxo+fLgkKT4+Xj179tSpU6d00003adWqVVq1apXL61SsWFFjxowpvo4BAAAUgRIX5qTMS55//PFHTZ48WfPnz1dqaqqaN2+ul19+WYMGDbro8xMTE3Xy5ElJ0vLly7V8+fJs64SEhBDmAACA7ZW4W5OUVMzNCgBAycHcrP8ocefMAQAAIP8IcwAAADZGmAMAALAxwhwAAICNEeYAAABsjDAHAABgY4Q5AAAAGyPMAQAA2BhhDgAAwMYIcwAAADZGmAMAALAxwhwAAICNEeYAAABsjDAHAABgY4Q5AAAAGyPMAQAA2BhhDgAAwMYIcwAAADZGmAMAALAxwhwAAICNEeYAAABsjDAHAABgY4Q5AAAAGyPMAQAA2BhhDgAAwMYIcwAAADZGmAMAALAxwhwAAICNEeYAAABsjDAHAABgY4Q5AAAAGyPMAQAA2BhhDgAAwMYIcwAAADZGmAMAALAxwhwAAICNEeYAAABsjDAHAABgY4Q5AAAAGyPMAQAA2BhhDgAAwMYIcwAAADZGmAMAALAxwhwAAICNEeYAAABsjDAHAABgY4Q5AAAAGyPMAQAA2BhhDgAAwMYIcwAAADZGmAMAALAxwhwAAICNEeYAAABsjDBXgsyYMUN169aVr6+vrr/+em3ZsiXP9b/66is1btxYvr6+at68uZYuXeqy/Nlnn1Xjxo3l5+enSpUqqUePHtq8ebPLOi+++KI6dOig8uXLq2LFioXdJbcwDpkYh0yMA2OQhXHIxDjgQoS5EmL+/PkaO3asJk+erO3bt6tly5YKDQ3V8ePHc1z/559/1p133qn7779fO3bs0G233abbbrtNu3fvdq7TsGFDvfPOO/rtt9/0448/qm7duurVq5diY2Od66SkpGjAgAF66KGHiryP+cE4ZGIcMjEOjEEWxiET44AcGeRLQkKCkWQSEhKKZPtt27Y1jzzyiPNxenq6qVGjhpk6dWqO6w8cOND06dPHpe366683o0aNyvU1svqwevXqbMs+/vhjExgY6F7xhYhxyMQ4ZGIcGIMsjEMmxuEfD7zh+X9FLb/ZgyNzJUBKSoq2bdumHj16ONscDod69OihsLCwHJ8TFhbmsr4khYaG5rp+SkqKPvjgAwUGBqply5aFV3whYhwyMQ6ZGAfGIAvjkIlxQG4IcyVAXFyc0tPTFRQU5NIeFBSkmJiYHJ8TExOTr/UXL16sChUqyNfXV2+88YZWrVqlK664onA7UEgYh0yMQybGgTHIwjhkYhyQG8JcKde1a1ft3LlTP//8s2666SYNHDgw13MrSjPGIRPjkIlxYAyyMA6ZGAd7I8yVAFdccYW8vLx07Ngxl/Zjx44pODg4x+cEBwfna30/Pz/Vr19f7dq10+zZs+Xt7a3Zs2cXbgcKCeOQiXHIxDgwBlkYh0yMA3JDmCsBypQpozZt2mjNmjXOtoyMDK1Zs0bt27fP8Tnt27d3WV+SVq1alev65283OTn50osuAoxDJsYhE+PAGGRhHDIxDsiNt6cLQKaxY8dq2LBhuvbaa9W2bVtNnz5dZ86c0b333itJGjp0qGrWrKmpU6dKkh577DF17txZr732mvr06aN58+bpl19+0QcffCBJOnPmjF588UX169dP1atXV1xcnGbMmKEjR45owIABzteNjIxUfHy8IiMjlZ6erp07d0qS6tevrwoVKhTvIIhxyMI4ZGIcGIMsjEMmxgE5KvoLa0uHor41iTHGvP3226ZOnTqmTJkypm3btmbTpk3OZZ07dzbDhg1zWX/BggWmYcOGpkyZMqZZs2ZmyZIlzmVnz541t99+u6lRo4YpU6aMqV69uunXr5/ZsmWLyzaGDRtmJGX7t27duiLr58UwDpkYh0yMA2OQhXHIxDhk8vRtSUrSrUksY4wp0rRYSiQmJiowMFAJCQkKCAjwdDkAAFzWRkz3dAXSh2OKdvv5zR6cMwcAAGBjhDkAAAAbI8wBAADYGFezljCXwzkA+eHpcWAMMjEOmRiHTIwDY5ClJIwD/sGROQAAABsjzAEAANgYYQ4AAMDGCHMAAAA2RpgDAACwMcIcAACAjRHmAAAAbKzEhrmtW7eqd+/eqlixovz8/NSuXTstWLCgQNtITk7W888/rwYNGsjX11c1atTQyJEjdfz48SKqGgAAoHiVyJsGr1u3TqGhofL19dXgwYPl7++vhQsXatCgQYqKitK4ceMuuo2MjAzdeuutWrFihdq1a6f+/fsrPDxcs2bN0po1a7Rp0yZVrVq1GHoDAABQdErckbm0tDSNGDFCDodDGzdu1AcffKDXXntNv/76qxo2bKiJEyfq0KFDF93OnDlztGLFCt155536+eef9dJLL2nhwoWaOXOmDhw4oKeffroYegMAAFC0SlyYW7t2rSIiInTXXXepVatWzvbAwEBNnDhRKSkpmjNnzkW38+GHH0qSpk6dKsuynO2jRo1SvXr19Pnnn+vs2bOFXj8AAEBxKnFhbv369ZKkXr16ZVsWGhoqSdqwYUOe2zh37pw2b96sRo0aKSQkxGWZZVnq2bOnzpw5o19++aVwigYAAPCQEnfOXHh4uCSpQYMG2ZYFBwerQoUKznVyExERoYyMjBy3cf62w8PDdeONN+a4TnJyspKTk52PExISJEnx8fFKTU2VJDkcDnl5eSk9PV0ZGRnOdbPa09LSZIxxtnt5ecnhcOTanpqaqpRzPnn2rTgkJqpQ+3Q+b+/MXS4tLS3Pdk+PQ2KiCr1PWXx8fJSRkaH09HRnm2VZ8vb2dmn39BhI0okT+etrfvt0fntu+9iF7SVpHAqrT+78PqWc8/xn7xMnUovkfe98F/t9SjlnyZNOnEgtsve9LBf7fSoJ+0JCQma/C/t97/z2i/0+lYT3hlOniuZ9L6s9Pj5eklz2sxyZEqZnz55GkgkPD89xeY0aNUxAQECe2/jpp5+MJDNkyJAcl3/wwQdGknn99ddz3cbkyZONJP7xj3/84x//+Mc/j/6LiorKM/eUuCNzJcWECRM0duxY5+OMjAzFx8erSpUqLufglSSJiYmqXbu2oqKiFBAQ4OlyPIZxyMQ4ZGIcGIMsjEMmxiGTHcbBGKPTp0+rRo0aea5X4sJcYGCgpH++1rxQYmKiKlWqdMnbOH+9nJQtW1Zly5Z1aatYsWKer1tSBAQElNgdszgxDpkYh0yMA2OQhXHIxDhkKunjkFdWyeL5L94vcP75bBeKiYlRUlJSrufCZalXr54cDkeu59bldV4eAACAnZS4MNe5c2dJ0sqVK7MtW7Fihcs6uSlXrpzatm2rffv2ZbsnnTFGq1atkp+fn6699tpCqhoAAMAzSlyY6969u+rVq6cvvvhCO3fudLYnJCRoypQpKlOmjIYOHepsj46O1t69e7N9pTpy5EhJmee+mfOuAnn//fd14MABDRkyROXKlSvazhSzsmXLavLkydm+Hr7cMA6ZGIdMjANjkIVxyMQ4ZCpN42AZc7HrXYtfbtN5HTp0SNOmTXOZzmv48OGaM2eOPv74Yw0fPtzZnpGRod69ezun8+rcubP+/PNPffPNN6pbt642b97MdF4AAMD2StyROUnq2rWrfvzxR91www2aP3++3n33XQUFBWnevHn5mpdVyrxHy//+9z89++yzio2N1RtvvKGffvpJ999/v8LCwghyAACgVCiRR+YAAACQPyXyyBwAAADyhzAHAABgY4Q5AAAAGyPMAQAA2BhhrpTI7ToWrm8BAKB0I8yVEpZl6ciRI5KklJQU/f333852XH4I9wDywntB6cKtSWzOGKPFixdr9uzZ+u2335SUlKQWLVqoefPmatOmjVq1aqX69eurbNmyMsYQ7i4j4eHhqlatmk6fPq1y5cqpSpUqni4JJQzvCTgf+4N9EeZsbtKkSZo2bZrKly+v2rVrKzU1VSkpKYqKipIxRi1bttQdd9yhoUOHKigoyNPlFrn09HQ5HI7L9g0pOTlZX331lWbOnKkdO3bI4XCoQYMGql+/vtq0aaMOHTrommuukb+/v6dLLXLGGKWnp8vLy+uy3R+yHD9+XLGxsapSpYpOnz6tqlWrqmLFip4uCx6Qnp6u8PBwnTx5UlLm78lVV111Wfx9KM0IczZ28OBBNWvWTF26dNFrr72mxo0bKy4uTlFRUYqIiNDGjRu1YsUKhYeHq2XLlpoyZYpuvvlmZWRkyOEoXd+wR0VFqXbt2s7HGRkZMsbIy8vLg1UVv3HjxunNN99USEiIGjRoIB8fH506dUq//fabEhMTVbt2bd1yyy2677771KZNG0+XW2QiIiJ01VVXOR9nZGQoIyND3t7eHqyq+EVHR+upp57SqlWrdOTIEfn7++vKK69UkyZNdP3116tjx45q3rx5qZibMjdZR5su133gfPv27dOECRO0dOlSpaSkqGzZsqpUqZLq1q2r9u3b66abblKHDh3k5+fn6VJRUAa29fzzz5vKlSub1atXG2OMSU1NdVmekJBgfv75ZzNmzBhjWZYJDg42O3bs8EClReuvv/4ylmWZ0NBQ88knn5i4uDiX5WlpaSY9Pd0YY0xGRoYxxpjk5ORir7OoHThwwPj6+poBAwaY48ePG2OMSUxMNJGRkWbz5s3m1VdfNR06dDA+Pj6mbt26Zs6cOcaYf8aktPjzzz+NZVmmSZMm5tVXXzXR0dEuy9PS0kxaWpox5p++JyUlmZiYmGy/Q3YWHR1t2rVrZyzLMjfffLMZMGCAGTRokGnXrp0pX768sSzLNGvWzDz33HPm6NGjni63yCQkJJhDhw65tJ2/D1wujhw5Ypo3b24cDocZNmyYGTdunHnyySfNLbfcYgIDA41lWaZSpUrmvvvuM5s3b/Z0uUUiPj7erF+/3pw7d87TpRQ6wpyNDR061FSvXt3ExMQYY/75w5TTH+d58+aZwMBA065du2KtsThMmTLFWJbl/HfFFVeYYcOGmSVLlmT745wV4t577z3TvXt3s2/fPk+UXCRefPFFU7lyZbNmzRpjjMn2xyo1NdUcOHDATJ8+3VStWtVYlmWWL1/uiVKL1Msvv+yyP1iWZbp06WLmzp1rUlJSXNY9f39o27at2b59uydKLhKTJk0ygYGBZvr06c62kydPmqioKLNx40bz9NNPm6ZNmxqHw2Hat29vfvzxR2NM6Qv3Y8eONZZlmRtvvNF89NFH5syZMy7LU1NTnR/2skRHR5tjx46VqrF4+umnTaVKlcysWbOcbcnJySYlJcVERkaa999/39xwww3G4XCYpk2bmsWLFxtjStf+8MQTTxjLssw111xjXnjhBbN79+5c183q9/79+83OnTuzvXeUNIQ5G5s2bZqxLMt89dVXzrYL35TO/0W89957zRVXXGH27t1bbDUWh1tuucX4+/ubWbNmmWHDhjmPOliWZerXr2+eeOIJs2XLFpfn/Otf/zKWZZmkpCQPVV34Hn74YVOxYkUTFRVljMn7TXjlypWmevXqplGjRqXuU2r//v1NuXLlzBdffGEmTZpkmjZt6twffHx8zODBg52BN0tp3B+aNm1qbrnlFudR2gv3h3Pnzplff/3VGXYaN25sjh075olSi1Tz5s2zhfvbb7/dLFmyxGW9rPFJTEw0Q4YMMaGhoaXqSG3Lli3NTTfd5PwZ5/T+EBsba95++21TuXJl4+/vb/7444/iLrNItWrVyjgcDlO5cmXnvtC1a1fz/vvvm8OHD2dbPykpydx5552mXbt2hDkUnY0bN5oKFSqYxo0bm61bt7osy8jIcAa7rP9OmTLF+Pn5ZQs2dnb8+HHTtm1bU7NmTWfb2bNnzeeff266d+/u8gZ+3XXXmbfeesssWLDAVK9e3fTt29eDlRe+2bNnG8uyzIwZM5xv1GlpabmGugkTJpgKFSqUqqNRsbGxpkOHDiY4ONjZlpycbJYtW2buv/9+U716def+ULVqVfOf//zHzJ07t9TtDzExMaZJkyamZ8+eF103NTXVvPXWW8ayLPPkk08WQ3XFJyIiwlStWtV07tzZbNy40Tz00EOmTp06zn2gUqVK5uGHH3b5HdixY4epVKmS6dy5s+cKL2RxcXHm2muvzdc3M6mpqWbevHnGsiwzatSoYqiuePz111+mRo0apl27dmbnzp3mhRdeMJ06dTK+vr7Gsizj7+9vBg4caL799ltz4sQJY4wxW7ZsMZUrVzZdu3b1cPUXR5izqaw/0B9++KHx8vIylmWZkSNHmtWrV5vExMRs6//999/mzjvvNFWqVCnuUotUZGSkufHGG02fPn2MMdnPhTt69KiZNm2ay6fzrF/eCz+Z291vv/1matasaSpXrmwWLVrksiwjI8P5tWtWuH/99deNr6+v+fnnn4u91qISExNjbrrpJtOzZ0+Tmpqa7dN0bGys+fTTT02/fv2Mn5+fS9gvLftD1ge5O+64wwQEBDjPfzp/H8hJ8+bNTbdu3czp06eLq9Qit3LlSmNZlhk3bpyz7dSpU2b+/PlmwIABznPFLMsyV111lXnppZfMk08+aSzLcn7NaHdZfytGjBhhLMsyixYtcn7Iy+vI4w033GCuu+46Z7Cxu7Vr1xqHw2H+/e9/O9tOnz5tVqxYYR5//HHTokUL575Qs2ZNM2bMGDNq1Cjb7AuEOZtLSkoy7777rqlWrZqxLMtUq1bN3HrrrWbKlClm9erVJj4+3mzevNmMGjXKlClTxuVNrTRISUkxa9euNT///LPLRQ7nX/SQZd++feaRRx4xlmWZypUre6LcIpP1hr1s2TJTq1Yt5wUhCxYsMPHx8dnWT0pKMgMHDix14d4YY8LDw83u3buz7Q8XHqGMjIw0zz//vClfvrypVKmSJ0otUh988IHzXLELzw1KT093GZOEhATTu3dvc/XVV3ui1CLz888/m9q1a5sPPvjAGJP9IrFDhw6Zt99+23Tp0sUl2JfG/WHp0qXGsizTsGFDs2LFCpdlWReEZO0Pp06dMrfddptp2LChJ0otEjt37jQNGjQwb731ljEm+znF0dHR5ssvvzTDhg0zV155pe32BcKcTV34hykpKclMnz7dtG/f3nh7ezt3RIfDYcqUKWMsyzL33ntvjucFlAYXBrcsWZ8+s35xt2zZYsqXL29GjhxZnOUVm9TUVPP111+7fMps2bKleeSRR8zChQvNnj17zDfffGMGDRpkvLy8zH/+8x9Pl1yssoJd1v4QFhZWqveHl156yTgcDmNZlhk2bJhZsWKFOXv2rHN51vvI6tWrTc2aNc2IESM8VWqRSElJMb///rvzIjFjcj9CuX//fnP33Xcby7LMI488UpxlFpvPP//cBAUFOc8Vmz9/vst5oln7w5IlS0yNGjVK3f6QmJiY7cNtTn87jhw5YkaPHm0syzIPP/xwcZV3SbjPXCkTFxen/fv3a9OmTfrhhx+Unp6uhg0bqkmTJrr//vs9XV6hy7oprDFGGRkZF72v3KOPPqoZM2Zo69atpfo+a5L03XffadasWVqxYoXS09MlZU7vZoyRj4+PHnnkET355JOX9c1CR48erZkzZ5a6/cH8/3urnTp1Sh999JFefvllxcbGysvLS23atNENN9ygrl27KjAwUFu3btU777yj06dPa+3atWrevLmnyy82F75vPP/883r22WdL3f6QJTk5WQsXLtTrr7+u7du3S5KqVaumzp07q2fPnipbtqx2796t2bNnq2zZslq5cqWaNWvm4aqLx4X7wuTJk/XCCy/YZl8gzNnQ8ePH9dtvv2n//v1KSkpS27Zt1bhxY11xxRXZwkxycrLLDUHNZTxdS2JiokaNGqV169YpJibG0+UUiZxCbUxMjNatW6effvpJPj4+qlGjhho3bqy+fft6sFLPO3PmjB555BEtXbpUx48f93Q5herC3/Nz585pzpw5+vTTTxUWFpZt/aZNm2rChAkaMmRIcZZZ5LJukJ71oS8nWWO1f/9+9e3bV2lpaYqIiCjmSouXMUaLFi3SBx98oJUrVyotLc1lefv27fX000/r5ptv9lCFnnXgwAHddtttOn36tP766y9Pl5MvhDmbWbZsmf773/9me0OuXLmyunfvrkGDBqlv377y8fFxLiuNMz5IuYfaKlWqOO/yfuGbeHJyso4fP+4yW4TdFeTne+F4lKZw7+5+npiYqICAgCKoqGSKjIzU6tWrtXv3bgUHB6tatWrq2LGj6tev7+nSPGrfvn267bbb1LdvX73yyiueLqdImMxTq1x+TxISErR+/XodOHBANWrUUIUKFXTdddepWrVqHqzUs/766y+NGjVKnTt31lNPPeXpcvKFMGcjUVFR6tKli86cOaPhw4era9euOnDggHbs2KFff/1Vu3btUnJyspo2baqJEyfqjjvuUJkyZUrVH+wseYXaHj16OEPt5TZ1T26B5vw5a9PS0kr9uOQn2KWlpcmyrFI35dvy5cu1e/du7dy5U0FBQbr22mtVv3591a5dW1WqVHH5oFeanT8O1apV03XXXaf69esrJCREVapUcZ6eceF7Y2n7/cjtqGR6erosyyqVH/QvlNeR2aJ4nkcU4/l5uERPPfWUqVSpklm4cGG2ZVFRUWb+/PlmyJAhzhPfX375ZQ9UWfQiIyNNvXr1TFBQkHnyySfN8uXLzcyZM82IESNM27Ztnbceufrqq83nn3/uvF1JbhdJ2FVMTIwZO3asWb58uTl58qTLsoyMjFJ15/a8MA6ZTp48af7v//7PWJblchGUZVmmSpUqpl+/fubjjz/OdquJ0jY++R2HC/eV0ja9V043kM/pPfD89ovdrsRu8jsGF7LjdI+EORu5/vrrTZcuXUxsbKwxxrhcpXm+tWvXmtatW5uyZcua2bNnF3eZRY5Qm2nSpEnGsixz5ZVXmj59+phXX33VbNmyJduMDlm3oTDGmHXr1plly5Z5otwiwzhkeuWVV0z58uXN7bffbtatW2f27dtn5s2bZ5577jlzyy23OKdwu+aaa8y3337r6XKLDOOQaebMmWbgwIFm8eLF2e4dmJ6eXuo+3ObkchoDwpxNnD592vTo0cM0btzYObfg+TvihZ84tm/fbipVqmT69evnXF5aEGoztWrVypQpU8a0a9fOefuZunXrmiFDhphZs2aZPXv2uKx/5swZ069fP+NwOFxuT2F3jEOmkJAQ06dPHxMXF5dt2ZEjR8zixYvNyJEjnUerPvzwQw9UWfQYh0x169Z13iT9+uuvN88884wJCwvL9rcg60jcmTNnzBtvvGHWrl3riXKLxOU0BoQ5G8m6M3lOweT8nTMr1N16662mYcOG5uDBg8VWY1Ej1GaKjIw0devWNW3atDEpKSkmLCzMPPPMM6Zly5bGsizj5eVlWrRoYUaPHm0WLFhgEhISzJYtW0xwcHCpmraKcci0Z88eU6FCBTNx4kRnW05HHpKTk82SJUtMvXr1TOXKlUvV7B/GMA5Zdu/ebSzLMtdee63p2bOn81uKChUqmNDQUPPmm29m+5Dzww8/GMuyzA033OChqgvX5TYGhDkbOXz4sHNaqkcffdRs27Yt25GFrE8YCQkJZsCAAaZOnTqeKLVIEWqN2bx5s6lcubIZNmyYMcY4Z7w4duyYWbZsmXnwwQdNSEiIsSzLlC9f3nTq1Mk5V+2FU33ZGeOQ6Y8//jC1atUygwYNMsZkvg9c+CHn/N+N7777rlSegsA4ZPryyy+NZVnm9ddfN8Zkzn7z8ssvm1atWjlDTfXq1c2dd95pPv30UxMfH29ee+0120xdlR+X2xgQ5mzm22+/dU41cu2115oXXnjBrFu3zhw8eNAl2M2dO9dUrVq1VE2UnIVQmzll1b/+9S/z+eef57g8JSXFHDx40Hz22Wdm4MCBpnLlyraamia/GId/XH/99cbf398sXbo027KsAJMVbE6cOGGuvPJKc8cddxRrjcWBcTDm/fffN5Zl5TgGW7ZsMY8//ripXbu2M9Q0bNjQBAcHm8DAwOIvtohcbmNAmLOBC78aPHHihHniiSdMnTp1nPOxduvWzdx9991m5MiR5p577jFly5Y1jRs3Nnv37vVQ1UWLUJs5f2JO5wWdL+uP1nvvvWerqWkK4nIfh6z3h82bN5uaNWsay7LMmDFjzObNm7N9yMm6KOTnn382NWrUcJl03O4Yh0wZGRkmLCzMPP744+bPP/90aT/f2bNnzeLFi82wYcNMYGCgsSzLjB49urjLLRKX4xgQ5mwiayeMiopy/mH67bffzNSpU01oaKgz2GVNIt+tW7dsk2vbHaE2U07n/WV9vZib8ePHG8uyzLZt24qytGLFOLhKS0szn3zyialevbqxLMs0a9bMPP744+arr74yv//+u3NcDh8+bO68807j7e3NOJTicTh9+nSut9i48HfnkUceMZZlmR07dhRDZcXnchoDbhpcwqWlpemnn37SRx99pP3798uyLJUvX17XXXedBg4cqNatW8sYo6ioKJ09e1YHDhxQ48aNVbt2bXl7e5e6GwZn9efw4cOqUaOGHA6Hdu/ercWLF2v9+vXas2ePoqKiJEmVKlVSq1at9NZbb5W6+QWzxiEmJkbVqlVzufHn+TcIlqTDhw+rT58+Onr0qGJjYz1VcpFgHLKLjY3VO++8owULFmj//v0qX768atasqQoVKqhy5crau3evYmNjde+992rmzJmeLrfIMA55y/rdiYiI0KBBg5SQkKDw8HBPl1WsStMYEOZKuGnTpumFF17Q6dOnVb9+fXl5eWnfvn3O5U2bNtXDDz+sO+64o1RPv0KozXThODgcDpUrV04tW7ZU//791aFDh2zPiYuL02effaYaNWpo0KBBHqi68DEO2Znz5uU9e/aswsPDtXXrVv3000/avHmz9u7dq6pVq6p27dp64IEHdPfdd8vPz8/TZRc6xqFgFi9erH79+mn8+PF6+eWXPV2OR5SKMfDA0UDk04EDB4yfn5+58cYbzYEDB8zhw4dNamqqiYqKMjNnzjRdu3Z1frXarVs3s3XrVk+XXGReffVVExAQYCzLMg0aNDCNGzd2ubN7s2bNzIwZM8yxY8c8XWqRutg4NGnSxLz++usmOjra5XnJycml6gaZjEP+pKenmzNnzpjU1FQTFxdX6k69yK/LcRzyexummJgY88knn2SbGaQ0uJzGgDBXgj3zzDOmWrVqZvXq1c62C3fOXbt2maFDhxpfX1/TqFEj88svvxR3mUWOUJupIOPQvXv3UnkekDGMQ5a///7b7N271/z999/ZlqWnp7u8V1z4vlGaAi3jkCmvcbiY0jKV2eU8BoS5Euxf//qXqVevnjl06JAx5p/bbWRkZGTb8aZPn24syzLDhw8v9jqLGqE206WMQ2m5WbIxjEOWqVOnmmuvvdZMmTLFrF271hw5ciTb+8KF91U7fvx4qZp70xjGIUt+xuFCpW0cLucxIMyVYC+88IKxLMv8/vvvua5z/htU//79TZ06dUxERERxlFdsCLWZGIdMjEOmrNtveHt7mypVqpi+ffuat99+22zZsiXHW7UkJSWZJ554wtx7772l6ogU45DpUsbB7kelslzOY0CYK8F+/PFHY1mWadWqlVmzZk2Ol1if/wds4sSJpnz58ubXX38t7lKLFKE2E+OQiXHIvJt9hQoVTIcOHcw777xjbr31VlOtWjVjWZYJCQkxw4YNM5999pnZvXu3OXnypDHGmE2bNpnAwEBz6623erT2wsQ4ZGIcGAPCXAmWlpZmxo0b5zyh+5133jExMTE5rhsfH2+GDh1qqlatWsxVFj1CbSbGIRPjYMyiRYuMt7e3efbZZ40xxhw8eNCsWLHCPPvss6ZTp06mQoUKxtvb27Ro0cKMGTPGLF++3HmPPTtOVZQbxiET48AYEOZs4L333jNXXXWVsSzL1KxZ04wePdosWbLE7Nq1y/z+++/myJEj5j//+Y/x9fU1Y8eO9XS5hY5Qm4lxyMQ4GPPVV18Zy7LM/PnzXdpTUlJMeHi4+frrr81jjz1mWrZsacqUKWP8/PxM+fLlS900ZoxDJsaBMSDM2UBGRobZv3+/GT9+vMtcckFBQaZWrVrGy8vLWJZl7rrrLhMVFeXpcovM5R5qszAOmS7nccjIyDB//PGHOXDggPPxhZKSksz27dvNl19+aXr16uWcy7g0YRwyMQ6MAWHOZpKSkszatWvNmDFjzMCBA02XLl1Mv379zNy5c7PNP1jaEGozMQ6ZGIec5fRH7NFHHzWWZZnt27d7oCLPYBwyMQ6XxxgwA4SNpaamysfHx9NleMSZM2e0ZcsWff/99zp69KiOHz+ugIAADRw4UP3795evr6+nSywWjEMmxiG7jIwMORwOHTx4ULfeeqtOnjypyMhIT5dV7BiHTIxD6R4Db08XAPddrkFOkvz8/NS1a1d17dr1sg61jEMmxiG7rHlqjxw5otTUVD388MMersgzGIdMjEPpHgOOzAFAKWaM0eHDh1W5cuXLeg5SxiET41A6x4AwBwAAYGMOTxcAAAAA9xHmAAAAbIwwBwAAYGOEOQAAABsjzAEAANgYYQ4AAMDGCHMAAAA2RpgDAACwMcIcAACAjf0/SO1gh5hmP28AAAAASUVORK5CYII=", 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" - ] - }, - "execution_count": 49, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ideal_distribution = Statevector.from_instruction(qc).probabilities_dict()\n", - "\n", - "plot_histogram(ideal_distribution)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 2: Optimize problem for quantum execution.\n", - "\n", - "Next, we transpile the circuits for our backend. We're going to compare the performance of the transpiler with `optimization_level` set to `0` (lowest) against `3` (highest). The lowest optimization level just does the bare minimum needed to get the circuit running on the device; it maps the circuit qubits to the device qubits, and adds swaps gates to allow all 2-qubit operations. The highest optimization level is much smarter and uses lots of tricks to reduce the overall gate count. Since multi-qubit gates have high error rates, and qubits decohere over time, the shorter circuits should give better results.\n", - "\n", - "In the following cell, we transpile `qc` for both values of `optimization_level`, print the number of CNOT gates, and add the transpiled circuits to a list. Some of the transpiler's algorithms are randomized, so we set a seed for reproducibility.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "CNOTs (optimization_level=0): 27\n", - "CNOTs (optimization_level=3): 14\n" - ] - } - ], - "source": [ - "# Need to add measurements to the circuit\n", - "qc.measure_all()\n", - "\n", - "circuits = []\n", - "for optimization_level in [0, 3]:\n", - " t_qc = transpile(qc, backend, optimization_level=optimization_level, seed_transpiler=0)\n", - " print(f\"CNOTs (optimization_level={optimization_level}): \", t_qc.count_ops()[\"cx\"])\n", - " circuits.append(t_qc)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Since CNOTs usually have a high error rate, the circuit transpiled with `optimization_level=3` should perform much better.\n", - "\n", - "Another way we can improve performance is through [dynamic decoupling](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-provider/qiskit_ibm_provider.transpiler.passes.scheduling.PadDynamicalDecoupling#paddynamicaldecoupling), where we apply a sequence of gates to idling qubits. This cancels out some unwanted interactions with the environment. In the following cell, we add dynamic decoupling to the circuit transpiled with `optimization_level=3`, and add it to our list.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit.transpiler import PassManager\n", - "from qiskit_ibm_runtime.transpiler.passes.scheduling import (\n", - " ASAPScheduleAnalysis,\n", - " PadDynamicalDecoupling,\n", - ")\n", - "from qiskit.circuit.library import XGate\n", - "\n", - "# Get gate durations so the transpiler knows how long each operation takes\n", - "durations = backend.target.durations()\n", - "\n", - "# This is the sequence we'll apply to idling qubits\n", - "dd_sequence = [XGate(), XGate()]\n", - "\n", - "# Run scheduling and dynamic decoupling passes on circuit\n", - "pm = PassManager([ASAPScheduleAnalysis(durations), PadDynamicalDecoupling(durations, dd_sequence)])\n", - "circ_dd = pm.run(circuits[1])\n", - "\n", - "# Add this new circuit to our list\n", - "circuits.append(circ_dd)" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "execution_count": 52, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "circ_dd.draw(output=\"mpl\", style=\"iqp\", idle_wires=False)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 3: Execute using Qiskit Primitives.\n", - "\n", - "At this point, we have a list of circuits transpiled for our system. In the following cell, we create an instance of the sampler primitive, and start a batched job using the context manager (`with ...:`), which automatically opens and closes the Batch for us. This is where we pass the `skip_transpilation=True` argument.\n", - "\n", - "Within the context manager, we sample the circuits and store the results to `result`.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "metadata": {}, - "outputs": [], - "source": [ - "with Batch(service=service, backend=backend):\n", - " sampler = Sampler()\n", - " job = sampler.run(\n", - " circuits=circuits, # sample all three circuits\n", - " skip_transpilation=True,\n", - " shots=8000,\n", - " )\n", - " result = job.result()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 4: Post-process, return result in classical format.\n", - "\n", - "Finally, we can plot the results from the device runs against the ideal distribution. You can see the results with `optimization_level=3` are closer to the ideal distribution due to the lower gate count, and `optimization_level=3 + dd` is even closer due to the dynamic decoupling we applied.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 54, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "binary_prob = [quasi_dist.binary_probabilities() for quasi_dist in result.quasi_dists]\n", - "plot_histogram(\n", - " binary_prob + [ideal_distribution],\n", - " bar_labels=False,\n", - " legend=[\n", - " \"optimization_level=0\",\n", - " \"optimization_level=3\",\n", - " \"optimization_level=3 + dd\",\n", - " \"ideal distribution\",\n", - " ],\n", - ")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can confirm this by computing the [Hellinger fidelity](https://docs.quantum-computing.ibm.com/api/qiskit/quantum_info) between each set of results and the ideal distribution (higher is better, and 1 is perfect fidelity).\n" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.958\n", - "0.961\n", - "0.963\n" - ] - } - ], - "source": [ - "from qiskit.quantum_info import hellinger_fidelity\n", - "\n", - "for counts in result.quasi_dists:\n", - " print(f\"{hellinger_fidelity(counts.binary_probabilities(), ideal_distribution):.3f}\")" - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.15.0'" - ] - }, - "execution_count": 56, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit_ibm_runtime\n", - "\n", - "qiskit_ibm_runtime.version.get_version_info()" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.45.0'" - ] - }, - "execution_count": 30, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit\n", - "\n", - "qiskit.version.get_version_info()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "env", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.6" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/docs/tutorials/variational_quantum_eigensolver/vqe_with_estimator.ipynb b/docs/tutorials/variational_quantum_eigensolver/vqe_with_estimator.ipynb new file mode 100644 index 000000000..74222a596 --- /dev/null +++ b/docs/tutorials/variational_quantum_eigensolver/vqe_with_estimator.ipynb @@ -0,0 +1,637 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "id": "a6f69b77", + "metadata": {}, + "source": [ + "## Background\n", + "\n", + "[Variational quantum algorithms](https://arxiv.org/abs/2012.09265) are promising candidate hybrid-algorithms for observing the utility of quantum computation on noisy near-term devices. Variational algorithms are characterized by the use of a classical optimization algorithm to iteratively update a parameterized trial solution, or \"ansatz\". Chief among these methods is the Variational Quantum Eigensolver (VQE) that aims to solve for the ground state of a given Hamiltonian represented as a linear combination of Pauli terms, with an ansatz circuit where the number of parameters to optimize over is polynomial in the number of qubits. Given that size of the full solution vector is exponential in the number of qubits, successful minimization using VQE requires, in general, additional problem specific information to define the structure of the ansatz circuit.\n", + "\n", + "\n", + "Executing a VQE algorithm requires the following 3 components:\n", + "\n", + " 1. Hamiltonian and ansatz (problem specification)\n", + " 2. Qiskit Runtime estimator\n", + " 3. Classical optimizer\n", + " \n", + "Although the Hamiltonian and ansatz require domain specific knowledge to construct, these details are immaterial to the Runtime, and we can execute a wide class of VQE problems in the same manner. " + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "7db2e559", + "metadata": {}, + "source": [ + "## Setup\n", + "\n", + "Here we import the tools needed for a VQE experiment. The primary imports can be grouped logically into three components that correspond to the three required elements." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "a0a48442", + "metadata": {}, + "outputs": [], + "source": [ + "# General imports\n", + "import numpy as np\n", + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "# Pre-defined ansatz circuit and operator class for Hamiltonian\n", + "from qiskit.circuit.library import EfficientSU2\n", + "from qiskit.quantum_info import SparsePauliOp\n", + "\n", + "# SciPy minimizer routine\n", + "from scipy.optimize import minimize\n", + "\n", + "# Plotting functions\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "bc380c46", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'ibmq_mumbai'" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from qiskit_ibm_runtime import QiskitRuntimeService, Session, Estimator, Options\n", + "\n", + "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", + "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", + "backend = service.least_busy(operational=True, simulator=False)\n", + "backend.name" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "988ee237", + "metadata": {}, + "source": [ + "## Step 1: Map classical inputs to a quantum problem\n", + "\n", + "Here we define the problem instance for our VQE algorithm. Although the problem in question can come from a variety of domains, the form for execution through Qiskit Runtime is the same. Qiskit provides a convenience class for expressing Hamiltonians in Pauli form, and a collection of widely used ansatz circuits in the [`qiskit.circuit.library`](https://docs.quantum-computing.ibm.com/api/qiskit/circuit_library).\n", + "\n", + "Here, our example Hamiltonian is derived from a quantum chemistry problem" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "0ad66539", + "metadata": {}, + "outputs": [], + "source": [ + "hamiltonian = SparsePauliOp.from_list(\n", + " [(\"YZ\", 0.3980), (\"ZI\", -0.3980), (\"ZZ\", -0.0113), (\"XX\", 0.1810)]\n", + ")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "acb83d48", + "metadata": {}, + "source": [ + "Our choice of ansatz is the `EfficientSU2` that, by default, linearly entangles qubits, making it ideal for quantum hardware with limited connectivity." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "59bffe5e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ansatz = EfficientSU2(hamiltonian.num_qubits)\n", + "ansatz.decompose().draw(\"mpl\", style=\"iqp\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "5bd1f7da", + "metadata": {}, + "source": [ + "From the previous figure we see that our ansatz circuit is defined by a vector of parameters, $\\theta_{i}$, with the total number given by:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "aa325696", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "16" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "num_params = ansatz.num_parameters\n", + "num_params" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Optimize problem for quantum execution.\n", + "\n", + "We can schedule a series of [`qiskit.transpiler`](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler) passes to optimize our circuit for a selected backend. This includes a few components:\n", + "\n", + "- [`optimization_level`](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler_preset#preset-pass-manager-generation): The lowest optimization level just does the bare minimum needed to get the circuit running on the device; it maps the circuit qubits to the device qubits and adds swap gates to allow all 2-qubit operations. The highest optimization level is much smarter and uses lots of tricks to reduce the overall gate count. Since multi-qubit gates have high error rates and qubits decohere over time, the shorter circuits should give better results.\n", + "- [Dynamical Decoupling](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_provider.transpiler.passes.scheduling.PadDynamicalDecoupling): We can apply a sequence of gates to idling qubits. This cancels out some unwanted interactions with the environment." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "from qiskit.transpiler import PassManager\n", + "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", + "from qiskit.transpiler.passes import (\n", + " ALAPScheduleAnalysis,\n", + " PadDynamicalDecoupling,\n", + " ConstrainedReschedule,\n", + ")\n", + "from qiskit.circuit.library import XGate\n", + "\n", + "target = backend.target\n", + "pm = generate_preset_pass_manager(target=target, optimization_level=3)\n", + "pm.scheduling = PassManager(\n", + " [\n", + " ALAPScheduleAnalysis(target=target),\n", + " ConstrainedReschedule(target.acquire_alignment, target.pulse_alignment),\n", + " PadDynamicalDecoupling(\n", + " target=target, dd_sequence=[XGate(), XGate()], pulse_alignment=target.pulse_alignment\n", + " ),\n", + " ]\n", + ")\n", + "\n", + "ansatz_ibm = pm.run(ansatz)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "ansatz_ibm.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also use `apply_layout` to transform our virtual observable to physical" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "SparsePauliOp(['IZIIYIIIIIIIIIIIIIIIIIIIIII', 'IIIIZIIIIIIIIIIIIIIIIIIIIII', 'IZIIZIIIIIIIIIIIIIIIIIIIIII', 'IXIIXIIIIIIIIIIIIIIIIIIIIII'],\n", + " coeffs=[ 0.398 +0.j, -0.398 +0.j, -0.0113+0.j, 0.181 +0.j])" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "hamiltonian_ibm = hamiltonian.apply_layout(ansatz_ibm.layout)\n", + "hamiltonian_ibm" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "b4d480b3", + "metadata": {}, + "source": [ + "## Step 3: Execute using Qiskit Primitives.\n", + "\n", + "Like many classical optimization problems, the solution to a VQE problem can be formulated as minimization of a scalar cost function. By definition, VQE looks to find the ground state solution to a Hamiltonian by optimizing the ansatz circuit parameters to minimize the expectation value (energy) of the Hamiltonian. With the Qiskit Runtime [`Estimator`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator) directly taking a Hamiltonian and parameterized ansatz, and returning the necessary energy, the cost function for a VQE instance is quite simple:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "b22a1b00", + "metadata": {}, + "outputs": [], + "source": [ + "def cost_func(params, ansatz, hamiltonian, estimator):\n", + " \"\"\"Return estimate of energy from estimator\n", + "\n", + " Parameters:\n", + " params (ndarray): Array of ansatz parameters\n", + " ansatz (QuantumCircuit): Parameterized ansatz circuit\n", + " hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n", + " estimator (Estimator): Estimator primitive instance\n", + "\n", + " Returns:\n", + " float: Energy estimate\n", + " \"\"\"\n", + " energy = estimator.run(ansatz, hamiltonian, parameter_values=params).result().values[0]\n", + " return energy" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "179ba2c4", + "metadata": {}, + "source": [ + "Note that, in addition to the array of optimization parameters that must be the first argument, we use additional arguments to pass the terms needed in the cost function." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "91afc41c", + "metadata": {}, + "source": [ + "### Creating a callback function\n", + "\n", + "Callback functions are a standard way for users to obtain additional information about the status of an iterative algorithm. The standard SciPy callback routine allows for returning only the interim vector at each iteration. However, it is possible to do much more than this. Here, we show how to use a mutable object, such as a dictionary, to store the current vector at each iteration, for example in case we need to restart the routine due to failure, and also return the current iteration number and average time per iteration." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "3b2f5808", + "metadata": {}, + "outputs": [], + "source": [ + "def build_callback(ansatz, hamiltonian, estimator, callback_dict):\n", + " \"\"\"Return callback function that uses Estimator instance,\n", + " and stores intermediate values into a dictionary.\n", + "\n", + " Parameters:\n", + " ansatz (QuantumCircuit): Parameterized ansatz circuit\n", + " hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n", + " estimator (Estimator): Estimator primitive instance\n", + " callback_dict (dict): Mutable dict for storing values\n", + "\n", + " Returns:\n", + " Callable: Callback function object\n", + " \"\"\"\n", + "\n", + " def callback(current_vector):\n", + " \"\"\"Callback function storing previous solution vector,\n", + " computing the intermediate cost value, and displaying number\n", + " of completed iterations and average time per iteration.\n", + "\n", + " Values are stored in pre-defined 'callback_dict' dictionary.\n", + "\n", + " Parameters:\n", + " current_vector (ndarray): Current vector of parameters\n", + " returned by optimizer\n", + " \"\"\"\n", + " # Keep track of the number of iterations\n", + " callback_dict[\"iters\"] += 1\n", + " # Set the prev_vector to the latest one\n", + " callback_dict[\"prev_vector\"] = current_vector\n", + " # Compute the value of the cost function at the current vector\n", + " # This adds an additional function evaluation\n", + " current_cost = (\n", + " estimator.run(ansatz, hamiltonian, parameter_values=current_vector).result().values[0]\n", + " )\n", + " callback_dict[\"cost_history\"].append(current_cost)\n", + " # Print to screen on single line\n", + " print(\n", + " \"Iters. done: {} [Current cost: {}]\".format(callback_dict[\"iters\"], current_cost),\n", + " end=\"\\r\",\n", + " flush=True,\n", + " )\n", + "\n", + " return callback" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "9f705072", + "metadata": {}, + "outputs": [], + "source": [ + "callback_dict = {\n", + " \"prev_vector\": None,\n", + " \"iters\": 0,\n", + " \"cost_history\": [],\n", + "}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now use a classical optimizer of our choice to minimize the cost function. Here, we use the [COBYLA routine from SciPy through the `minimize` function](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html). Note that when running on real quantum hardware, the choice of optimizer is important, as not all optimizers handle noisy cost function landscapes equally well.\n", + "\n", + "To begin the routine, we specify a random initial set of parameters:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "x0 = 2 * np.pi * np.random.random(num_params)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Because we are sending a large number of jobs that we would like to execute together, we use a [`Session`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Session) to execute all the generated circuits in one block. Here `args` is the standard SciPy way to supply the additional parameters needed by the cost function." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "e642648e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iters. done: 138 [Current cost: -0.6369264209287736]\r" + ] + } + ], + "source": [ + "# To run on local simulator:\n", + "# 1. Use the Estimator from qiskit.primitives instead.\n", + "# 2. Remove the Session context manager below.\n", + "\n", + "options = Options()\n", + "options.transpilation.skip_transpilation = True\n", + "options.execution.shots = 10000\n", + "\n", + "with Session(backend=backend):\n", + " estimator = Estimator(options=options)\n", + " callback = build_callback(ansatz_ibm, hamiltonian_ibm, estimator, callback_dict)\n", + " res = minimize(\n", + " cost_func,\n", + " x0,\n", + " args=(ansatz_ibm, hamiltonian_ibm, estimator),\n", + " method=\"cobyla\",\n", + " callback=callback,\n", + " )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "At the terminus of this routine we have a result in the standard SciPy `OptimizeResult` format. From this we see that it took `nfev` number of cost function evaluations to obtain the solution vector of parameter angles (`x`) that, when plugged into the ansatz circuit, yield the approximate ground state solution we were looking for." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + " message: Optimization terminated successfully.\n", + " success: True\n", + " status: 1\n", + " fun: -0.6207577318293181\n", + " x: [ 4.235e+00 1.298e+00 ... 6.596e+00 5.874e+00]\n", + " nfev: 138\n", + " maxcv: 0.0" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "res" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 4: Post-process, return result in classical format." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "733431ad", + "metadata": {}, + "source": [ + "If the procedure terminates correctly, then the `prev_vector` and `iters` values in our `callback_dict` dictionary should be equal to the solution vector and total number of function evaluations, respectively. This is easy to verify:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "30630583", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "all(callback_dict[\"prev_vector\"] == res.x)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "72ae1d21", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "callback_dict[\"iters\"] == res.nfev" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "19459b48", + "metadata": {}, + "source": [ + "We can also now view the progress towards convergence as monitored by the cost history at each iteration:" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "8501d609", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "ax.plot(range(callback_dict[\"iters\"]), callback_dict[\"cost_history\"])\n", + "ax.set_xlabel(\"Iterations\")\n", + "ax.set_ylabel(\"Cost\")\n", + "plt.draw()" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "ee3ac2fa", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'0.19.1'" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit_ibm_runtime\n", + "\n", + "qiskit_ibm_runtime.version.get_version_info()" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "'1.0.0rc1'" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import qiskit\n", + "\n", + "qiskit.version.get_version_info()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/docs/tutorials/vqe_with_estimator.ipynb b/docs/tutorials/vqe_with_estimator.ipynb deleted file mode 100644 index 57987e522..000000000 --- a/docs/tutorials/vqe_with_estimator.ipynb +++ /dev/null @@ -1,644 +0,0 @@ -{ - "cells": [ - { - "attachments": {}, - "cell_type": "markdown", - "id": "224fc5e2", - "metadata": {}, - "source": [ - "# Variational Quantum Eigensolver" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "a6f69b77", - "metadata": {}, - "source": [ - "## Background\n", - "\n", - "[Variational quantum algorithms](https://arxiv.org/abs/2012.09265) are promising candidate hybrid-algorithms for observing the utility of quantum computation on noisy near-term devices. Variational algorithms are characterized by the use of a classical optimization algorithm to iteratively update a parameterized trial solution, or \"ansatz\". Chief among these methods is the Variational Quantum Eigensolver (VQE) that aims to solve for the ground state of a given Hamiltonian represented as a linear combination of Pauli terms, with an ansatz circuit where the number of parameters to optimize over is polynomial in the number of qubits. Given that size of the full solution vector is exponential in the number of qubits, successful minimization using VQE requires, in general, additional problem specific information to define the structure of the ansatz circuit.\n", - "\n", - "\n", - "Executing a VQE algorithm requires the following 3 components:\n", - "\n", - " 1. Hamiltonian and ansatz (problem specification)\n", - " 2. Qiskit Runtime estimator\n", - " 3. Classical optimizer\n", - " \n", - "Although the Hamiltonian and ansatz require domain specific knowledge to construct, these details are immaterial to the Runtime, and we can execute a wide class of VQE problems in the same manner. " - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "7db2e559", - "metadata": {}, - "source": [ - "## Setup\n", - "\n", - "Here we import the tools needed for a VQE experiment. The primary imports can be grouped logically into three components that correspond to the three required elements." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "a0a48442", - "metadata": {}, - "outputs": [], - "source": [ - "# General imports\n", - "import numpy as np\n", - "\n", - "# Pre-defined ansatz circuit and operator class for Hamiltonian\n", - "from qiskit.circuit.library import EfficientSU2\n", - "from qiskit.quantum_info import SparsePauliOp\n", - "\n", - "# Qiskit Runtime\n", - "from qiskit_ibm_runtime import QiskitRuntimeService, Estimator, Session, Options\n", - "\n", - "# SciPy minimizer routine\n", - "from scipy.optimize import minimize\n", - "\n", - "# Plotting functions\n", - "import matplotlib.pyplot as plt" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "bc380c46", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'ibmq_manila'" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# To run on hardware, select the backend with the fewest number of jobs in the queue\n", - "service = QiskitRuntimeService(channel=\"ibm_quantum\")\n", - "backend = service.least_busy(operational=True, simulator=False)\n", - "backend.name" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "988ee237", - "metadata": {}, - "source": [ - "## Step 1: Map classical inputs to a quantum problem\n", - "\n", - "Here we define the problem instance for our VQE algorithm. Although the problem in question can come from a variety of domains, the form for execution through Qiskit Runtime is the same. Qiskit provides a convenience class for expressing Hamiltonians in Pauli form, and a collection of widely used ansatz circuits in the [`qiskit.circuit.library`](https://docs.quantum-computing.ibm.com/api/qiskit/circuit_library).\n", - "\n", - "Here, our example Hamiltonian is derived from a quantum chemistry problem" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "0ad66539", - "metadata": {}, - "outputs": [], - "source": [ - "hamiltonian = SparsePauliOp.from_list(\n", - " [(\"YZ\", 0.3980), (\"ZI\", -0.3980), (\"ZZ\", -0.0113), (\"XX\", 0.1810)]\n", - ")" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "acb83d48", - "metadata": {}, - "source": [ - "Our choice of ansatz is the `EfficientSU2` that, by default, linearly entangles qubits, making it ideal for quantum hardware with limited connectivity." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "59bffe5e", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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BXC5Hu3btaj03bNgwzJs3D2lpafD19QUAnDp1ComJiVi2bJkodRMJQS6X4Zv3+0Cj1WLrfaah7RTshj2fPQ5He6VI1RGJ470ZEVBVarD8v7ENjmvpbYdf1gxEC6/671tGJFUTR7RBabkaMxefQENfMHCyV2LHJ48hItRdvOKIBGSSZ2gaEhcXB61Wi6CgINja1v7C6OTJk+Ht7Y0RI0Zg9+7diIqKwtixY9GtWzeMGDHCSBUTNY6VUoHNS/th6/L+6NvVu87zoYHOWD2vB6K/GQpvD2ndQItIFzKZDMtmd8Nv6wZhRL+WkMtltZ5v4WWHD2ZG4K8fRiI00MVIVRIZ1vQxofjz++F49onWsFIqaj3n5myFuZPa43zUyHrfJ4ikwmTP0NxLbOztT+r+ebkZADg6OuLQoUN4+eWXMWbMGFhYWGDYsGFYsWIF5HKz6/3IBMjlMkQ+7o/Ix/1xNfUWeoz/GXm3VPBwscbF7aNqzfJHZKoG9GiOAT2aIy2rFOFP/4S8QhU8XKyQtPdpfm+MzEKXMA/894NH8J/XuyNkRBRyC1Vwd7bCjf1jYG1ldoeCZILMbi9uqKEBbt9Es75L1YikLqiVE6ytbn86p7SUs5khs+PrZQdr5Z0MKNjMkNlxd7GuOUtjpVSwmSGTYXZ78v0aGilzCW2FnsunwtLeBqVpOTgy81O4tGmBxzbNQ1FiBn4b8x4q8oqgsFGi13+mwT08EFqNFmcWf4/UPScBAF3mT4DfiJ7Ij03GoUkfGfkV6acs+TxSP3sRmvJiKD1awe/Vjai4HoeriwbDunlbBL37GyydPZG+cR4KTmyH3NIKMoUlfMZ/AKfOAwEA2TtXIGfvZ5Db2CN05TnjviDSm64ZuMMpqDme+PUjXPluP/585xsAQOjkYQieOBDq0grsGjDHSK+kcXTNAADc3LsGOXs+BRQWkMnkCF52CnKlNdK+noP8o1tgG9gZreftMO4LIr3pmgEHfy/0XDYVVk52UFgrcePAX4hZtBHQaiWXAV33+9wDG5C9awUqbiTAd9JyNBv+Ss06NKoypHz6PMqungbkcjQf/yFcev0fADATEqDrft96TH+ETR4KpyBfxCz6FvFf7KlZR+c3n0GrId1RraqCRl2NM0u+R8bh8wCa/vuCEBm4o/xGAhJei4DHwMlo8cJKANI4NjK7hubQoUPGLsFgHl45A8de/Qz5cSloPaY/ur7zLK798DuKEjNqBbDd1OHQVFZhe8+ZsG/hiaF7FyPr+EWoCkoQ895GFF6+gZaDuxnxlTROyicT4Tfra9gGhCP3wAakff063B+dBOvmbWsF0D60N7yfng+5lQ3Kks/j8rw+6PB1BhTWdmg24lXYBnTCja9eMdrroMbTNQMAILNQoOeyqUj95c9aj8ev34382GR0WzRRxMqFoWsGCk/tRP4fmxD80Uko7JxQdSsHMoUlAMB30jJYtwxD4akdxnkR9EB0zUDXd57F9V/+RMJXe6GwssSwX5Ygs18s0g+dlVwGdN3vbQMjEDBnK7KiFtdZR9ZPyyG3tEK7ddegyk7GpTnd4dC+Hywc3ZgJCdB1v8+7kIjDUz5G+5mj6qwj+1QCzq+IQnVFJVxCW2HwT4uwNXwy1OWqJp8JITIAAFp1Fa6vmQyXh56s9bgUjo14vt1EuLbzh7qsAvlxKQCAxK2H0eLxLpAr6/asfiN64fK3vwEASm7cRNbxOLQc3F3McgVXlnQWCht72AaEAwDc+j2HW3/uglZdWWesU8RgyK1u333XplV7QKuF+laOmOWSAeiTAQAIfy0SKT+fQHFSpohVGo4+Gcj6aRl8xiyAws4JAGDp5AGZQlFnHEmLPhnQarWwdLw9GYjCWgm5pQXKbxaKWK0w9Nnvbf07wqZFCGT1fCe24OgWuA+aCgCwauYPh3Z9UXjyJ4PWTsLQZ78viE/FravpgEZT57n0Q2dRXXF7vylIuA7IZLB2czRo7UIQKgMAkLFlEVx6RsLKJ8iQJRuE2Z2hMVX2LT3hEtwSw/f/Pb20hY0VbL3q3hDUvrk7StL+PoAvuXETds2lPVWjKjsZ5amxiH8lvOYxjaoMlXnpDS6Xd/BrWHkFQOnZysAVkqHpkwH3TkHwiGiD30YvQvjsp8Us02D0yUDFjXiUXotBxg8Loa1Swa3fs/B8YpaI1ZIh6JOBP9/5Go/+900EP/s4lE52OL9yG/IvNjzFe1PU2L/9/1SZcx1WHn+/Dyg9/VCZc12oMsmA9NnvdRU0ph9KUrNrHSs1VUJloPTyKZReOoGgRfuR+cNCgas0PDY0JiTn7FXsH/t+zc9jLn5lxGrEZxfUHUELf635+fwEjwbHF50/iIwfFqLNwv38gryJ0CUDChslHlryAg6/8B8xSxOFrhnQVqtRmZ2Mth8eQXVpAS7PewRKrwA4dx0mVqlkILq+DwQ/NwjJO44i9tOfYO3miIHbFiL33DVkHrkgVqmC0fdvP5keIY9/vB9uj46zI/Hb6PeEKE0UD5oBjaoM19dNQ8AbUZI9HmJDYyJKUrNrnWWxtLeBha01yrLy645Nz4W9r0fN5QX2LTyR8cd5sUo1CKtmAajM/fvTtOqyIlRXlELp1rze8cUX/0DKqklo/fbPsPZtK1aZZEC6ZsChlRfsm7tj0LZ3AQBKRztALoPSyR5HX14tZsmC0icDSo+WcOkzFjKFAhaO7nCKGILSyyfZ0EicPu8DwZMGYnuv22flKvKKkH7wDLx6hkmuodH3b/+9KD1aQpWTCkvX2/diqbyZAsfwxwWtlQxDn/3+fpr1CEWvldNw8NklKErMELJMgxEiA6rMRFTmXMeVt/vdXkdpIbQaDdQlBfB/5b+C12wI/A6NiciPS4GmqhrefToAAIInDkTyzmPQVKrrjE39+QTaPnv7D7V9C0949QzD9X1/1hknJbYB4ZApLFF0bj8AIGfvGrg+PBoyC2WdscVxR5C8YgJav7UTtv6mN9ududI1A4WXruOHds8jqts0RHWbhvgv9uDaD4ck3cwA+mXAtc8zKDqzDwCgUZWj+OJhZsEE6PM+UJx6E837dQJw+/Icr17tUHhJepdY6bPfN8SlVyRy930O4PYlPMUXD8P5oZFCl0sGoM9+35BmD4Wg96czcWjiRyiITzVEqQYhRAZs/Nqj48YctP8iBe2/SIHnE6/A/bF/SaaZAdjQmJQj0z9BxLxxGHX8U3j1DEPMexvrHXdxzU4orJUYdWI1Bmx+G6fmfQlVfrHI1QrP/7VNSP/2TVyc0hrFFw/Dd9Kyeselfvo8tFUqpKyahPhXwhH/SjjKU2JFrpYMQdcMmCpdM9BsxGuoKsxG3PRQJMzuAqfOg+HSK1LkaskQdM3A0ZdXI2hsfww/sBzDfl2KzOhYJO84JnK1wtB1v889+A0u/MsXBcd+ROYP7+LCv3xRlnQWANDsyTnQqMoROyUQV98diBaTV8PCUdrfLTUnuu73rZ/ui8i/1qHVEz0QPvtpRP61Dq7t/AEAvf4zDQqlJR5eMQ3D9y/D8P3L4BzcUsyX0WhCZEDqeMmZCSm8dB27B71x33HqchX+mLpChIrEZePXHiEfx9x3XLvPr4pQDRmDrhm427n/bDVQNeLTNQNypbWkPnkj3emagfyLyfhlxNsiVGR4uu737o9OhPujE+t9TmFth4C5WwSujMSi635/bethXNt6uN7ntveaKXBV4hEiA3fzGfvugxclMp6hMXHVVWpYuThg+P5lOk0/2GX+BLSf+SRUhSUiVGd4Mgsl1EV5iH8lHFWFN+87PnvnClz/fBosHPjJnKnQNwOhk4fhoSUvoMIEzloC+mcg7es5yIpaDAs7FxGqIzGYYwb03e8bwkxIk777fUOkmAkhMyCFYyOZVqvVGrsIqq2qrAKbAscbuwy9jEv8Dpa21oKtr1wN9N4r2OpEET0EsGni5zx9H9uM9JtlaO5pi7QDY41dToOklgNmgBkQmtQyAAibA2bAMJgBw2IGjJMBnqEhIiIiIiLJYkNDRERERESS1cRPjJonCxsrjEv8zthl6MXCxkrQ9Vkrbp+2lBJrhbErMC1SywEzwAwITWoZAITNATNAzAAzoCs2NE2QTCYT9Fp8KZLJmv51yGRY5p4DZoCYAWbA3DEDzICueMkZERERERFJFhsaIiIiIiKSLDY0REREREQkWWxoiIiIiIhIstjQEBERERGRZLGhISIiIiIiyWJDQ0REREREksWGhoiIiIiIJIsNDRERERERSRYbGiIiIiIikiw2NEREREREJFlsaIiIiIiISLLY0BARERERkWSxoSEiIiIiIsliQ0NERERERJLFhoaIiIiIiCSLDQ0REREREUmWhbELoLq0Wi3U5Spjl6EXCxsryGQywdan1QIV1YKtThTWCkDAX4HZk1oOmAFmQGhSywAgbA6YAWIGmAFdsaFpgtTlKmwKHG/sMvQyLvE7WNpaC7a+imqg917BVieK6CGADRMlGKnlgBlgBoQmtQwAwuaAGSBmgBnQFS85IyIiIiIiyWJDQ0REREREksWGhoiIiIiIJIsNDRERERERSRYbGiIiIiIikizOxUFkwsor1LhwJR9/xefiwtUC5N+6Pf1lQZEKy76+gIhQd3QOcYOzo5WRKyUyjKoqDeISC/BXfC7OXc6vlYH3159FRIg7IkLd4elmY+RKiQyjulqDK6lF+Cs+F2cScmsykF+kwvzVf6FziBsiQt3RwstO0KnnicTEhobIBP0Vn4vPfojH5l+SUKGqO4l9WUU15q44DeD2fPFDerfAtNEhGNTLF3I539BI+q6k3MLarQn4ZudVFBZX1nm+rKIa81efqfn54U7NMG10CJ4a4AelpULMUokMIj27FF9su4z12y4jM6eszvPlFdV4f/25mp/bB7lg2ugQjBsaCAc7pYiVEj04NjREJuRKyi1MXnQUf8Rk6byMVgvsOXIDe47cQFArR6yb3wv9uvkYsEoiw8nKLcPMxScQtT9Fr+WOns3G0bPZaLbMBivndsfoQQH8tJokqbi0Ev9eGYN1UZdQXa3VebnYqwV46f3jmLviNBZN64yZz4RCoeA3E0ga2NCYEK8eYRi0fWGtx6pKy1GUlInEqCNI+GovtNUaI1VneMWxh3Hl7X61HpNb28HKpw3c+k6A57CZkClMc5fXaLT4ZFMc5q2KqfeMjK6uphah/wu/4KWng/HRa91gb2spYJWGxwyYbwYAYPPeRMxYfKLmkprGyM4rx9g3DuPH31Kw5u2eaCaxS9HMPQOAeefg0KkM/GtBNFIzShq9juLSKry67BS2HUjBhkW9EdTKScAKxWHuOTDHDJjWqyEAQNL2aKQdOgPIZLDxcEbryEfQbeFEOAU1x4k564xdnsG59BkLp4ghgFaLqoIs5B3+FmkbXkNFWgJaTV9v7PIEV1WlwbNv/YEf9iUJts61Wy/hVGwO9q0dCA9XaR3QAcyAuWVAq9Vi3qoYLPnqgmDr3H4wBTHxOTiwfrAkD+jMPQOA+eVgfdQlTH3vGLS6n5Rp0NGz2ej6zC7sWf04enVqJsxKRWbuOTCnDPBcognKi01G0rZoJEUdQdzaXdgzdB5K03PR5plHYeXmaOzyDM42oDPc+o6HW78J8Bo1B8EfnYSlmy9y93+Jqls5xi5PUNXVGox787CgzcwdZxLy8OiLv6CgqPGfdhsLM2A+GQCANz8Rtpm543pmKR75114kpxULvm5DM/cMAOaVgy+iLmHKIuGamTtuFVdi4NR9OHn+prArFom558CcMsCGxgyoy1XIOXMVMrkcjq2k+SnLg1BY28Gu7UOAVgtVVqKxyxHU/NVn8ONvyQZbf+zVAjz9+iFohX6XFBkzYLoZ2PDTFSzdIHwzc0dmThmGTP8V5RVqg21DDOaeAcB0c3D4dCamvHfMYOsvLVdj6Izf6p1YQGrMPQemmgGADY3ZcPC7HVxVYeOvq5WyO8G1sHc1ciXCOXXhJpZ+rd+B3OnNw3Fj/xic3jxc52UOnMzAuh8v6Vtek8MMmF4GrmeW4JWPTuq1TGMycCn5Fuav/kvf8pocc88AYHo5KCmrwqT5R/Q6M9OYDOTfUv3vcjZpf7gFMAemloE7zKKhyc3Nxdy5c9G6dWtYW1ujRYsWePnll1FaWornn38eMpkMq1evNnaZgrGwUcLK1QFWbo5wDm6J7h++ALf2Acg5cxVFSZnGLs/gNKoyqItyUXUrB+Upsbj++XSUJ52FbVA3WDdvY+zyBKGqrMakd6Kh0ej35uLlbgvfZnbwcrfVa7k5H59GaoZ0LrthBkw/A1qtFpMXHkVxaZVeyzU2Ax9vvIgT57P1WsaYzD0DgHnk4N8rTyNFzwkAGpuBXYev4/u90vpU39xzYA4ZuMPkJwU4d+4cBg8ejKysLNjZ2SE0NBQZGRlYtWoVEhMTkZ+fDwAIDw83bqEC6jR3DDrNHVPrsZQ9J3HqzS+NVJG4MjcvQObmBbUec+4xCi2nfGakioQXtT8ZCUmFom2vpKwKKzbGYeUbD4m2zQfBDJh+Bv6MzcGvx9NF255WC7y//hz2fDZQtG0+CHPPAGD6OcjMKcO6KHHPni/6/ByeGRIomSnNzT0Hpp6Bu5l0Q5Obm4snnngCWVlZmD17NhYsWAAHBwcAwEcffYQ33ngDFhYWkMlk6NChg5GrFc7ljb8h5ecTkFtawCW4JdpNHwk7bzdUq/6+udwja18F5DL8MeXjmseUzvYYeXgFYhZ9i6Tt0cYoXRDuAyfDpWcktNVVKE+NRdb2pajMTYPM0rpmTHFcNK4tGlxnWa26ElpNNSJ+avzUx2JYsyVB9G1+s+sqPpgZATsJTOXMDDADhvDL0TQkpxXD39dB9G3ry9wzAJh+Dr7cfhlqtbiXgF1JvYVDpzLx6EPSuFeZuefA1DNwN5O+5GzWrFlIS0vDjBkzsHz58ppmBgDmzp2Ljh07Qq1Ww8/PD46OpjPbRVFSFjKjY5F+6CwurtmJg88tgXt4IHosnVIz5sSbX8Cza1v4j+xV89hDH76Am39eknR4AcDKOwiO4Y/BKWIwvEbNReu3fkbZtdO4vnZqzRiHsN7otKWk1j9ha67AwsEdPs+8Z8Tq7y/2Sj6OnxN/xplbxZUGmU3NEJgB085AQZEKW3413GQY96LVAuu3SeP7ZOaeAcC0c6DRaLE+6rJRtr12q/gfJjSWuefAlDPwTybb0CQkJGDLli1wd3fH4sWL6x0TEREBAOjYsWPNY3caoG7dusHKykoyp1UbkhNzGYlRR+A/shc8urQFAFQWluD47LXo/sELsGnmglZDH4JXzzCceMP05mW3D+kJ174TUHB0C0oSjtc7RlOlQtKSUbAPfRjekfNErlA/v5823nW/h2Okec0xM2BaGTh5/iZUlcb51PCwEfP3IMw9A4Bp5SDxRhHSskuNsu3DMZmSnRzA3HNgShn4J5NtaDZv3gyNRoNx48bB3t6+3jE2NrdvGHh3Q3Pt2jVs27YNXl5e6Nq1qyi1iuH8iiho1NXoNGd0zWPpv59Dys/H0Wf1LDy05EUcn70WqgLTnPXDe/R8QK5Axvfv1Pv89TVToamqgN/L34hbWCP8FZ9rxG3nGW3bD4oZMKEMJBgvA+cu50OtluYdxs09A4Dp5MCY7wN5hSpcz5TuPmLuOTCVDPyTyTY0hw4dAgD069fvnmPS0tIA1G5o+vTpg8zMTOzatQuPPfaYYYsUUXFKFpJ3HoNPnw7w7B5S83jMwm/h4O+F9ENnkXbwjBErNCxr79Zw7T0GxRcOojiu9inkmz+vwq2Y3Qh8cwfkVvrN+mIMZy8Zr6m4lFyI0jL9ZpVqKpgB08nAmQTjZaBCVS3qhBxCMvcMAKaTA2NmoCls/0GYew5MJQP/ZLKTAqSmpgIAWrVqVe/zarUax47dvhHV3Q2NXC58j9elSxdkZWXpPN5SK8cCdBO8jgufbIP/yF7oNGc0fv2/dwHcvslUSepNFCRcf6B1twlqgyqZcJ9aypQ2aLbyqmDrAwCvyLeQH70ZGd+/g7Yf/A4AKL7wO9K+fQNB7/wCq2Z+D7T+Nm2CoK0sF6DShmU6vw7I6/9S8unNwxucitPL3abm3zf2j7nnuKzcMnQdu6vO41otEBjcERaaIj2r1p8hcsAMmEYGchz+BVjW/7ddqAwA985B/8eHw0qdonvBjSS1DADC5sAQGQAMmwOxMlBgNxKw6lTvc2Jk4F+TX8ZMleHvzWTux0PmlgEvLy/ExMQ0almTbWhKS29fW1peXv8vdcuWLcjNzYWDgwP8/f0NWktWVhbS03WfXlQpUwCNuIFt1ok4fOP9f/d8/tbVdHzrO/qezz+IjMwMVGqFu6ZdbmWr96/AoX1fROy893W9Ni1Cas3WocpOQdKyp+E7cRkc2vdtXKF3ycjIgEYlwp2UHXHPc6t37i9wPxYKuU7j6pOdlQNUGf5yh8bkgBkwkwwEqoF7TLYnRgZy8wqBEsNPGS21DADC5qAxGQCMmwPRMuCrAqzqf0qMDBQWFqMwv2lmADCd9wJmQHcm29B4eXmhoKAAZ86cQY8ePWo9l5mZiTlz5gAAOnToYPAv/nt5eek13lIrByR2ibaPt4/gn04bkkZVhsTFI+HUbTg8h84QZJ0+Pj7inKGRa++5e2TlNvxHxMvdBhYKOdTVGmTl3rvWhtbj1cwdCu093kkFJLUcMAPiZSDHUoHKezwnVAYaWpe7mxOsnJrrUuoDkVoGAGFzYOgMAMLnQKwMFNgqca89XYwMODvZw86GGagPM9D4DOh7vHw3k21oHnvsMSQkJGDp0qUYMGAA2rS5fUfU06dPY8KECcjNvf0Jsxg31NT39FlVWQU2BY43UDWGceXqFVjaWt9/oI7K1UDvvYKtro6C49tQnnweFelXUHB0S53nw1bHQ+nRUq91XrlyFTYiJKrH+F04eSGn3ufquzTgbjf2j4FvMztk5ZajxYAf9N62lVKB60lxsLQ0/NfvpJYDZkC8DDw77w9s3H2t3ucMnQEAOH1sH/yaG/5eNFLLACBsDgydAUD4HIiVgUWfn8WCNfV/z0OMDGzdtBYDehi+oWEGmAFdmWxDM3fuXHz//fe4ceMGwsLCEBwcjIqKCly7dg2DBw+Gn58ffv3111rfnzFX+55acP9BJsat3wS49Ztg7DIaJSLU/Z4NjaF1bOMqSjMjNmZAWiJC3e7Z0Biaq5MVWvnUP3OmlJljBgDp5iAi1M2o2+8cYtztG4o55kCqGfgn0zsy+R9fX19ER0dj6NChsLa2RkpKClxdXbFu3Trs2bMHV65cAQA2NCQ5EaHuRty2ab6JkbQYOwOmcH8ykjZjZsDPxx5uzsKdjSYSgsmeoQGAkJAQ7N69u87jJSUlSElJgVwuR7t27YxQGVHjDerlCwsLGdRq8W9sNuwR/S5BIjKEbu094OlqjZv5FaJve1gfZoCMz8vdFl3C3BETJ/79aPg+QE2RyZ6haUhcXBy0Wi2CgoJga1t3asOoqChERUUhPj6+1s+NnUqOSEjeHrZ4sr+f6Nv1b+6AQb18Rd8u0T8pLRV4/sm2om/X1toCzw0PEn27RPV56emQ+w8ygGmjjbNdooaYZUMTGxsL4N6Xm0VGRiIyMhI//vhjrZ9Xr14tWo1EDTHGG8rUyGDI5bzUhpqGKZFtRd8fnxkSACcHpajbJLqXMYMC4Czy/ti3qzdCApxF3SaRLtjQ1EOr1db7zzfffCNilUT39kgXLzwh4mn/wBYOmD6Gn8pR09HKxwEvjwsVbXtODkosmNpZtO0R3Y+tjQU+mBkh2vYUChmWvdZVtO0R6cOkv0NzL/draKTKJbQVei6fCkt7G5Sm5eDIzE/h0qYFHts0D0WJGfhtzHuoyCtC6zH9ETZ5KJyCfBGz6FvEf7GnZh1d5k+A34ieyI9NxqFJHxnx1eivLPk8Uj97EZryYig9WsHv1Y2ouB6Hq4sGw7p5WwS9+xssnT2RvvEtFJ7eBZlcAQDwGvVvuPa5fbfktK/nIP/oFtgGdkbreTuM+GoaJpPJsO6dXogemYXC4nvdkUM4Gxb2hp3tPe5k2ITomoGHV06Hd58OUOUVAQAyjlxAzHsbAZhHBhI/fBKqm8k1y5WnXEDgmzvg3H04sneuQM7ezyC3sUfoynPGezE6eH9GF+w+cgNXU4sMvq0Vc7rD16txNyEUk64ZcPD3Qo/FL8La3QkyCwXOf/wjUnYdBwCETh6G4IkDoS6twK4Bc4z8iu5P1/0+98AGZO9agYobCfCdtBzNhr9Ss46GnmvK7wtTnw5B1P4U/H460+DbemNSB3QJ8zD4dhpDiOOfTv8ei5aPd4G2+vY9ZGJX70DyzmMAmv77ghAZSPlkIorO7YeF0+3/x44dB8B30jIATTsDd5hlQ3Po0CFjl2AQD6+cgWOvfob8uBS0HtMfXd95Ftd++B1FiRm13pTyLiTi8JSP0X7mqDrriHlvIwov30DLwd3ELF0QKZ9MhN+sr2EbEI7cAxuQ9vXrcH90Eqybt611YNbsyTloPuEDAEBlXjripofAMfwxWDi6w3fSMli3DEPhqR3GeRF68Pawxefze2HM3N91XubOTdLud+O1u73+XHv06eKtd33GoGsGACBu7a5ab2Z3mEMGAuf9VPPfpVdjcHXhIDh2HgQAaDbiVdgGdMKNr14RuXr92dpY4L/v90Hff+1FZZVuN7JrTAaefLQVJo6QxndndM3Awytn4NqW33H1+4OwcnPEE/uW4uafl1CWlY/49buRH5uMbosmGu+F6EHX/d42MAIBc7YiK2pxnXU09FxTfl+Qy2XYsKg3uozdibxClU7LNCYDnUPc8M7UTo2qUQxCHP/ErdmJs0s2AwBsvVwx8shKZERfgCq/uMm/LwiRAeD28dHdTc4dTTkDd5jlJWemyLWdP9RlFciPSwEAJG49jBaPd4FcWbdnLYhPxa2r6YBGYrffbUBZ0lkobOxhGxAOAHDr9xxu/bkLWnXdsxcW9s41/60pLwG0Wmgl+rsYPSgAK+d213l817G70GLAD/e98dodE4a1xtJXpXGJgT4ZMEX6ZOBuuQe+glvf8ZBbSvO7IT06NsPW5f1hYaHb92n0zUDfrt7YtLivJKZq1icDrmGtkHbw9o0ZVXlFyI9Lgd+InmKWKwh99ntb/46waRECmbzuoU9DzzV1fs0dsG/tQDja63YWXd8MBPs74Zc1A2GlVDxImQYj1PFPZdHfDZ6FnTVkMpkkci9UBqTOPN7pzYB9S0+4BLfE8P3Lah6zsLGCrZerEasSjyo7GeWpsYh/JbzmMY2qDJV56fWOv/nzKtzc+xmq8tLQasaXsHT2FKlS4b08vh2srSww/cPjqK4Wbirnl54Oxqdv9pDMRAD6ZiDkhSFoPaY/StNzcXbp5po3Q6nSNwO3ny9HQfRmtP0wWoQKDWdEv1bY+ckARM4+hLIKtWDrHdanBbYs6w8ba2m8VeqTgbwLSQh8qg8urtkJ+5ae8OzaFiU3jHPD3gfRmP3eFHUJ88DvXw7B4Gm/CjqdeUSoO35Z8zg8XG0EW6fQhDz+CXl+CIInDoStjxuOz16LijzDX876oITMwM2fP0HegQ1QerSEz7j3a5okKZDGX2nSSc7Zq9g/9v2an8dc/MqI1YjPLqg7ghb+WvPz+Qn3vtbX84lZ8HxiFsqSzyN5xXg4hj8OC0fp3jRySmQwIkLdMGl+NC5eK3igdXm4WGPt2z3x1AB/gaoTj64ZOLNkM8qyCwCtFi0Hd8Njm97C9p4zoS4T/74mQtInAwBQcDwKVj5tYOPX3tClGdyQ3i1wYduTeH5BNP6IyXqgddnZWGDpq13x0tMhkmno79A1A0dnrUaXd5/D8P3LUJKWi8zoWGirq8UqU1D67vemqnOoOy5uH4UZi09g66/J91+gAQqFDG8+3xHzp4RDadk0z8zcTajjn4Sv9iLhq71wCW2FPqtnIeOP81AVlAhVpsEIkQGf8R/A0sUbMrkcBSd+wtVFg9Fu7VUobOyFLNVgTO+ck5kqSc2GXfO/7xxsaW8DC1trlGXlG7Eq8Vg1C0Bl7vWan6vLilBdUQqlW/MGl7P17wila3MUXzxs4AoNr0uYB2J+GIFF0zvDw0X/uzhbWynw4lNtEb/jKUk2M/pkoCwrH9DePpt1/Zc/UVVcBqfWPqLVagiNyUDuga/g/tjzYpQnisAWjjj05RCseasnWvno/yasUMjwfwP8cGHbk5g+JlRyzYw+GShJy8HhF5Zj14A5ODRpKZSOtii8fEPMcgXR2L/9psrD1QZblvVH1H/6o11rl0at47GHfPDnpuF4b0aEJJoZQxz/FMSnoiwrH149w4Qo0aCEyoDSrXnNpWguPZ6EwsYRFemXBa3VkNjQmIj8uBRoqqrh3acDACB44kAk7zwGTaVwl180ZbYB4ZApLFF0bj8AIGfvGrg+PBoyi7rfCyi/Hl/z36rMRJQlnYV1C/GmfzUkK6UC86d0wo39Y7BpcV/07+YN+wZmJ7O0kKNLmDs+ntMdGQfHYv2Ch+HeiGaoKdAnA7bef1+K4NE5CFauDihKfrBP9Y1NnwwAQEXmNZRdi4Frn7FilmlwcrkML40OQeKeSPz86QAM79sSrk5WDY4PC3TGgqmdkLpvNH78z6MI8HUUsWLh6JMBa3cn4H/fD/Dp2xFObXyR9NNRUesVgr77vbl4aoA/Lmx7Eke+HopnhgTC26PuTcTv1rqlI14eF4ZLO5/C/vWD0TnUvcHxTYlQxz9Obf6+cbRDq2ZwbeePwitpgtZqCEJloDL379dacvkk1MV5sPZuLWithsRLzkzIkemf4OGV06Fc8iKKU7JwZMYquLSte6+S1k/3Rac3xkLpbIeWg7ohbOpwHHxuCfIvPtgpamPzf20TUlZNwvW1L8HKuzX8X/sO5akX64xL/+9cqLKTIbOwhExugZZTVsOmhWndY8VKqcAzQwPxzNBAaDRaXEm9hQtX8lFcWgWNRgtbGwsE+zujXWuXJvtFz8bQNQMPr5wBGw8naKs1UFdU4vCL/0FVse4z/jRVumYAAPIObIBzj6egsJXmwfv9KBRyDHukJYY90hJarRYp6SU4dzkPBUWVUFdrYK1UoHVLR3Rs4yqJKcl1pWsGWjzeBe1njIS2WoOy7AIcGPchqisMPwW8Iei63+ce/AYZm95GdUkBCk/tQPaO5Wj99s+wDejU4HNSJZPJ0DvCC70jvAAAGTdLcSYhD7mFFais0sDKUoGW3nboFOwGZ8d7N/1SIMTxT5e3J8C+pSe0VWpoqjU4Oe+r2xMISIAQGUj5ZCKqbmVDJldArrRB4NwfobBzMsKraRw2NCak8NJ17B70xn3HXdt6GNe2HjZ8QSKz8WuPkI9j7juu9fzdIlTTdMjlMgT7OyPY39nYpRicrhn4bfQiEaoRn64ZAIDmEz40cDVNh0wmg7+vA/x9HYxdisHpmoGr3x/E1e8PilCR4em637s/OhHuj07U+zlT4eNpBx/Ppn8vpcYQ4vjn4LP1T2UsBUJkoM17BwSuSly85MzEVVepYeXigOH7l8Ha7f6fxHaZPwHtZz4JVWHT/xKcLmQWSqiL8hD/SjiqCm/ed3za13OQFbUYFnaNu/aYmh5mQL8MZO9cgeufT4OFg3QuOaGG6ZuB0MnD8NCSF1CRXyxCdYah737fEL4vSJO++31DpPi+YG4ZkGm1WuHmeSVBVJVVYFPgeGOXoZdxid/B0la4716Uq4HeewVbnSiihwA2POcpGKnlgBlgBoQmtQwAwuaAGSBmgBnQFc/QEBERERGRZLGhISIiIiIiyeIlZ02QVquFulxl7DL0YmFjBZlMuHs2aLVAhcTu8WatqJkFlQQgtRwwA8yA0KSWAUDYHDADxAwwA7piQ0NERERERJLFS86IiIiIiEiy2NAQEREREZFksaEhIiIiIiLJYkNDRERERESSxYaGiIiIiIgkiw0NERERERFJFhsaIiIiIiKSLDY0REREREQkWWxoiIiIiIhIstjQEBERERGRZLGhISIiIiIiyWJDQ0REREREksWGhoiIiIiIJIsNDRERERERSRYbGiIiIiIikiw2NEREREREJFlsaIiIiIiISLLY0BARERERkWSxoSEiIiIiIsliQ0NERERERJLFhoaIiIiIiCSLDQ0REREREUkWGxoiIiIiIpIsNjRERERERCRZbGiIiIiIiEiy/h8QBNX2a6Z7lwAAAABJRU5ErkJggg==", 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" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ansatz = EfficientSU2(hamiltonian.num_qubits)\n", - "ansatz.decompose().draw(\"mpl\", style=\"iqp\")" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "5bd1f7da", - "metadata": {}, - "source": [ - "From the previous figure we see that our ansatz circuit is defined by a vector of parameters, $\\theta_{i}$, with the total number given by:" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "aa325696", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "16" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "num_params = ansatz.num_parameters\n", - "num_params" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 2: Optimize problem for quantum execution.\n", - "\n", - "We can schedule a series of [`qiskit.transpiler`](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler) passes to optimize our circuit for a selected backend. This includes a few components:\n", - "\n", - "- [`optimization_level`](https://docs.quantum-computing.ibm.com/api/qiskit/transpiler_preset#preset-pass-manager-generation): The lowest optimization level just does the bare minimum needed to get the circuit running on the device; it maps the circuit qubits to the device qubits and adds swap gates to allow all 2-qubit operations. The highest optimization level is much smarter and uses lots of tricks to reduce the overall gate count. Since multi-qubit gates have high error rates and qubits decohere over time, the shorter circuits should give better results.\n", - "- [Dynamical Decoupling](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_provider.transpiler.passes.scheduling.PadDynamicalDecoupling): We can apply a sequence of gates to idling qubits. This cancels out some unwanted interactions with the environment." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "from qiskit.transpiler import PassManager\n", - "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", - "from qiskit_ibm_runtime.transpiler.passes.scheduling import (\n", - " ALAPScheduleAnalysis,\n", - " PadDynamicalDecoupling,\n", - ")\n", - "from qiskit.circuit.library import XGate\n", - "\n", - "target = backend.target\n", - "pm = generate_preset_pass_manager(target=target, optimization_level=3)\n", - "pm.scheduling = PassManager(\n", - " [\n", - " ALAPScheduleAnalysis(durations=target.durations()),\n", - " PadDynamicalDecoupling(\n", - " durations=target.durations(),\n", - " dd_sequences=[XGate(), XGate()],\n", - " pulse_alignment=target.pulse_alignment,\n", - " ),\n", - " ]\n", - ")\n", - "\n", - "ansatz_ibm = pm.run(ansatz)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "ansatz_ibm.draw(output=\"mpl\", idle_wires=False, style=\"iqp\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can also use `apply_layout` to transform our virtual observable to physical" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "SparsePauliOp(['IIIZY', 'IIIIZ', 'IIIZZ', 'IIIXX'],\n", - " coeffs=[ 0.398 +0.j, -0.398 +0.j, -0.0113+0.j, 0.181 +0.j])" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "hamiltonian_ibm = hamiltonian.apply_layout(ansatz_ibm.layout)\n", - "hamiltonian_ibm" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "b4d480b3", - "metadata": {}, - "source": [ - "## Step 3: Execute using Qiskit Primitives.\n", - "\n", - "Like many classical optimization problems, the solution to a VQE problem can be formulated as minimization of a scalar cost function. By definition, VQE looks to find the ground state solution to a Hamiltonian by optimizing the ansatz circuit parameters to minimize the expectation value (energy) of the Hamiltonian. With the Qiskit Runtime [`Estimator`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Estimator) directly taking a Hamiltonian and parameterized ansatz, and returning the necessary energy, the cost function for a VQE instance is quite simple:" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "b22a1b00", - "metadata": {}, - "outputs": [], - "source": [ - "def cost_func(params, ansatz, hamiltonian, estimator):\n", - " \"\"\"Return estimate of energy from estimator\n", - "\n", - " Parameters:\n", - " params (ndarray): Array of ansatz parameters\n", - " ansatz (QuantumCircuit): Parameterized ansatz circuit\n", - " hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n", - " estimator (Estimator): Estimator primitive instance\n", - "\n", - " Returns:\n", - " float: Energy estimate\n", - " \"\"\"\n", - " energy = estimator.run(ansatz, hamiltonian, parameter_values=params).result().values[0]\n", - " return energy" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "179ba2c4", - "metadata": {}, - "source": [ - "Note that, in addition to the array of optimization parameters that must be the first argument, we use additional arguments to pass the terms needed in the cost function." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "91afc41c", - "metadata": {}, - "source": [ - "### Creating a callback function\n", - "\n", - "Callback functions are a standard way for users to obtain additional information about the status of an iterative algorithm. The standard SciPy callback routine allows for returning only the interim vector at each iteration. However, it is possible to do much more than this. Here, we show how to use a mutable object, such as a dictionary, to store the current vector at each iteration, for example in case we need to restart the routine due to failure, and also return the current iteration number and average time per iteration." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "3b2f5808", - "metadata": {}, - "outputs": [], - "source": [ - "def build_callback(ansatz, hamiltonian, estimator, callback_dict):\n", - " \"\"\"Return callback function that uses Estimator instance,\n", - " and stores intermediate values into a dictionary.\n", - "\n", - " Parameters:\n", - " ansatz (QuantumCircuit): Parameterized ansatz circuit\n", - " hamiltonian (SparsePauliOp): Operator representation of Hamiltonian\n", - " estimator (Estimator): Estimator primitive instance\n", - " callback_dict (dict): Mutable dict for storing values\n", - "\n", - " Returns:\n", - " Callable: Callback function object\n", - " \"\"\"\n", - "\n", - " def callback(current_vector):\n", - " \"\"\"Callback function storing previous solution vector,\n", - " computing the intermediate cost value, and displaying number\n", - " of completed iterations and average time per iteration.\n", - "\n", - " Values are stored in pre-defined 'callback_dict' dictionary.\n", - "\n", - " Parameters:\n", - " current_vector (ndarray): Current vector of parameters\n", - " returned by optimizer\n", - " \"\"\"\n", - " # Keep track of the number of iterations\n", - " callback_dict[\"iters\"] += 1\n", - " # Set the prev_vector to the latest one\n", - " callback_dict[\"prev_vector\"] = current_vector\n", - " # Compute the value of the cost function at the current vector\n", - " # This adds an additional function evaluation\n", - " current_cost = (\n", - " estimator.run(ansatz, hamiltonian, parameter_values=current_vector).result().values[0]\n", - " )\n", - " callback_dict[\"cost_history\"].append(current_cost)\n", - " # Print to screen on single line\n", - " print(\n", - " \"Iters. done: {} [Current cost: {}]\".format(callback_dict[\"iters\"], current_cost),\n", - " end=\"\\r\",\n", - " flush=True,\n", - " )\n", - "\n", - " return callback" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "9f705072", - "metadata": {}, - "outputs": [], - "source": [ - "callback_dict = {\n", - " \"prev_vector\": None,\n", - " \"iters\": 0,\n", - " \"cost_history\": [],\n", - "}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can now use a classical optimizer of our choice to minimize the cost function. Here, we use the [COBYLA routine from SciPy through the `minimize` function](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.minimize.html). Note that when running on real quantum hardware, the choice of optimizer is important, as not all optimizers handle noisy cost function landscapes equally well.\n", - "\n", - "To begin the routine, we specify a random initial set of parameters:" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "x0 = 2 * np.pi * np.random.random(num_params)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "Because we are sending a large number of jobs that we would like to execute together, we use a [`Session`](https://docs.quantum-computing.ibm.com/api/qiskit-ibm-runtime/qiskit_ibm_runtime.Session) to execute all the generated circuits in one block. Here `args` is the standard SciPy way to supply the additional parameters needed by the cost function." - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "e642648e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Iters. done: 159 [Current cost: -0.6369410251499279]\r" - ] - } - ], - "source": [ - "# To run on local simulator:\n", - "# 1. Use the Estimator from qiskit.primitives instead.\n", - "# 2. Remove the Session context manager below.\n", - "\n", - "options = Options()\n", - "options.transpilation.skip_transpilation = True\n", - "options.execution.shots = 10000\n", - "\n", - "with Session(backend=backend):\n", - " estimator = Estimator(options=options)\n", - " callback = build_callback(ansatz_ibm, hamiltonian_ibm, estimator, callback_dict)\n", - " res = minimize(\n", - " cost_func,\n", - " x0,\n", - " args=(ansatz_ibm, hamiltonian_ibm, estimator),\n", - " method=\"cobyla\",\n", - " callback=callback,\n", - " )" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "At the terminus of this routine we have a result in the standard SciPy `OptimizeResult` format. From this we see that it took `nfev` number of cost function evaluations to obtain the solution vector of parameter angles (`x`) that, when plugged into the ansatz circuit, yield the approximate ground state solution we were looking for." - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - " message: Optimization terminated successfully.\n", - " success: True\n", - " status: 1\n", - " fun: -0.6342900302279935\n", - " x: [ 5.653e+00 3.403e+00 ... 3.342e+00 6.535e+00]\n", - " nfev: 159\n", - " maxcv: 0.0" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "res" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 4: Post-process, return result in classical format." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "733431ad", - "metadata": {}, - "source": [ - "If the procedure terminates correctly, then the `prev_vector` and `iters` values in our `callback_dict` dictionary should be equal to the solution vector and total number of function evaluations, respectively. This is easy to verify:" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "30630583", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "True" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "all(callback_dict[\"prev_vector\"] == res.x)" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "72ae1d21", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "True" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "callback_dict[\"iters\"] == res.nfev" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "19459b48", - "metadata": {}, - "source": [ - "We can also now view the progress towards convergence as monitored by the cost history at each iteration:" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "8501d609", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "fig, ax = plt.subplots()\n", - "ax.plot(range(callback_dict[\"iters\"]), callback_dict[\"cost_history\"])\n", - "ax.set_xlabel(\"Iterations\")\n", - "ax.set_ylabel(\"Cost\")\n", - "plt.draw()" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "ee3ac2fa", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.14.1'" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit_ibm_runtime\n", - "\n", - "qiskit_ibm_runtime.version.get_version_info()" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'0.45.0'" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "import qiskit\n", - "\n", - "qiskit.version.get_version_info()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/qiskit_ibm_runtime/api/session.py b/qiskit_ibm_runtime/api/session.py index d2e0b221b..9972c1096 100644 --- a/qiskit_ibm_runtime/api/session.py +++ b/qiskit_ibm_runtime/api/session.py @@ -19,7 +19,7 @@ import sys from typing import Dict, Optional, Any, Tuple, Union from pathlib import PurePath -import pkg_resources +import importlib.metadata from requests import Session, RequestException, Response from requests.adapters import HTTPAdapter @@ -74,7 +74,7 @@ def _get_client_header() -> str: pkg_versions = {"qiskit_ibm_runtime": f"qiskit_ibm_runtime-{ibm_runtime_version}"} for pkg_name in qiskit_pkgs: try: - version_info = f"{pkg_name}-{pkg_resources.get_distribution(pkg_name).version}" + version_info = f"{pkg_name}-{importlib.metadata.version(pkg_name)}" if pkg_name in sys.modules: version_info += "*" diff --git a/qiskit_ibm_runtime/base_primitive.py b/qiskit_ibm_runtime/base_primitive.py index d94dfe6fe..fc5f0db62 100644 --- a/qiskit_ibm_runtime/base_primitive.py +++ b/qiskit_ibm_runtime/base_primitive.py @@ -32,6 +32,7 @@ from .runtime_job import RuntimeJob from .ibm_backend import IBMBackend from .utils.default_session import get_cm_session +from .utils.deprecation import issue_deprecation_msg from .utils.utils import validate_isa_circuits from .constants import DEFAULT_DECODERS from .qiskit_runtime_service import QiskitRuntimeService @@ -138,7 +139,7 @@ def _run(self, pubs: Union[list[EstimatorPub], list[SamplerPub]]) -> RuntimeJob: if self._backend: for pub in pubs: if hasattr(self._backend, "target") and not self._backend.configuration().simulator: - validate_isa_circuits([pub.circuit], self._backend.target, raise_exc=True) + validate_isa_circuits([pub.circuit], self._backend.target) self._backend.check_faulty(pub.circuit) @@ -295,6 +296,12 @@ def __init__( raise ValueError( "A backend or session must be specified when not using ibm_cloud channel." ) + issue_deprecation_msg( + "Not providing a backend is deprecated", + "0.21.0", + "Passing in a backend will be required, please provide a backend.", + 3, + ) # Check if initialized within a IBMBackend session. If so, issue a warning. if get_cm_provider_session(): warnings.warn( @@ -312,10 +319,12 @@ def _run_primitive(self, primitive_inputs: Dict, user_kwargs: Dict) -> RuntimeJo Submitted job. """ if ( - self._backend + self._backend # pylint: disable=too-many-boolean-expressions and isinstance(self._backend, IBMBackend) and isinstance(self._backend.service, QiskitRuntimeService) - and hasattr(self._backend, "target") + and not self._backend.simulator + and getattr(self._backend, "target", None) + and self._service._channel_strategy != "q-ctrl" ): validate_isa_circuits(primitive_inputs["circuits"], self._backend.target) diff --git a/qiskit_ibm_runtime/fake_provider/__init__.py b/qiskit_ibm_runtime/fake_provider/__init__.py index a61d0ddba..80f822394 100644 --- a/qiskit_ibm_runtime/fake_provider/__init__.py +++ b/qiskit_ibm_runtime/fake_provider/__init__.py @@ -105,6 +105,7 @@ .. autosummary:: :toctree: ../stubs/ + FakeAlgiers FakeAlmadenV2 FakeArmonkV2 FakeAthensV2 @@ -112,18 +113,23 @@ FakeBelemV2 FakeBoeblingenV2 FakeBogotaV2 + FakeBrisbane FakeBrooklynV2 FakeBurlingtonV2 FakeCairoV2 FakeCambridgeV2 FakeCasablancaV2 + FakeCusco FakeEssexV2 FakeGeneva FakeGuadalupeV2 FakeHanoiV2 FakeJakartaV2 FakeJohannesburgV2 + FakeKawasaki FakeKolkataV2 + FakeKyiv + FakeKyoto FakeLagosV2 FakeLimaV2 FakeLondonV2 @@ -133,12 +139,15 @@ FakeMontrealV2 FakeMumbaiV2 FakeNairobiV2 + FakeOsaka FakeOslo FakeOurenseV2 FakeParisV2 + FakePeekskill FakePerth FakePrague FakePoughkeepsieV2 + FakeQuebec FakeQuitoV2 FakeRochesterV2 FakeRomeV2 @@ -149,6 +158,7 @@ FakeSydneyV2 .. FakeTenerifeV2 # no v2 version .. FakeTokyoV2 # no v2 version + FakeTorino FakeTorontoV2 FakeValenciaV2 FakeVigoV2 diff --git a/qiskit_ibm_runtime/fake_provider/backends/__init__.py b/qiskit_ibm_runtime/fake_provider/backends/__init__.py index 3d02c5412..7b137a244 100644 --- a/qiskit_ibm_runtime/fake_provider/backends/__init__.py +++ b/qiskit_ibm_runtime/fake_provider/backends/__init__.py @@ -16,6 +16,7 @@ """ # BackendV2 Backends +from .algiers import FakeAlgiers from .almaden import FakeAlmadenV2 from .armonk import FakeArmonkV2 from .athens import FakeAthensV2 @@ -23,18 +24,23 @@ from .belem import FakeBelemV2 from .boeblingen import FakeBoeblingenV2 from .bogota import FakeBogotaV2 +from .brisbane import FakeBrisbane from .brooklyn import FakeBrooklynV2 from .burlington import FakeBurlingtonV2 from .cairo import FakeCairoV2 from .cambridge import FakeCambridgeV2 from .casablanca import FakeCasablancaV2 +from .cusco import FakeCusco from .essex import FakeEssexV2 from .geneva import FakeGeneva from .guadalupe import FakeGuadalupeV2 from .hanoi import FakeHanoiV2 from .jakarta import FakeJakartaV2 from .johannesburg import FakeJohannesburgV2 +from .kawasaki import FakeKawasaki from .kolkata import FakeKolkataV2 +from .kyiv import FakeKyiv +from .kyoto import FakeKyoto from .lagos import FakeLagosV2 from .lima import FakeLimaV2 from .london import FakeLondonV2 @@ -44,12 +50,15 @@ from .montreal import FakeMontrealV2 from .mumbai import FakeMumbaiV2 from .nairobi import FakeNairobiV2 +from .osaka import FakeOsaka from .oslo import FakeOslo from .ourense import FakeOurenseV2 from .paris import FakeParisV2 +from .peekskill import FakePeekskill from .perth import FakePerth from .prague import FakePrague from .poughkeepsie import FakePoughkeepsieV2 +from .quebec import FakeQuebec from .quito import FakeQuitoV2 from .rochester import FakeRochesterV2 from .rome import FakeRomeV2 @@ -57,6 +66,7 @@ from .sherbrooke import FakeSherbrooke from .singapore import FakeSingaporeV2 from .sydney import FakeSydneyV2 +from .torino import FakeTorino from .toronto import FakeTorontoV2 from .valencia import FakeValenciaV2 from .vigo import FakeVigoV2 diff --git a/qiskit_ibm_runtime/fake_provider/backends/algiers/__init__.py b/qiskit_ibm_runtime/fake_provider/backends/algiers/__init__.py new file mode 100644 index 000000000..c5df08eeb --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/algiers/__init__.py @@ -0,0 +1,15 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2019, 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Mock algiers backend""" + +from .fake_algiers import FakeAlgiers diff --git a/qiskit_ibm_runtime/fake_provider/backends/algiers/conf_algiers.json b/qiskit_ibm_runtime/fake_provider/backends/algiers/conf_algiers.json new file mode 100644 index 000000000..d7cfac594 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/algiers/conf_algiers.json @@ -0,0 +1 @@ +{"backend_name": "ibm_algiers", "backend_version": "1.6.16", "n_qubits": 27, "basis_gates": ["cx", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "rz", "parameters": ["theta"], "qasm_def": "gate rz(theta) q { U(0, 0, theta) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "sx", "parameters": [], "qasm_def": "gate sx q { U(pi/2, 3*pi/2, pi/2) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "x", "parameters": [], "qasm_def": "gate x q { U(pi, 0, pi) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "cx", "parameters": [], "qasm_def": "gate cx q0, q1 { CX q0, q1; }", "coupling_map": [[0, 1], [1, 0], [1, 2], [1, 4], [2, 1], [2, 3], [3, 2], [3, 5], [4, 1], [4, 7], [5, 3], [5, 8], [6, 7], [7, 4], [7, 6], [7, 10], [8, 5], [8, 9], [8, 11], [9, 8], [10, 7], [10, 12], [11, 8], [11, 14], [12, 10], [12, 13], [12, 15], [13, 12], [13, 14], [14, 11], [14, 13], [14, 16], [15, 12], [15, 18], [16, 14], [16, 19], [17, 18], [18, 15], [18, 17], [18, 21], [19, 16], [19, 20], [19, 22], [20, 19], [21, 18], [21, 23], [22, 19], [22, 25], [23, 21], [23, 24], [24, 23], [24, 25], [25, 22], [25, 24], [25, 26], [26, 25]]}, {"name": "reset", "parameters": null, "qasm_def": null}], "local": false, "simulator": false, "conditional": false, "open_pulse": true, "memory": true, "max_shots": 100000, "coupling_map": [[0, 1], [1, 0], [1, 2], [1, 4], [2, 1], [2, 3], [3, 2], [3, 5], [4, 1], [4, 7], [5, 3], [5, 8], [6, 7], [7, 4], [7, 6], [7, 10], [8, 5], [8, 9], [8, 11], [9, 8], [10, 7], [10, 12], [11, 8], [11, 14], [12, 10], [12, 13], [12, 15], [13, 12], [13, 14], [14, 11], [14, 13], [14, 16], [15, 12], [15, 18], [16, 14], [16, 19], [17, 18], [18, 15], [18, 17], [18, 21], [19, 16], [19, 20], [19, 22], [20, 19], [21, 18], [21, 23], [22, 19], [22, 25], [23, 21], [23, 24], [24, 23], [24, 25], [25, 22], [25, 24], [25, 26], [26, 25]], "dynamic_reprate_enabled": true, "supported_instructions": ["cx", "id", "delay", "measure", "reset", "rz", "sx", "x", "if_else", "for_loop", "switch_case"], "rep_delay_range": [0.0, 500.0], "default_rep_delay": 250.0, "max_experiments": 300, "sample_name": "family: Falcon, revision: 5.11", "n_registers": 1, "credits_required": true, "online_date": "2021-04-05T04:00:00+00:00", "description": "27 qubit device", "dt": 0.2222222222222222, "dtm": 0.2222222222222222, "processor_type": {"family": "Falcon", "revision": "5.11"}, "parametric_pulses": ["gaussian", "gaussian_square", "gaussian_square_drag", "drag", "constant"], "allow_q_object": true, "clops": 2207, "clops_h": "None", "clops_v": 2207, "coords": [[1, 2], [2, 2], [2, 3], [2, 4], [3, 2], [3, 4], [4, 1], [4, 2], [4, 4], [4, 5], [5, 2], [5, 4], [6, 2], [6, 3], [6, 4], [7, 2], [7, 4], [8, 1], [8, 2], [8, 4], [8, 5], [9, 2], [9, 4], [10, 2], [10, 3], [10, 4], [11, 4]], "measure_esp_enabled": false, "multi_meas_enabled": true, "parallel_compilation": true, "quantum_volume": 128, "qubit_channel_mapping": [["m0", "d0", "u1", "u0"], ["u4", "u3", "u2", "u8", "u1", "u0", "m1", "d1"], ["m2", "u4", "u2", "u5", "d2", "u6"], ["u7", "u10", "u5", "d3", "m3", "u6"], ["u13", "m4", "u9", "u3", "u8", "d4"], ["u7", "d5", "u11", "u10", "m5", "u16"], ["d6", "u14", "u12", "m6"], ["u13", "d7", "u12", "u9", "u20", "u15", "m7", "u14"], ["u18", "u22", "m8", "u17", "d8", "u11", "u19", "u16"], ["u19", "u17", "d9", "m9"], ["m10", "d10", "u21", "u24", "u20", "u15"], ["u18", "u22", "u29", "u23", "m11", "d11"], ["u25", "d12", "m12", "u21", "u24", "u32", "u26", "u27"], ["u30", "m13", "u25", "u28", "d13", "u27"], ["u30", "u31", "u28", "m14", "u34", "u29", "u23", "d14"], ["u26", "m15", "u37", "d15", "u32", "u33"], ["u31", "u35", "u40", "u34", "m16", "d16"], ["u36", "m17", "u38", "d17"], ["m18", "u44", "u37", "u39", "d18", "u33", "u38", "u36"], ["u35", "u41", "u40", "u42", "d19", "u43", "m19", "u46"], ["u43", "d20", "m20", "u41"], ["u44", "m21", "u45", "u39", "d21", "u48"], ["u52", "u42", "d22", "m22", "u46", "u47"], ["d23", "u49", "u45", "u50", "m23", "u48"], ["d24", "u49", "u53", "m24", "u50", "u51"], ["m25", "u54", "u52", "u53", "d25", "u47", "u55", "u51"], ["u55", "d26", "u54", "m26"]], "supported_features": ["qobj", "qasm3", "parameters"], "timing_constraints": {"acquire_alignment": 16, "granularity": 16, "min_length": 64, "pulse_alignment": 16}, "uchannels_enabled": true, "url": "None", "n_uchannels": 56, "u_channel_lo": [[{"q": 1, "scale": [1.0, 0.0]}], [{"q": 0, "scale": [1.0, 0.0]}], [{"q": 2, "scale": [1.0, 0.0]}], [{"q": 4, "scale": [1.0, 0.0]}], [{"q": 1, "scale": [1.0, 0.0]}], [{"q": 3, "scale": [1.0, 0.0]}], [{"q": 2, "scale": [1.0, 0.0]}], [{"q": 5, "scale": [1.0, 0.0]}], [{"q": 1, "scale": [1.0, 0.0]}], [{"q": 7, "scale": [1.0, 0.0]}], [{"q": 3, "scale": [1.0, 0.0]}], [{"q": 8, "scale": [1.0, 0.0]}], [{"q": 7, "scale": [1.0, 0.0]}], [{"q": 4, "scale": [1.0, 0.0]}], [{"q": 6, "scale": [1.0, 0.0]}], [{"q": 10, "scale": [1.0, 0.0]}], [{"q": 5, "scale": [1.0, 0.0]}], [{"q": 9, "scale": [1.0, 0.0]}], [{"q": 11, "scale": [1.0, 0.0]}], [{"q": 8, "scale": [1.0, 0.0]}], [{"q": 7, "scale": [1.0, 0.0]}], [{"q": 12, "scale": [1.0, 0.0]}], [{"q": 8, "scale": [1.0, 0.0]}], [{"q": 14, "scale": [1.0, 0.0]}], [{"q": 10, "scale": [1.0, 0.0]}], [{"q": 13, "scale": [1.0, 0.0]}], [{"q": 15, "scale": [1.0, 0.0]}], [{"q": 12, "scale": [1.0, 0.0]}], [{"q": 14, "scale": [1.0, 0.0]}], [{"q": 11, "scale": [1.0, 0.0]}], [{"q": 13, "scale": [1.0, 0.0]}], [{"q": 16, "scale": [1.0, 0.0]}], [{"q": 12, "scale": [1.0, 0.0]}], [{"q": 18, "scale": [1.0, 0.0]}], [{"q": 14, "scale": [1.0, 0.0]}], [{"q": 19, "scale": [1.0, 0.0]}], [{"q": 18, "scale": [1.0, 0.0]}], [{"q": 15, "scale": [1.0, 0.0]}], [{"q": 17, "scale": [1.0, 0.0]}], [{"q": 21, "scale": [1.0, 0.0]}], [{"q": 16, "scale": [1.0, 0.0]}], [{"q": 20, "scale": [1.0, 0.0]}], [{"q": 22, "scale": [1.0, 0.0]}], [{"q": 19, "scale": [1.0, 0.0]}], [{"q": 18, "scale": [1.0, 0.0]}], [{"q": 23, "scale": [1.0, 0.0]}], [{"q": 19, "scale": [1.0, 0.0]}], [{"q": 25, "scale": [1.0, 0.0]}], [{"q": 21, "scale": [1.0, 0.0]}], [{"q": 24, "scale": [1.0, 0.0]}], [{"q": 23, "scale": [1.0, 0.0]}], [{"q": 25, "scale": [1.0, 0.0]}], [{"q": 22, "scale": [1.0, 0.0]}], [{"q": 24, "scale": [1.0, 0.0]}], [{"q": 26, "scale": [1.0, 0.0]}], [{"q": 25, "scale": [1.0, 0.0]}]], "meas_levels": [1, 2], "qubit_lo_range": [[4.446248807603483, 5.446248807603483], [4.336040434589742, 5.336040434589742], [4.553233007164219, 5.553233007164219], [4.696613151975914, 5.696613151975914], [4.4590786224531165, 5.4590786224531165], [4.617648479620899, 5.617648479620899], [4.487114609638608, 5.487114609638608], [4.3824511106257305, 5.3824511106257305], [4.518662816655313, 5.518662816655313], [4.404233395293412, 5.404233395293412], [4.449044175232115, 5.449044175232115], [4.595122420582114, 5.595122420582114], [4.564200295428892, 5.564200295428892], [4.613826937078962, 5.613826937078962], [4.4867753786507025, 5.4867753786507025], [4.307068120797327, 5.307068120797328], [4.340624240934397, 5.340624240934397], [4.388191510248538, 5.388191510248538], [4.50968724498873, 5.50968724498873], [4.718663310842294, 5.718663310842294], [4.46190027416345, 5.46190027416345], [4.556479337728322, 5.556479337728322], [4.478398881710825, 5.478398881710825], [4.713688210641528, 5.713688210641528], [4.523834034855124, 5.523834034855124], [4.397169531307483, 5.397169531307483], [4.340543414933506, 5.340543414933506]], "meas_lo_range": [[6.682333511, 7.682333511], [6.7848285740000005, 7.7848285740000005], [6.656635066000001, 7.656635066000001], [6.78238553, 7.782385530000001], [6.7297906880000005, 7.7297906880000005], [6.735618893000001, 7.735618893000001], [6.854962329, 7.854962329], [6.599837422, 7.599837422], [6.596746328, 7.596746328], [6.8187382770000005, 7.8187382770000005], [6.6686637630000005, 7.6686637630000005], [6.724839654, 7.724839654], [6.8291957420000005, 7.8291957420000005], [6.717515072, 7.717515072], [6.775359312000001, 7.775359312000001], [6.7769424350000005, 7.7769424350000005], [6.653391272, 7.653391272], [6.8456216350000005, 7.8456216350000005], [6.6029343460000005, 7.6029343460000005], [6.586879072, 7.586879072], [6.825932929, 7.825932929], [6.725693265, 7.725693265], [6.713867862000001, 7.713867862000001], [6.781297014000001, 7.781297014000001], [6.640965798000001, 7.640965798000001], [6.763616893, 7.763616893000001], [6.635071079760153, 7.635071079760153]], "meas_kernels": ["hw_qmfk"], "discriminators": ["linear_discriminator", "quadratic_discriminator", "hw_qmfk"], "rep_times": [1000.0], "meas_map": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]], "acquisition_latency": [], "conditional_latency": [], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{26}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{14,16}(\\sigma_{14}^{+}\\sigma_{16}^{-}+\\sigma_{14}^{-}\\sigma_{16}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{17,18}(\\sigma_{17}^{+}\\sigma_{18}^{-}+\\sigma_{17}^{-}\\sigma_{18}^{+}) \\\\ & + J_{11,14}(\\sigma_{11}^{+}\\sigma_{14}^{-}+\\sigma_{11}^{-}\\sigma_{14}^{+}) + J_{10,12}(\\sigma_{10}^{+}\\sigma_{12}^{-}+\\sigma_{10}^{-}\\sigma_{12}^{+}) + J_{13,14}(\\sigma_{13}^{+}\\sigma_{14}^{-}+\\sigma_{13}^{-}\\sigma_{14}^{+}) + J_{16,19}(\\sigma_{16}^{+}\\sigma_{19}^{-}+\\sigma_{16}^{-}\\sigma_{19}^{+}) \\\\ & + J_{7,10}(\\sigma_{7}^{+}\\sigma_{10}^{-}+\\sigma_{7}^{-}\\sigma_{10}^{+}) + J_{12,15}(\\sigma_{12}^{+}\\sigma_{15}^{-}+\\sigma_{12}^{-}\\sigma_{15}^{+}) + J_{22,25}(\\sigma_{22}^{+}\\sigma_{25}^{-}+\\sigma_{22}^{-}\\sigma_{25}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) \\\\ & + J_{8,11}(\\sigma_{8}^{+}\\sigma_{11}^{-}+\\sigma_{8}^{-}\\sigma_{11}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) \\\\ & + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) + J_{18,21}(\\sigma_{18}^{+}\\sigma_{21}^{-}+\\sigma_{18}^{-}\\sigma_{21}^{+}) + J_{4,7}(\\sigma_{4}^{+}\\sigma_{7}^{-}+\\sigma_{4}^{-}\\sigma_{7}^{+}) \\\\ & + J_{21,23}(\\sigma_{21}^{+}\\sigma_{23}^{-}+\\sigma_{21}^{-}\\sigma_{23}^{+}) + J_{3,5}(\\sigma_{3}^{+}\\sigma_{5}^{-}+\\sigma_{3}^{-}\\sigma_{5}^{+}) + J_{5,8}(\\sigma_{5}^{+}\\sigma_{8}^{-}+\\sigma_{5}^{-}\\sigma_{8}^{+}) + J_{1,4}(\\sigma_{1}^{+}\\sigma_{4}^{-}+\\sigma_{1}^{-}\\sigma_{4}^{+}) \\\\ & + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{19,22}(\\sigma_{19}^{+}\\sigma_{22}^{-}+\\sigma_{19}^{-}\\sigma_{22}^{+}) + J_{15,18}(\\sigma_{15}^{+}\\sigma_{18}^{-}+\\sigma_{15}^{-}\\sigma_{18}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) \\\\ & + \\Omega_{d,0}(U_{0}^{(0,1)}(t))\\sigma_{0}^{X} + \\Omega_{d,1}(U_{1}^{(1,0)}(t)+U_{3}^{(1,4)}(t)+U_{2}^{(1,2)}(t))\\sigma_{1}^{X} \\\\ & + \\Omega_{d,2}(U_{5}^{(2,3)}(t)+U_{4}^{(2,1)}(t))\\sigma_{2}^{X} + \\Omega_{d,3}(U_{6}^{(3,2)}(t)+U_{7}^{(3,5)}(t))\\sigma_{3}^{X} \\\\ & + \\Omega_{d,4}(U_{9}^{(4,7)}(t)+U_{8}^{(4,1)}(t))\\sigma_{4}^{X} + \\Omega_{d,5}(U_{11}^{(5,8)}(t)+U_{10}^{(5,3)}(t))\\sigma_{5}^{X} \\\\ & + \\Omega_{d,6}(U_{12}^{(6,7)}(t))\\sigma_{6}^{X} + \\Omega_{d,7}(U_{14}^{(7,6)}(t)+U_{13}^{(7,4)}(t)+U_{15}^{(7,10)}(t))\\sigma_{7}^{X} \\\\ & + \\Omega_{d,8}(U_{18}^{(8,11)}(t)+U_{16}^{(8,5)}(t)+U_{17}^{(8,9)}(t))\\sigma_{8}^{X} + \\Omega_{d,9}(U_{19}^{(9,8)}(t))\\sigma_{9}^{X} \\\\ & + \\Omega_{d,10}(U_{20}^{(10,7)}(t)+U_{21}^{(10,12)}(t))\\sigma_{10}^{X} + \\Omega_{d,11}(U_{22}^{(11,8)}(t)+U_{23}^{(11,14)}(t))\\sigma_{11}^{X} \\\\ & + \\Omega_{d,12}(U_{24}^{(12,10)}(t)+U_{25}^{(12,13)}(t)+U_{26}^{(12,15)}(t))\\sigma_{12}^{X} + \\Omega_{d,13}(U_{28}^{(13,14)}(t)+U_{27}^{(13,12)}(t))\\sigma_{13}^{X} \\\\ & + \\Omega_{d,14}(U_{31}^{(14,16)}(t)+U_{30}^{(14,13)}(t)+U_{29}^{(14,11)}(t))\\sigma_{14}^{X} + \\Omega_{d,15}(U_{33}^{(15,18)}(t)+U_{32}^{(15,12)}(t))\\sigma_{15}^{X} \\\\ & + \\Omega_{d,16}(U_{35}^{(16,19)}(t)+U_{34}^{(16,14)}(t))\\sigma_{16}^{X} + \\Omega_{d,17}(U_{36}^{(17,18)}(t))\\sigma_{17}^{X} \\\\ & + \\Omega_{d,18}(U_{37}^{(18,15)}(t)+U_{39}^{(18,21)}(t)+U_{38}^{(18,17)}(t))\\sigma_{18}^{X} + \\Omega_{d,19}(U_{42}^{(19,22)}(t)+U_{40}^{(19,16)}(t)+U_{41}^{(19,20)}(t))\\sigma_{19}^{X} \\\\ & + \\Omega_{d,20}(U_{43}^{(20,19)}(t))\\sigma_{20}^{X} + \\Omega_{d,21}(U_{44}^{(21,18)}(t)+U_{45}^{(21,23)}(t))\\sigma_{21}^{X} \\\\ & + \\Omega_{d,22}(U_{46}^{(22,19)}(t)+U_{47}^{(22,25)}(t))\\sigma_{22}^{X} + \\Omega_{d,23}(U_{49}^{(23,24)}(t)+U_{48}^{(23,21)}(t))\\sigma_{23}^{X} \\\\ & + \\Omega_{d,24}(U_{50}^{(24,23)}(t)+U_{51}^{(24,25)}(t))\\sigma_{24}^{X} + \\Omega_{d,25}(U_{54}^{(25,26)}(t)+U_{53}^{(25,24)}(t)+U_{52}^{(25,22)}(t))\\sigma_{25}^{X} \\\\ & + \\Omega_{d,26}(U_{55}^{(26,25)}(t))\\sigma_{26}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,26,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,26,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,26,-delta{i}/2*O{i}]", "_SUM[i,0,26,omegad{i}*X{i}||D{i}]", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq14q16*Sp14*Sm16", "jq14q16*Sm14*Sp16", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq17q18*Sp17*Sm18", "jq17q18*Sm17*Sp18", "jq11q14*Sp11*Sm14", "jq11q14*Sm11*Sp14", "jq10q12*Sp10*Sm12", "jq10q12*Sm10*Sp12", "jq13q14*Sp13*Sm14", "jq13q14*Sm13*Sp14", "jq16q19*Sp16*Sm19", "jq16q19*Sm16*Sp19", "jq7q10*Sp7*Sm10", "jq7q10*Sm7*Sp10", "jq12q15*Sp12*Sm15", "jq12q15*Sm12*Sp15", "jq22q25*Sp22*Sm25", "jq22q25*Sm22*Sp25", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq8q11*Sp8*Sm11", "jq8q11*Sm8*Sp11", "jq0q1*Sp0*Sm1", "jq0q1*Sm0*Sp1", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq19q20*Sp19*Sm20", "jq19q20*Sm19*Sp20", "jq6q7*Sp6*Sm7", "jq6q7*Sm6*Sp7", "jq24q25*Sp24*Sm25", "jq24q25*Sm24*Sp25", "jq18q21*Sp18*Sm21", "jq18q21*Sm18*Sp21", "jq4q7*Sp4*Sm7", "jq4q7*Sm4*Sp7", "jq21q23*Sp21*Sm23", "jq21q23*Sm21*Sp23", "jq3q5*Sp3*Sm5", "jq3q5*Sm3*Sp5", "jq5q8*Sp5*Sm8", "jq5q8*Sm5*Sp8", "jq1q4*Sp1*Sm4", "jq1q4*Sm1*Sp4", "jq2q3*Sp2*Sm3", "jq2q3*Sm2*Sp3", "jq19q22*Sp19*Sm22", "jq19q22*Sm19*Sp22", "jq15q18*Sp15*Sm18", "jq15q18*Sm15*Sp18", "jq25q26*Sp25*Sm26", "jq25q26*Sm25*Sp26", "omegad1*X0||U0", "omegad0*X1||U1", "omegad4*X1||U3", "omegad2*X1||U2", "omegad3*X2||U5", "omegad1*X2||U4", "omegad2*X3||U6", "omegad5*X3||U7", "omegad7*X4||U9", "omegad1*X4||U8", "omegad8*X5||U11", "omegad3*X5||U10", "omegad7*X6||U12", "omegad6*X7||U14", "omegad4*X7||U13", "omegad10*X7||U15", "omegad11*X8||U18", "omegad5*X8||U16", "omegad9*X8||U17", "omegad8*X9||U19", "omegad7*X10||U20", "omegad12*X10||U21", "omegad8*X11||U22", "omegad14*X11||U23", "omegad10*X12||U24", "omegad13*X12||U25", "omegad15*X12||U26", "omegad14*X13||U28", "omegad12*X13||U27", "omegad16*X14||U31", "omegad13*X14||U30", "omegad11*X14||U29", "omegad18*X15||U33", "omegad12*X15||U32", "omegad19*X16||U35", "omegad14*X16||U34", "omegad18*X17||U36", "omegad15*X18||U37", "omegad21*X18||U39", "omegad17*X18||U38", "omegad22*X19||U42", "omegad16*X19||U40", "omegad20*X19||U41", "omegad19*X20||U43", "omegad18*X21||U44", "omegad23*X21||U45", "omegad19*X22||U46", "omegad25*X22||U47", "omegad24*X23||U49", "omegad21*X23||U48", "omegad23*X24||U50", "omegad25*X24||U51", "omegad26*X25||U54", "omegad24*X25||U53", "omegad22*X25||U52", "omegad25*X26||U55"], "osc": {}, "qub": {"0": 3, "1": 3, "2": 3, "3": 3, "4": 3, "5": 3, "6": 3, "7": 3, "8": 3, "9": 3, "10": 3, "11": 3, "12": 3, "13": 3, "14": 3, "15": 3, "16": 3, "17": 3, "18": 3, "19": 3, "20": 3, "21": 3, "22": 3, "23": 3, "24": 3, "25": 3, "26": 3}, "vars": {"delta0": -2.1622826015485503, "delta1": -2.19094846948798, "delta10": -2.165641789507037, "delta11": -2.153588280908217, "delta12": -2.149269831098767, "delta13": -2.1494043600753567, "delta14": -2.166723789069752, "delta15": -2.139516334526724, "delta16": -2.156979169308944, "delta17": -2.1781025499595423, "delta18": -2.162119393246999, "delta19": -2.058544640838485, "delta2": -2.1460247721995067, "delta20": -2.1641632766861605, "delta21": -2.150299554253934, "delta22": -2.1645188765442502, "delta23": -2.1287260375040225, "delta24": -2.14687381685653, "delta25": -2.166662107981824, "delta26": -1.9666552852491166, "delta3": -2.131518241734603, "delta4": -2.1558636417441077, "delta5": -2.1396291496108106, "delta6": -2.164412572163615, "delta7": -2.171509874597629, "delta8": -2.0847625020447587, "delta9": -2.170793497320232, "jq0q1": 0.011658408259756836, "jq10q12": 0.01217892994105004, "jq11q14": 0.011710632176852606, "jq12q13": 0.01235286257193023, "jq12q15": 0.01069408900329158, "jq13q14": 0.012512245649176587, "jq14q16": 0.011290740650832585, "jq15q18": 0.011307458021039633, "jq16q19": 0.013919332699150137, "jq17q18": 0.011577202053600077, "jq18q21": 0.012445157388140017, "jq19q20": 0.012094656628184, "jq19q22": 0.012615495880226221, "jq1q2": 0.011726940202180874, "jq1q4": 0.011423209003638088, "jq21q23": 0.01254108888890023, "jq22q25": 0.011483385385923197, "jq23q24": 0.012286138821259791, "jq24q25": 0.01189270352827205, "jq25q26": 0.011547849558933123, "jq2q3": 0.012243673651327744, "jq3q5": 0.012538317917394829, "jq4q7": 0.011984580638207336, "jq5q8": 0.012633302437594748, "jq6q7": 0.011750407381754977, "jq7q10": 0.011284590637237827, "jq8q11": 0.011814341082307415, "jq8q9": 0.011795351249621012, "omegad0": 0.8043180622397951, "omegad1": 0.845086506401278, "omegad10": 1.008616298529125, "omegad11": 0.9316267525151758, "omegad12": 1.1617398921078528, "omegad13": 0.9191234388066172, "omegad14": 0.7214965437852621, "omegad15": 0.9179461465979629, "omegad16": 0.8995936666118417, "omegad17": 0.77986016511056, "omegad18": 0.8509689233666445, "omegad19": 0.5282318858529043, "omegad2": 0.859668941725556, "omegad20": 0.9421544528167258, "omegad21": 0.8627517626176934, "omegad22": 0.9147699666287735, "omegad23": 1.018798559767531, "omegad24": 0.958004041591501, "omegad25": 1.2119306004926544, "omegad26": 0.8213216926045044, "omegad3": 1.0807219923750793, "omegad4": 0.9073682058751147, "omegad5": 0.9179633133119361, "omegad6": 1.3718056717951415, "omegad7": 0.8027777023371467, "omegad8": 1.2330258284732332, "omegad9": 0.7231993997796026, "wq0": 31.078197833588753, "wq1": 30.385738203540647, "wq10": 31.09576164640114, "wq11": 32.01359833128282, "wq12": 31.819308888853335, "wq13": 32.13112227451372, "wq14": 31.332833789343017, "wq15": 30.203699787205156, "wq16": 30.414539108216346, "wq17": 30.713413075873607, "wq18": 31.47679329127817, "wq19": 32.78982863780148, "wq2": 31.750399384369143, "wq20": 31.176538898314153, "wq21": 31.770796680871758, "wq22": 31.28020270684474, "wq23": 32.75856916131827, "wq24": 31.56568019351045, "wq25": 30.769823645878716, "wq26": 30.4140312634751, "wq3": 32.65128340359126, "wq4": 31.158809937745804, "wq5": 32.15513373446398, "wq6": 31.334965240501962, "wq7": 30.67734508130625, "wq8": 31.533188471297183, "wq9": 30.81420721228702}}, "channels": {"acquire0": {"operates": {"qubits": [0]}, "purpose": "acquire", "type": "acquire"}, "acquire1": {"operates": {"qubits": [1]}, "purpose": "acquire", "type": "acquire"}, "acquire10": {"operates": {"qubits": [10]}, "purpose": "acquire", "type": "acquire"}, "acquire11": {"operates": {"qubits": [11]}, "purpose": "acquire", "type": "acquire"}, "acquire12": {"operates": {"qubits": [12]}, "purpose": "acquire", "type": "acquire"}, "acquire13": {"operates": {"qubits": [13]}, "purpose": "acquire", "type": "acquire"}, "acquire14": {"operates": {"qubits": [14]}, "purpose": "acquire", "type": "acquire"}, "acquire15": {"operates": {"qubits": [15]}, "purpose": "acquire", "type": "acquire"}, "acquire16": {"operates": {"qubits": [16]}, "purpose": "acquire", "type": "acquire"}, "acquire17": {"operates": {"qubits": [17]}, "purpose": "acquire", "type": "acquire"}, "acquire18": {"operates": {"qubits": [18]}, "purpose": "acquire", "type": "acquire"}, "acquire19": {"operates": {"qubits": [19]}, "purpose": "acquire", "type": "acquire"}, "acquire2": {"operates": {"qubits": [2]}, "purpose": "acquire", "type": "acquire"}, "acquire20": {"operates": {"qubits": [20]}, "purpose": "acquire", "type": "acquire"}, "acquire21": {"operates": {"qubits": [21]}, "purpose": "acquire", "type": "acquire"}, "acquire22": {"operates": {"qubits": [22]}, "purpose": "acquire", "type": "acquire"}, "acquire23": {"operates": {"qubits": [23]}, "purpose": "acquire", "type": "acquire"}, "acquire24": {"operates": {"qubits": [24]}, "purpose": "acquire", "type": "acquire"}, "acquire25": {"operates": {"qubits": [25]}, "purpose": "acquire", "type": "acquire"}, "acquire26": {"operates": {"qubits": [26]}, "purpose": "acquire", "type": "acquire"}, "acquire3": {"operates": {"qubits": [3]}, "purpose": "acquire", "type": "acquire"}, "acquire4": {"operates": {"qubits": [4]}, "purpose": "acquire", "type": "acquire"}, "acquire5": {"operates": {"qubits": [5]}, "purpose": "acquire", "type": "acquire"}, "acquire6": {"operates": {"qubits": [6]}, "purpose": "acquire", "type": "acquire"}, "acquire7": {"operates": {"qubits": [7]}, "purpose": "acquire", "type": "acquire"}, "acquire8": {"operates": {"qubits": [8]}, "purpose": "acquire", "type": "acquire"}, "acquire9": {"operates": {"qubits": [9]}, "purpose": "acquire", "type": "acquire"}, "d0": {"operates": {"qubits": [0]}, "purpose": "drive", "type": "drive"}, "d1": {"operates": {"qubits": [1]}, "purpose": "drive", "type": "drive"}, "d10": {"operates": {"qubits": [10]}, "purpose": "drive", "type": "drive"}, "d11": {"operates": {"qubits": [11]}, "purpose": "drive", "type": "drive"}, "d12": {"operates": {"qubits": [12]}, "purpose": "drive", "type": "drive"}, "d13": {"operates": {"qubits": [13]}, "purpose": "drive", "type": "drive"}, "d14": {"operates": {"qubits": [14]}, "purpose": "drive", "type": "drive"}, "d15": {"operates": {"qubits": [15]}, "purpose": "drive", "type": "drive"}, "d16": {"operates": {"qubits": [16]}, "purpose": "drive", "type": "drive"}, "d17": {"operates": {"qubits": [17]}, "purpose": "drive", "type": "drive"}, "d18": {"operates": {"qubits": [18]}, "purpose": "drive", "type": "drive"}, "d19": {"operates": {"qubits": [19]}, "purpose": "drive", "type": "drive"}, "d2": {"operates": {"qubits": [2]}, "purpose": "drive", "type": "drive"}, "d20": {"operates": {"qubits": [20]}, "purpose": "drive", "type": "drive"}, "d21": {"operates": {"qubits": [21]}, "purpose": "drive", "type": "drive"}, "d22": {"operates": {"qubits": [22]}, "purpose": "drive", "type": "drive"}, "d23": {"operates": {"qubits": [23]}, "purpose": "drive", "type": "drive"}, "d24": {"operates": {"qubits": [24]}, "purpose": "drive", "type": "drive"}, "d25": {"operates": {"qubits": [25]}, "purpose": "drive", "type": "drive"}, "d26": {"operates": {"qubits": [26]}, "purpose": "drive", "type": "drive"}, "d3": {"operates": {"qubits": [3]}, "purpose": "drive", "type": "drive"}, "d4": {"operates": {"qubits": [4]}, "purpose": "drive", "type": "drive"}, "d5": {"operates": {"qubits": [5]}, "purpose": "drive", "type": "drive"}, "d6": {"operates": {"qubits": [6]}, "purpose": "drive", "type": "drive"}, "d7": {"operates": {"qubits": [7]}, "purpose": "drive", "type": "drive"}, "d8": {"operates": {"qubits": [8]}, "purpose": "drive", "type": "drive"}, "d9": {"operates": {"qubits": [9]}, "purpose": "drive", "type": "drive"}, "m0": {"operates": {"qubits": [0]}, "purpose": "measure", "type": "measure"}, "m1": {"operates": {"qubits": [1]}, "purpose": "measure", "type": "measure"}, "m10": {"operates": {"qubits": [10]}, "purpose": "measure", "type": "measure"}, "m11": {"operates": {"qubits": [11]}, "purpose": "measure", "type": "measure"}, "m12": {"operates": {"qubits": [12]}, "purpose": "measure", "type": "measure"}, "m13": {"operates": {"qubits": [13]}, "purpose": "measure", "type": "measure"}, "m14": {"operates": {"qubits": [14]}, "purpose": "measure", "type": "measure"}, "m15": {"operates": {"qubits": [15]}, "purpose": "measure", "type": "measure"}, "m16": {"operates": {"qubits": [16]}, "purpose": "measure", "type": "measure"}, "m17": {"operates": {"qubits": [17]}, "purpose": "measure", "type": "measure"}, "m18": {"operates": {"qubits": [18]}, "purpose": "measure", "type": "measure"}, "m19": {"operates": {"qubits": [19]}, "purpose": "measure", "type": "measure"}, "m2": {"operates": {"qubits": [2]}, "purpose": "measure", "type": "measure"}, "m20": {"operates": {"qubits": [20]}, "purpose": "measure", "type": "measure"}, "m21": {"operates": {"qubits": [21]}, "purpose": "measure", "type": "measure"}, "m22": {"operates": {"qubits": [22]}, "purpose": "measure", "type": "measure"}, "m23": {"operates": {"qubits": [23]}, "purpose": "measure", "type": "measure"}, "m24": {"operates": {"qubits": [24]}, "purpose": "measure", "type": "measure"}, "m25": {"operates": {"qubits": [25]}, "purpose": "measure", "type": "measure"}, "m26": {"operates": {"qubits": [26]}, "purpose": 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"parameters": {"amp": [0.23077587023102858, 0.0], "beta": -1.4656698865632507, "duration": 160, "sigma": 40}}]}], "meas_kernel": {"name": "hw_qmfk", "params": {}}, "discriminator": {"name": "hw_qmfk", "params": {}}, "_data": {}} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/algiers/fake_algiers.py b/qiskit_ibm_runtime/fake_provider/backends/algiers/fake_algiers.py new file mode 100644 index 000000000..136521e70 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/algiers/fake_algiers.py @@ -0,0 +1,28 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2021, 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Algiers device (27 qubit). +""" + +import os +from qiskit_ibm_runtime.fake_provider import fake_backend + + +class FakeAlgiers(fake_backend.FakeBackendV2): + """A fake 27 qubit backend.""" + + dirname = os.path.dirname(__file__) # type: ignore + conf_filename = "conf_algiers.json" # type: ignore + props_filename = "props_algiers.json" # type: ignore + defs_filename = "defs_algiers.json" # type: ignore + backend_name = "fake_algiers" # type: ignore diff --git a/qiskit_ibm_runtime/fake_provider/backends/algiers/props_algiers.json b/qiskit_ibm_runtime/fake_provider/backends/algiers/props_algiers.json new file mode 100644 index 000000000..1ff205aab --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/algiers/props_algiers.json @@ -0,0 +1 @@ +{"backend_name": "ibm_algiers", "backend_version": "1.6.16", "last_update_date": "2024-02-28T08:32:31-05:00", "qubits": [[{"date": "2024-02-28T04:01:01-05:00", "name": "T1", "unit": "us", "value": 125.88397075066983}, {"date": "2024-02-28T04:08:21-05:00", "name": "T2", "unit": "us", "value": 121.65227414635687}, {"date": "2024-02-28T08:32:31-05:00", "name": "frequency", "unit": "GHz", "value": 4.946248807603483}, {"date": "2024-02-28T08:32:31-05:00", "name": "anharmonicity", "unit": "GHz", "value": -0.3441379643980549}, {"date": "2024-02-28T03:53:30-05:00", "name": "readout_error", "unit": "", "value": 0.007600000000000051}, {"date": "2024-02-28T03:53:30-05:00", "name": "prob_meas0_prep1", "unit": "", "value": 0.008000000000000007}, {"date": "2024-02-28T03:53:30-05:00", "name": "prob_meas1_prep0", "unit": "", "value": 0.0072}, {"date": 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You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Brisbane backend (127 qubit). +""" + +from .fake_brisbane import FakeBrisbane diff --git a/qiskit_ibm_runtime/fake_provider/backends/brisbane/conf_brisbane.json b/qiskit_ibm_runtime/fake_provider/backends/brisbane/conf_brisbane.json new file mode 100644 index 000000000..a5c9fb704 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/brisbane/conf_brisbane.json @@ -0,0 +1 @@ +{"backend_name": "ibm_brisbane", "backend_version": "1.1.17", "n_qubits": 127, "basis_gates": ["ecr", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], 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7.275373876634924], [6.451754377, 7.451754377], [6.334575194, 7.334575194], [6.404545375121012, 7.404545375121012], [6.46125977306879, 7.461259773068791]], "meas_kernels": ["hw_qmfk"], "discriminators": ["quadratic_discriminator", "hw_qmfk", "linear_discriminator"], "rep_times": [1000.0], "meas_map": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]], "acquisition_latency": [], "conditional_latency": [], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{126}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{62,72}(\\sigma_{62}^{+}\\sigma_{72}^{-}+\\sigma_{62}^{-}\\sigma_{72}^{+}) + J_{67,68}(\\sigma_{67}^{+}\\sigma_{68}^{-}+\\sigma_{67}^{-}\\sigma_{68}^{+}) + J_{44,45}(\\sigma_{44}^{+}\\sigma_{45}^{-}+\\sigma_{44}^{-}\\sigma_{45}^{+}) + J_{99,100}(\\sigma_{99}^{+}\\sigma_{100}^{-}+\\sigma_{99}^{-}\\sigma_{100}^{+}) \\\\ & + J_{108,112}(\\sigma_{108}^{+}\\sigma_{112}^{-}+\\sigma_{108}^{-}\\sigma_{112}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{40,41}(\\sigma_{40}^{+}\\sigma_{41}^{-}+\\sigma_{40}^{-}\\sigma_{41}^{+}) + J_{0,14}(\\sigma_{0}^{+}\\sigma_{14}^{-}+\\sigma_{0}^{-}\\sigma_{14}^{+}) \\\\ & + J_{17,30}(\\sigma_{17}^{+}\\sigma_{30}^{-}+\\sigma_{17}^{-}\\sigma_{30}^{+}) + J_{100,101}(\\sigma_{100}^{+}\\sigma_{101}^{-}+\\sigma_{100}^{-}\\sigma_{101}^{+}) + J_{91,98}(\\sigma_{91}^{+}\\sigma_{98}^{-}+\\sigma_{91}^{-}\\sigma_{98}^{+}) + J_{100,110}(\\sigma_{100}^{+}\\sigma_{110}^{-}+\\sigma_{100}^{-}\\sigma_{110}^{+}) \\\\ & + J_{75,90}(\\sigma_{75}^{+}\\sigma_{90}^{-}+\\sigma_{75}^{-}\\sigma_{90}^{+}) + J_{41,42}(\\sigma_{41}^{+}\\sigma_{42}^{-}+\\sigma_{41}^{-}\\sigma_{42}^{+}) + J_{96,97}(\\sigma_{96}^{+}\\sigma_{97}^{-}+\\sigma_{96}^{-}\\sigma_{97}^{+}) + J_{18,19}(\\sigma_{18}^{+}\\sigma_{19}^{-}+\\sigma_{18}^{-}\\sigma_{19}^{+}) \\\\ & + J_{55,68}(\\sigma_{55}^{+}\\sigma_{68}^{-}+\\sigma_{55}^{-}\\sigma_{68}^{+}) + J_{9,10}(\\sigma_{9}^{+}\\sigma_{10}^{-}+\\sigma_{9}^{-}\\sigma_{10}^{+}) + J_{49,55}(\\sigma_{49}^{+}\\sigma_{55}^{-}+\\sigma_{49}^{-}\\sigma_{55}^{+}) + J_{106,107}(\\sigma_{106}^{+}\\sigma_{107}^{-}+\\sigma_{106}^{-}\\sigma_{107}^{+}) \\\\ & + J_{47,48}(\\sigma_{47}^{+}\\sigma_{48}^{-}+\\sigma_{47}^{-}\\sigma_{48}^{+}) + J_{42,43}(\\sigma_{42}^{+}\\sigma_{43}^{-}+\\sigma_{42}^{-}\\sigma_{43}^{+}) + J_{107,108}(\\sigma_{107}^{+}\\sigma_{108}^{-}+\\sigma_{107}^{-}\\sigma_{108}^{+}) + J_{73,85}(\\sigma_{73}^{+}\\sigma_{85}^{-}+\\sigma_{73}^{-}\\sigma_{85}^{+}) \\\\ & + J_{38,39}(\\sigma_{38}^{+}\\sigma_{39}^{-}+\\sigma_{38}^{-}\\sigma_{39}^{+}) + J_{20,33}(\\sigma_{20}^{+}\\sigma_{33}^{-}+\\sigma_{20}^{-}\\sigma_{33}^{+}) + J_{48,49}(\\sigma_{48}^{+}\\sigma_{49}^{-}+\\sigma_{48}^{-}\\sigma_{49}^{+}) + J_{103,104}(\\sigma_{103}^{+}\\sigma_{104}^{-}+\\sigma_{103}^{-}\\sigma_{104}^{+}) \\\\ & + J_{80,81}(\\sigma_{80}^{+}\\sigma_{81}^{-}+\\sigma_{80}^{-}\\sigma_{81}^{+}) + J_{75,76}(\\sigma_{75}^{+}\\sigma_{76}^{-}+\\sigma_{75}^{-}\\sigma_{76}^{+}) + J_{66,73}(\\sigma_{66}^{+}\\sigma_{73}^{-}+\\sigma_{66}^{-}\\sigma_{73}^{+}) + J_{85,86}(\\sigma_{85}^{+}\\sigma_{86}^{-}+\\sigma_{85}^{-}\\sigma_{86}^{+}) \\\\ & + J_{81,82}(\\sigma_{81}^{+}\\sigma_{82}^{-}+\\sigma_{81}^{-}\\sigma_{82}^{+}) + J_{110,118}(\\sigma_{110}^{+}\\sigma_{118}^{-}+\\sigma_{110}^{-}\\sigma_{118}^{+}) + J_{16,26}(\\sigma_{16}^{+}\\sigma_{26}^{-}+\\sigma_{16}^{-}\\sigma_{26}^{+}) + J_{90,94}(\\sigma_{90}^{+}\\sigma_{94}^{-}+\\sigma_{90}^{-}\\sigma_{94}^{+}) \\\\ & + J_{118,119}(\\sigma_{118}^{+}\\sigma_{119}^{-}+\\sigma_{118}^{-}\\sigma_{119}^{+}) + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{22,23}(\\sigma_{22}^{+}\\sigma_{23}^{-}+\\sigma_{22}^{-}\\sigma_{23}^{+}) + J_{77,78}(\\sigma_{77}^{+}\\sigma_{78}^{-}+\\sigma_{77}^{-}\\sigma_{78}^{+}) \\\\ & + J_{49,50}(\\sigma_{49}^{+}\\sigma_{50}^{-}+\\sigma_{49}^{-}\\sigma_{50}^{+}) + J_{104,105}(\\sigma_{104}^{+}\\sigma_{105}^{-}+\\sigma_{104}^{-}\\sigma_{105}^{+}) + J_{114,115}(\\sigma_{114}^{+}\\sigma_{115}^{-}+\\sigma_{114}^{-}\\sigma_{115}^{+}) + J_{45,46}(\\sigma_{45}^{+}\\sigma_{46}^{-}+\\sigma_{45}^{-}\\sigma_{46}^{+}) \\\\ & + J_{50,51}(\\sigma_{50}^{+}\\sigma_{51}^{-}+\\sigma_{50}^{-}\\sigma_{51}^{+}) + J_{105,106}(\\sigma_{105}^{+}\\sigma_{106}^{-}+\\sigma_{105}^{-}\\sigma_{106}^{+}) + J_{72,81}(\\sigma_{72}^{+}\\sigma_{81}^{-}+\\sigma_{72}^{-}\\sigma_{81}^{+}) + J_{82,83}(\\sigma_{82}^{+}\\sigma_{83}^{-}+\\sigma_{82}^{-}\\sigma_{83}^{+}) \\\\ & + J_{46,47}(\\sigma_{46}^{+}\\sigma_{47}^{-}+\\sigma_{46}^{-}\\sigma_{47}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) + J_{78,79}(\\sigma_{78}^{+}\\sigma_{79}^{-}+\\sigma_{78}^{-}\\sigma_{79}^{+}) + J_{83,84}(\\sigma_{83}^{+}\\sigma_{84}^{-}+\\sigma_{83}^{-}\\sigma_{84}^{+}) \\\\ & + J_{115,116}(\\sigma_{115}^{+}\\sigma_{116}^{-}+\\sigma_{115}^{-}\\sigma_{116}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) + J_{79,80}(\\sigma_{79}^{+}\\sigma_{80}^{-}+\\sigma_{79}^{-}\\sigma_{80}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) \\\\ & + J_{56,57}(\\sigma_{56}^{+}\\sigma_{57}^{-}+\\sigma_{56}^{-}\\sigma_{57}^{+}) + J_{93,106}(\\sigma_{93}^{+}\\sigma_{106}^{-}+\\sigma_{93}^{-}\\sigma_{106}^{+}) + J_{116,117}(\\sigma_{116}^{+}\\sigma_{117}^{-}+\\sigma_{116}^{-}\\sigma_{117}^{+}) + J_{20,21}(\\sigma_{20}^{+}\\sigma_{21}^{-}+\\sigma_{20}^{-}\\sigma_{21}^{+}) \\\\ & + J_{12,17}(\\sigma_{12}^{+}\\sigma_{17}^{-}+\\sigma_{12}^{-}\\sigma_{17}^{+}) + J_{41,53}(\\sigma_{41}^{+}\\sigma_{53}^{-}+\\sigma_{41}^{-}\\sigma_{53}^{+}) + J_{57,58}(\\sigma_{57}^{+}\\sigma_{58}^{-}+\\sigma_{57}^{-}\\sigma_{58}^{+}) + J_{87,93}(\\sigma_{87}^{+}\\sigma_{93}^{-}+\\sigma_{87}^{-}\\sigma_{93}^{+}) \\\\ & + J_{30,31}(\\sigma_{30}^{+}\\sigma_{31}^{-}+\\sigma_{30}^{-}\\sigma_{31}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) + J_{79,91}(\\sigma_{79}^{+}\\sigma_{91}^{-}+\\sigma_{79}^{-}\\sigma_{91}^{+}) + J_{26,27}(\\sigma_{26}^{+}\\sigma_{27}^{-}+\\sigma_{26}^{-}\\sigma_{27}^{+}) \\\\ & + J_{21,22}(\\sigma_{21}^{+}\\sigma_{22}^{-}+\\sigma_{21}^{-}\\sigma_{22}^{+}) + J_{58,71}(\\sigma_{58}^{+}\\sigma_{71}^{-}+\\sigma_{58}^{-}\\sigma_{71}^{+}) + J_{31,32}(\\sigma_{31}^{+}\\sigma_{32}^{-}+\\sigma_{31}^{-}\\sigma_{32}^{+}) + J_{4,15}(\\sigma_{4}^{+}\\sigma_{15}^{-}+\\sigma_{4}^{-}\\sigma_{15}^{+}) \\\\ & + J_{86,87}(\\sigma_{86}^{+}\\sigma_{87}^{-}+\\sigma_{86}^{-}\\sigma_{87}^{+}) + J_{113,114}(\\sigma_{113}^{+}\\sigma_{114}^{-}+\\sigma_{113}^{-}\\sigma_{114}^{+}) + J_{104,111}(\\sigma_{104}^{+}\\sigma_{111}^{-}+\\sigma_{104}^{-}\\sigma_{111}^{+}) + J_{123,124}(\\sigma_{123}^{+}\\sigma_{124}^{-}+\\sigma_{123}^{-}\\sigma_{124}^{+}) \\\\ & + J_{27,28}(\\sigma_{27}^{+}\\sigma_{28}^{-}+\\sigma_{27}^{-}\\sigma_{28}^{+}) + J_{34,43}(\\sigma_{34}^{+}\\sigma_{43}^{-}+\\sigma_{34}^{-}\\sigma_{43}^{+}) + J_{119,120}(\\sigma_{119}^{+}\\sigma_{120}^{-}+\\sigma_{119}^{-}\\sigma_{120}^{+}) + J_{64,65}(\\sigma_{64}^{+}\\sigma_{65}^{-}+\\sigma_{64}^{-}\\sigma_{65}^{+}) \\\\ & + J_{54,64}(\\sigma_{54}^{+}\\sigma_{64}^{-}+\\sigma_{54}^{-}\\sigma_{64}^{+}) + J_{32,36}(\\sigma_{32}^{+}\\sigma_{36}^{-}+\\sigma_{32}^{-}\\sigma_{36}^{+}) + J_{60,61}(\\sigma_{60}^{+}\\sigma_{61}^{-}+\\sigma_{60}^{-}\\sigma_{61}^{+}) + J_{5,6}(\\sigma_{5}^{+}\\sigma_{6}^{-}+\\sigma_{5}^{-}\\sigma_{6}^{+}) \\\\ & + J_{14,18}(\\sigma_{14}^{+}\\sigma_{18}^{-}+\\sigma_{14}^{-}\\sigma_{18}^{+}) + J_{87,88}(\\sigma_{87}^{+}\\sigma_{88}^{-}+\\sigma_{87}^{-}\\sigma_{88}^{+}) + J_{97,98}(\\sigma_{97}^{+}\\sigma_{98}^{-}+\\sigma_{97}^{-}\\sigma_{98}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) \\\\ & + J_{112,126}(\\sigma_{112}^{+}\\sigma_{126}^{-}+\\sigma_{112}^{-}\\sigma_{126}^{+}) + J_{28,29}(\\sigma_{28}^{+}\\sigma_{29}^{-}+\\sigma_{28}^{-}\\sigma_{29}^{+}) + J_{45,54}(\\sigma_{45}^{+}\\sigma_{54}^{-}+\\sigma_{45}^{-}\\sigma_{54}^{+}) + J_{36,51}(\\sigma_{36}^{+}\\sigma_{51}^{-}+\\sigma_{36}^{-}\\sigma_{51}^{+}) \\\\ & + J_{88,89}(\\sigma_{88}^{+}\\sigma_{89}^{-}+\\sigma_{88}^{-}\\sigma_{89}^{+}) + J_{120,121}(\\sigma_{120}^{+}\\sigma_{121}^{-}+\\sigma_{120}^{-}\\sigma_{121}^{+}) + J_{15,22}(\\sigma_{15}^{+}\\sigma_{22}^{-}+\\sigma_{15}^{-}\\sigma_{22}^{+}) + J_{24,34}(\\sigma_{24}^{+}\\sigma_{34}^{-}+\\sigma_{24}^{-}\\sigma_{34}^{+}) \\\\ & + J_{84,85}(\\sigma_{84}^{+}\\sigma_{85}^{-}+\\sigma_{84}^{-}\\sigma_{85}^{+}) + J_{29,30}(\\sigma_{29}^{+}\\sigma_{30}^{-}+\\sigma_{29}^{-}\\sigma_{30}^{+}) + J_{61,62}(\\sigma_{61}^{+}\\sigma_{62}^{-}+\\sigma_{61}^{-}\\sigma_{62}^{+}) + J_{70,74}(\\sigma_{70}^{+}\\sigma_{74}^{-}+\\sigma_{70}^{-}\\sigma_{74}^{+}) \\\\ & + J_{121,122}(\\sigma_{121}^{+}\\sigma_{122}^{-}+\\sigma_{121}^{-}\\sigma_{122}^{+}) + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{122,123}(\\sigma_{122}^{+}\\sigma_{123}^{-}+\\sigma_{122}^{-}\\sigma_{123}^{+}) + J_{62,63}(\\sigma_{62}^{+}\\sigma_{63}^{-}+\\sigma_{62}^{-}\\sigma_{63}^{+}) \\\\ & + J_{117,118}(\\sigma_{117}^{+}\\sigma_{118}^{-}+\\sigma_{117}^{-}\\sigma_{118}^{+}) + J_{109,114}(\\sigma_{109}^{+}\\sigma_{114}^{-}+\\sigma_{109}^{-}\\sigma_{114}^{+}) + J_{94,95}(\\sigma_{94}^{+}\\sigma_{95}^{-}+\\sigma_{94}^{-}\\sigma_{95}^{+}) + J_{37,52}(\\sigma_{37}^{+}\\sigma_{52}^{-}+\\sigma_{37}^{-}\\sigma_{52}^{+}) \\\\ & + J_{58,59}(\\sigma_{58}^{+}\\sigma_{59}^{-}+\\sigma_{58}^{-}\\sigma_{59}^{+}) + J_{3,4}(\\sigma_{3}^{+}\\sigma_{4}^{-}+\\sigma_{3}^{-}\\sigma_{4}^{+}) + J_{33,39}(\\sigma_{33}^{+}\\sigma_{39}^{-}+\\sigma_{33}^{-}\\sigma_{39}^{+}) + J_{95,96}(\\sigma_{95}^{+}\\sigma_{96}^{-}+\\sigma_{95}^{-}\\sigma_{96}^{+}) \\\\ & + J_{68,69}(\\sigma_{68}^{+}\\sigma_{69}^{-}+\\sigma_{68}^{-}\\sigma_{69}^{+}) + J_{63,64}(\\sigma_{63}^{+}\\sigma_{64}^{-}+\\sigma_{63}^{-}\\sigma_{64}^{+}) + J_{71,77}(\\sigma_{71}^{+}\\sigma_{77}^{-}+\\sigma_{71}^{-}\\sigma_{77}^{+}) + J_{111,122}(\\sigma_{111}^{+}\\sigma_{122}^{-}+\\sigma_{111}^{-}\\sigma_{122}^{+}) \\\\ & + J_{4,5}(\\sigma_{4}^{+}\\sigma_{5}^{-}+\\sigma_{4}^{-}\\sigma_{5}^{+}) + J_{59,60}(\\sigma_{59}^{+}\\sigma_{60}^{-}+\\sigma_{59}^{-}\\sigma_{60}^{+}) + J_{96,109}(\\sigma_{96}^{+}\\sigma_{109}^{-}+\\sigma_{96}^{-}\\sigma_{109}^{+}) + J_{124,125}(\\sigma_{124}^{+}\\sigma_{125}^{-}+\\sigma_{124}^{-}\\sigma_{125}^{+}) \\\\ & + J_{69,70}(\\sigma_{69}^{+}\\sigma_{70}^{-}+\\sigma_{69}^{-}\\sigma_{70}^{+}) + J_{35,47}(\\sigma_{35}^{+}\\sigma_{47}^{-}+\\sigma_{35}^{-}\\sigma_{47}^{+}) + J_{101,102}(\\sigma_{101}^{+}\\sigma_{102}^{-}+\\sigma_{101}^{-}\\sigma_{102}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) \\\\ & + J_{10,11}(\\sigma_{10}^{+}\\sigma_{11}^{-}+\\sigma_{10}^{-}\\sigma_{11}^{+}) + J_{65,66}(\\sigma_{65}^{+}\\sigma_{66}^{-}+\\sigma_{65}^{-}\\sigma_{66}^{+}) + J_{37,38}(\\sigma_{37}^{+}\\sigma_{38}^{-}+\\sigma_{37}^{-}\\sigma_{38}^{+}) + J_{28,35}(\\sigma_{28}^{+}\\sigma_{35}^{-}+\\sigma_{28}^{-}\\sigma_{35}^{+}) \\\\ & + J_{102,103}(\\sigma_{102}^{+}\\sigma_{103}^{-}+\\sigma_{102}^{-}\\sigma_{103}^{+}) + J_{92,102}(\\sigma_{92}^{+}\\sigma_{102}^{-}+\\sigma_{92}^{-}\\sigma_{102}^{+}) + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{98,99}(\\sigma_{98}^{+}\\sigma_{99}^{-}+\\sigma_{98}^{-}\\sigma_{99}^{+}) \\\\ & + J_{43,44}(\\sigma_{43}^{+}\\sigma_{44}^{-}+\\sigma_{43}^{-}\\sigma_{44}^{+}) + J_{52,56}(\\sigma_{52}^{+}\\sigma_{56}^{-}+\\sigma_{52}^{-}\\sigma_{56}^{+}) + J_{125,126}(\\sigma_{125}^{+}\\sigma_{126}^{-}+\\sigma_{125}^{-}\\sigma_{126}^{+}) + J_{39,40}(\\sigma_{39}^{+}\\sigma_{40}^{-}+\\sigma_{39}^{-}\\sigma_{40}^{+}) \\\\ & + J_{8,16}(\\sigma_{8}^{+}\\sigma_{16}^{-}+\\sigma_{8}^{-}\\sigma_{16}^{+}) + J_{66,67}(\\sigma_{66}^{+}\\sigma_{67}^{-}+\\sigma_{66}^{-}\\sigma_{67}^{+}) + J_{11,12}(\\sigma_{11}^{+}\\sigma_{12}^{-}+\\sigma_{11}^{-}\\sigma_{12}^{+}) + J_{76,77}(\\sigma_{76}^{+}\\sigma_{77}^{-}+\\sigma_{76}^{-}\\sigma_{77}^{+}) \\\\ & + J_{83,92}(\\sigma_{83}^{+}\\sigma_{92}^{-}+\\sigma_{83}^{-}\\sigma_{92}^{+}) + J_{74,89}(\\sigma_{74}^{+}\\sigma_{89}^{-}+\\sigma_{74}^{-}\\sigma_{89}^{+}) + J_{7,8}(\\sigma_{7}^{+}\\sigma_{8}^{-}+\\sigma_{7}^{-}\\sigma_{8}^{+}) + J_{53,60}(\\sigma_{53}^{+}\\sigma_{60}^{-}+\\sigma_{53}^{-}\\sigma_{60}^{+}) \\\\ & + \\Omega_{d,1}(U_{0}^{(1,0)}(t))\\sigma_{1}^{X} + \\Omega_{d,2}(U_{1}^{(2,1)}(t))\\sigma_{2}^{X} \\\\ & + \\Omega_{d,3}(U_{2}^{(3,2)}(t))\\sigma_{3}^{X} + \\Omega_{d,4}(U_{5}^{(4,15)}(t)+U_{4}^{(4,5)}(t)+U_{3}^{(4,3)}(t))\\sigma_{4}^{X} \\\\ & + \\Omega_{d,6}(U_{7}^{(6,7)}(t)+U_{6}^{(6,5)}(t))\\sigma_{6}^{X} + \\Omega_{d,7}(U_{8}^{(7,8)}(t))\\sigma_{7}^{X} \\\\ & + \\Omega_{d,8}(U_{9}^{(8,9)}(t))\\sigma_{8}^{X} + \\Omega_{d,10}(U_{10}^{(10,9)}(t)+U_{11}^{(10,11)}(t))\\sigma_{10}^{X} \\\\ & + \\Omega_{d,11}(U_{12}^{(11,12)}(t))\\sigma_{11}^{X} + \\Omega_{d,12}(U_{13}^{(12,17)}(t))\\sigma_{12}^{X} \\\\ & + \\Omega_{d,13}(U_{14}^{(13,12)}(t))\\sigma_{13}^{X} + \\Omega_{d,14}(U_{15}^{(14,0)}(t)+U_{16}^{(14,18)}(t))\\sigma_{14}^{X} \\\\ & + \\Omega_{d,15}(U_{17}^{(15,22)}(t))\\sigma_{15}^{X} + \\Omega_{d,16}(U_{19}^{(16,26)}(t)+U_{18}^{(16,8)}(t))\\sigma_{16}^{X} \\\\ & + \\Omega_{d,17}(U_{20}^{(17,30)}(t))\\sigma_{17}^{X} + \\Omega_{d,18}(U_{21}^{(18,19)}(t))\\sigma_{18}^{X} \\\\ & + \\Omega_{d,20}(U_{22}^{(20,19)}(t)+U_{23}^{(20,33)}(t))\\sigma_{20}^{X} + \\Omega_{d,21}(U_{25}^{(21,22)}(t)+U_{24}^{(21,20)}(t))\\sigma_{21}^{X} \\\\ & + \\Omega_{d,22}(U_{26}^{(22,23)}(t))\\sigma_{22}^{X} + \\Omega_{d,24}(U_{28}^{(24,34)}(t)+U_{27}^{(24,23)}(t))\\sigma_{24}^{X} \\\\ & + \\Omega_{d,25}(U_{29}^{(25,24)}(t))\\sigma_{25}^{X} + \\Omega_{d,26}(U_{30}^{(26,25)}(t))\\sigma_{26}^{X} \\\\ & + \\Omega_{d,27}(U_{31}^{(27,26)}(t))\\sigma_{27}^{X} + \\Omega_{d,28}(U_{33}^{(28,29)}(t)+U_{32}^{(28,27)}(t)+U_{34}^{(28,35)}(t))\\sigma_{28}^{X} \\\\ & + \\Omega_{d,30}(U_{36}^{(30,31)}(t)+U_{35}^{(30,29)}(t))\\sigma_{30}^{X} + \\Omega_{d,31}(U_{37}^{(31,32)}(t))\\sigma_{31}^{X} \\\\ & + \\Omega_{d,32}(U_{38}^{(32,36)}(t))\\sigma_{32}^{X} + \\Omega_{d,33}(U_{39}^{(33,39)}(t))\\sigma_{33}^{X} \\\\ & + \\Omega_{d,34}(U_{40}^{(34,43)}(t))\\sigma_{34}^{X} + \\Omega_{d,35}(U_{41}^{(35,47)}(t))\\sigma_{35}^{X} \\\\ & + \\Omega_{d,36}(U_{42}^{(36,51)}(t))\\sigma_{36}^{X} + \\Omega_{d,37}(U_{43}^{(37,38)}(t))\\sigma_{37}^{X} \\\\ & + \\Omega_{d,39}(U_{44}^{(39,38)}(t))\\sigma_{39}^{X} + \\Omega_{d,40}(U_{46}^{(40,41)}(t)+U_{45}^{(40,39)}(t))\\sigma_{40}^{X} \\\\ & + \\Omega_{d,41}(U_{47}^{(41,53)}(t))\\sigma_{41}^{X} + \\Omega_{d,42}(U_{49}^{(42,43)}(t)+U_{48}^{(42,41)}(t))\\sigma_{42}^{X} \\\\ & + \\Omega_{d,43}(U_{50}^{(43,44)}(t))\\sigma_{43}^{X} + \\Omega_{d,44}(U_{51}^{(44,45)}(t))\\sigma_{44}^{X} \\\\ & + \\Omega_{d,46}(U_{53}^{(46,47)}(t)+U_{52}^{(46,45)}(t))\\sigma_{46}^{X} + \\Omega_{d,48}(U_{54}^{(48,47)}(t)+U_{55}^{(48,49)}(t))\\sigma_{48}^{X} \\\\ & + \\Omega_{d,50}(U_{56}^{(50,49)}(t)+U_{57}^{(50,51)}(t))\\sigma_{50}^{X} + \\Omega_{d,52}(U_{59}^{(52,56)}(t)+U_{58}^{(52,37)}(t))\\sigma_{52}^{X} \\\\ & + \\Omega_{d,53}(U_{60}^{(53,60)}(t))\\sigma_{53}^{X} + \\Omega_{d,54}(U_{62}^{(54,64)}(t)+U_{61}^{(54,45)}(t))\\sigma_{54}^{X} \\\\ & + \\Omega_{d,55}(U_{64}^{(55,68)}(t)+U_{63}^{(55,49)}(t))\\sigma_{55}^{X} + \\Omega_{d,56}(U_{65}^{(56,57)}(t))\\sigma_{56}^{X} \\\\ & + \\Omega_{d,57}(U_{66}^{(57,58)}(t))\\sigma_{57}^{X} + \\Omega_{d,58}(U_{67}^{(58,59)}(t)+U_{68}^{(58,71)}(t))\\sigma_{58}^{X} \\\\ & + \\Omega_{d,59}(U_{69}^{(59,60)}(t))\\sigma_{59}^{X} + \\Omega_{d,60}(U_{70}^{(60,61)}(t))\\sigma_{60}^{X} \\\\ & + \\Omega_{d,62}(U_{72}^{(62,63)}(t)+U_{73}^{(62,72)}(t)+U_{71}^{(62,61)}(t))\\sigma_{62}^{X} + \\Omega_{d,63}(U_{74}^{(63,64)}(t))\\sigma_{63}^{X} \\\\ & + \\Omega_{d,65}(U_{76}^{(65,66)}(t)+U_{75}^{(65,64)}(t))\\sigma_{65}^{X} + \\Omega_{d,67}(U_{78}^{(67,68)}(t)+U_{77}^{(67,66)}(t))\\sigma_{67}^{X} \\\\ & + \\Omega_{d,69}(U_{79}^{(69,68)}(t)+U_{80}^{(69,70)}(t))\\sigma_{69}^{X} + \\Omega_{d,73}(U_{81}^{(73,66)}(t))\\sigma_{73}^{X} \\\\ & + \\Omega_{d,74}(U_{83}^{(74,89)}(t)+U_{82}^{(74,70)}(t))\\sigma_{74}^{X} + \\Omega_{d,75}(U_{84}^{(75,90)}(t))\\sigma_{75}^{X} \\\\ & + \\Omega_{d,76}(U_{85}^{(76,75)}(t))\\sigma_{76}^{X} + \\Omega_{d,77}(U_{86}^{(77,71)}(t)+U_{88}^{(77,78)}(t)+U_{87}^{(77,76)}(t))\\sigma_{77}^{X} \\\\ & + \\Omega_{d,79}(U_{90}^{(79,80)}(t)+U_{89}^{(79,78)}(t))\\sigma_{79}^{X} + \\Omega_{d,80}(U_{91}^{(80,81)}(t))\\sigma_{80}^{X} \\\\ & + \\Omega_{d,81}(U_{93}^{(81,82)}(t)+U_{92}^{(81,72)}(t))\\sigma_{81}^{X} + \\Omega_{d,82}(U_{94}^{(82,83)}(t))\\sigma_{82}^{X} \\\\ & + \\Omega_{d,83}(U_{95}^{(83,92)}(t))\\sigma_{83}^{X} + \\Omega_{d,84}(U_{96}^{(84,83)}(t))\\sigma_{84}^{X} \\\\ & + \\Omega_{d,85}(U_{97}^{(85,73)}(t)+U_{99}^{(85,86)}(t)+U_{98}^{(85,84)}(t))\\sigma_{85}^{X} + \\Omega_{d,86}(U_{100}^{(86,87)}(t))\\sigma_{86}^{X} \\\\ & + \\Omega_{d,87}(U_{101}^{(87,88)}(t))\\sigma_{87}^{X} + \\Omega_{d,88}(U_{102}^{(88,89)}(t))\\sigma_{88}^{X} \\\\ & + \\Omega_{d,91}(U_{103}^{(91,79)}(t))\\sigma_{91}^{X} + \\Omega_{d,92}(U_{104}^{(92,102)}(t))\\sigma_{92}^{X} \\\\ & + \\Omega_{d,93}(U_{105}^{(93,87)}(t)+U_{106}^{(93,106)}(t))\\sigma_{93}^{X} + \\Omega_{d,94}(U_{107}^{(94,90)}(t)+U_{108}^{(94,95)}(t))\\sigma_{94}^{X} \\\\ & + \\Omega_{d,95}(U_{109}^{(95,96)}(t))\\sigma_{95}^{X} + \\Omega_{d,97}(U_{111}^{(97,98)}(t)+U_{110}^{(97,96)}(t))\\sigma_{97}^{X} \\\\ & + \\Omega_{d,98}(U_{112}^{(98,91)}(t))\\sigma_{98}^{X} + \\Omega_{d,99}(U_{113}^{(99,98)}(t))\\sigma_{99}^{X} \\\\ & + \\Omega_{d,100}(U_{114}^{(100,99)}(t)+U_{115}^{(100,110)}(t))\\sigma_{100}^{X} + \\Omega_{d,101}(U_{117}^{(101,102)}(t)+U_{116}^{(101,100)}(t))\\sigma_{101}^{X} \\\\ & + \\Omega_{d,102}(U_{118}^{(102,103)}(t))\\sigma_{102}^{X} + \\Omega_{d,104}(U_{119}^{(104,103)}(t))\\sigma_{104}^{X} \\\\ & + \\Omega_{d,105}(U_{121}^{(105,106)}(t)+U_{120}^{(105,104)}(t))\\sigma_{105}^{X} + \\Omega_{d,107}(U_{122}^{(107,106)}(t))\\sigma_{107}^{X} \\\\ & + \\Omega_{d,108}(U_{123}^{(108,107)}(t)+U_{124}^{(108,112)}(t))\\sigma_{108}^{X} + \\Omega_{d,109}(U_{125}^{(109,96)}(t))\\sigma_{109}^{X} \\\\ & + \\Omega_{d,110}(U_{126}^{(110,118)}(t))\\sigma_{110}^{X} + \\Omega_{d,111}(U_{127}^{(111,104)}(t))\\sigma_{111}^{X} \\\\ & + \\Omega_{d,112}(U_{128}^{(112,126)}(t))\\sigma_{112}^{X} + \\Omega_{d,113}(U_{129}^{(113,114)}(t))\\sigma_{113}^{X} \\\\ & + \\Omega_{d,114}(U_{130}^{(114,109)}(t)+U_{131}^{(114,115)}(t))\\sigma_{114}^{X} + \\Omega_{d,116}(U_{133}^{(116,117)}(t)+U_{132}^{(116,115)}(t))\\sigma_{116}^{X} \\\\ & + \\Omega_{d,117}(U_{134}^{(117,118)}(t))\\sigma_{117}^{X} + \\Omega_{d,118}(U_{135}^{(118,119)}(t))\\sigma_{118}^{X} \\\\ & + \\Omega_{d,120}(U_{136}^{(120,119)}(t))\\sigma_{120}^{X} + \\Omega_{d,121}(U_{137}^{(121,120)}(t))\\sigma_{121}^{X} \\\\ & + \\Omega_{d,122}(U_{140}^{(122,123)}(t)+U_{138}^{(122,111)}(t)+U_{139}^{(122,121)}(t))\\sigma_{122}^{X} + \\Omega_{d,124}(U_{141}^{(124,123)}(t))\\sigma_{124}^{X} \\\\ & + \\Omega_{d,125}(U_{142}^{(125,124)}(t)+U_{143}^{(125,126)}(t))\\sigma_{125}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,126,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,126,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,126,-delta{i}/2*O{i}]", "_SUM[i,0,126,omegad{i}*X{i}||D{i}]", "jq62q72*Sp62*Sm72", "jq62q72*Sm62*Sp72", "jq67q68*Sp67*Sm68", "jq67q68*Sm67*Sp68", "jq44q45*Sp44*Sm45", "jq44q45*Sm44*Sp45", "jq99q100*Sp99*Sm100", "jq99q100*Sm99*Sp100", "jq108q112*Sp108*Sm112", "jq108q112*Sm108*Sp112", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq40q41*Sp40*Sm41", "jq40q41*Sm40*Sp41", "jq0q14*Sp0*Sm14", "jq0q14*Sm0*Sp14", "jq17q30*Sp17*Sm30", "jq17q30*Sm17*Sp30", "jq100q101*Sp100*Sm101", "jq100q101*Sm100*Sp101", "jq91q98*Sp91*Sm98", "jq91q98*Sm91*Sp98", "jq100q110*Sp100*Sm110", "jq100q110*Sm100*Sp110", "jq75q90*Sp75*Sm90", "jq75q90*Sm75*Sp90", "jq41q42*Sp41*Sm42", "jq41q42*Sm41*Sp42", "jq96q97*Sp96*Sm97", "jq96q97*Sm96*Sp97", "jq18q19*Sp18*Sm19", "jq18q19*Sm18*Sp19", "jq55q68*Sp55*Sm68", "jq55q68*Sm55*Sp68", "jq9q10*Sp9*Sm10", "jq9q10*Sm9*Sp10", "jq49q55*Sp49*Sm55", "jq49q55*Sm49*Sp55", "jq106q107*Sp106*Sm107", "jq106q107*Sm106*Sp107", "jq47q48*Sp47*Sm48", "jq47q48*Sm47*Sp48", "jq42q43*Sp42*Sm43", "jq42q43*Sm42*Sp43", "jq107q108*Sp107*Sm108", "jq107q108*Sm107*Sp108", "jq73q85*Sp73*Sm85", "jq73q85*Sm73*Sp85", "jq38q39*Sp38*Sm39", "jq38q39*Sm38*Sp39", "jq20q33*Sp20*Sm33", "jq20q33*Sm20*Sp33", "jq48q49*Sp48*Sm49", "jq48q49*Sm48*Sp49", "jq103q104*Sp103*Sm104", "jq103q104*Sm103*Sp104", "jq80q81*Sp80*Sm81", "jq80q81*Sm80*Sp81", "jq75q76*Sp75*Sm76", "jq75q76*Sm75*Sp76", "jq66q73*Sp66*Sm73", "jq66q73*Sm66*Sp73", "jq85q86*Sp85*Sm86", "jq85q86*Sm85*Sp86", "jq81q82*Sp81*Sm82", "jq81q82*Sm81*Sp82", "jq110q118*Sp110*Sm118", "jq110q118*Sm110*Sp118", "jq16q26*Sp16*Sm26", "jq16q26*Sm16*Sp26", "jq90q94*Sp90*Sm94", "jq90q94*Sm90*Sp94", "jq118q119*Sp118*Sm119", "jq118q119*Sm118*Sp119", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq22q23*Sp22*Sm23", "jq22q23*Sm22*Sp23", "jq77q78*Sp77*Sm78", "jq77q78*Sm77*Sp78", "jq49q50*Sp49*Sm50", "jq49q50*Sm49*Sp50", "jq104q105*Sp104*Sm105", "jq104q105*Sm104*Sp105", "jq114q115*Sp114*Sm115", "jq114q115*Sm114*Sp115", "jq45q46*Sp45*Sm46", "jq45q46*Sm45*Sp46", "jq50q51*Sp50*Sm51", "jq50q51*Sm50*Sp51", "jq105q106*Sp105*Sm106", "jq105q106*Sm105*Sp106", "jq72q81*Sp72*Sm81", "jq72q81*Sm72*Sp81", "jq82q83*Sp82*Sm83", "jq82q83*Sm82*Sp83", "jq46q47*Sp46*Sm47", "jq46q47*Sm46*Sp47", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq78q79*Sp78*Sm79", 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"jq113q114*Sm113*Sp114", "jq104q111*Sp104*Sm111", "jq104q111*Sm104*Sp111", "jq123q124*Sp123*Sm124", "jq123q124*Sm123*Sp124", "jq27q28*Sp27*Sm28", "jq27q28*Sm27*Sp28", "jq34q43*Sp34*Sm43", "jq34q43*Sm34*Sp43", "jq119q120*Sp119*Sm120", "jq119q120*Sm119*Sp120", "jq64q65*Sp64*Sm65", "jq64q65*Sm64*Sp65", "jq54q64*Sp54*Sm64", "jq54q64*Sm54*Sp64", "jq32q36*Sp32*Sm36", "jq32q36*Sm32*Sp36", "jq60q61*Sp60*Sm61", "jq60q61*Sm60*Sp61", "jq5q6*Sp5*Sm6", "jq5q6*Sm5*Sp6", "jq14q18*Sp14*Sm18", "jq14q18*Sm14*Sp18", "jq87q88*Sp87*Sm88", "jq87q88*Sm87*Sp88", "jq97q98*Sp97*Sm98", "jq97q98*Sm97*Sp98", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq112q126*Sp112*Sm126", "jq112q126*Sm112*Sp126", "jq28q29*Sp28*Sm29", "jq28q29*Sm28*Sp29", "jq45q54*Sp45*Sm54", "jq45q54*Sm45*Sp54", "jq36q51*Sp36*Sm51", "jq36q51*Sm36*Sp51", "jq88q89*Sp88*Sm89", "jq88q89*Sm88*Sp89", "jq120q121*Sp120*Sm121", "jq120q121*Sm120*Sp121", "jq15q22*Sp15*Sm22", "jq15q22*Sm15*Sp22", "jq24q34*Sp24*Sm34", "jq24q34*Sm24*Sp34", "jq84q85*Sp84*Sm85", "jq84q85*Sm84*Sp85", "jq29q30*Sp29*Sm30", "jq29q30*Sm29*Sp30", "jq61q62*Sp61*Sm62", "jq61q62*Sm61*Sp62", "jq70q74*Sp70*Sm74", "jq70q74*Sm70*Sp74", "jq121q122*Sp121*Sm122", "jq121q122*Sm121*Sp122", "jq2q3*Sp2*Sm3", "jq2q3*Sm2*Sp3", "jq122q123*Sp122*Sm123", "jq122q123*Sm122*Sp123", "jq62q63*Sp62*Sm63", "jq62q63*Sm62*Sp63", "jq117q118*Sp117*Sm118", "jq117q118*Sm117*Sp118", "jq109q114*Sp109*Sm114", "jq109q114*Sm109*Sp114", "jq94q95*Sp94*Sm95", "jq94q95*Sm94*Sp95", "jq37q52*Sp37*Sm52", "jq37q52*Sm37*Sp52", "jq58q59*Sp58*Sm59", "jq58q59*Sm58*Sp59", "jq3q4*Sp3*Sm4", "jq3q4*Sm3*Sp4", "jq33q39*Sp33*Sm39", "jq33q39*Sm33*Sp39", "jq95q96*Sp95*Sm96", "jq95q96*Sm95*Sp96", "jq68q69*Sp68*Sm69", "jq68q69*Sm68*Sp69", "jq63q64*Sp63*Sm64", "jq63q64*Sm63*Sp64", "jq71q77*Sp71*Sm77", "jq71q77*Sm71*Sp77", "jq111q122*Sp111*Sm122", "jq111q122*Sm111*Sp122", "jq4q5*Sp4*Sm5", "jq4q5*Sm4*Sp5", "jq59q60*Sp59*Sm60", "jq59q60*Sm59*Sp60", "jq96q109*Sp96*Sm109", "jq96q109*Sm96*Sp109", "jq124q125*Sp124*Sm125", "jq124q125*Sm124*Sp125", "jq69q70*Sp69*Sm70", "jq69q70*Sm69*Sp70", "jq35q47*Sp35*Sm47", "jq35q47*Sm35*Sp47", "jq101q102*Sp101*Sm102", "jq101q102*Sm101*Sp102", "jq0q1*Sp0*Sm1", "jq0q1*Sm0*Sp1", "jq10q11*Sp10*Sm11", "jq10q11*Sm10*Sp11", "jq65q66*Sp65*Sm66", "jq65q66*Sm65*Sp66", "jq37q38*Sp37*Sm38", "jq37q38*Sm37*Sp38", "jq28q35*Sp28*Sm35", "jq28q35*Sm28*Sp35", "jq102q103*Sp102*Sm103", "jq102q103*Sm102*Sp103", "jq92q102*Sp92*Sm102", "jq92q102*Sm92*Sp102", "jq6q7*Sp6*Sm7", "jq6q7*Sm6*Sp7", "jq98q99*Sp98*Sm99", "jq98q99*Sm98*Sp99", "jq43q44*Sp43*Sm44", "jq43q44*Sm43*Sp44", "jq52q56*Sp52*Sm56", "jq52q56*Sm52*Sp56", "jq125q126*Sp125*Sm126", "jq125q126*Sm125*Sp126", "jq39q40*Sp39*Sm40", "jq39q40*Sm39*Sp40", "jq8q16*Sp8*Sm16", "jq8q16*Sm8*Sp16", "jq66q67*Sp66*Sm67", "jq66q67*Sm66*Sp67", "jq11q12*Sp11*Sm12", "jq11q12*Sm11*Sp12", "jq76q77*Sp76*Sm77", "jq76q77*Sm76*Sp77", "jq83q92*Sp83*Sm92", "jq83q92*Sm83*Sp92", "jq74q89*Sp74*Sm89", "jq74q89*Sm74*Sp89", "jq7q8*Sp7*Sm8", "jq7q8*Sm7*Sp8", "jq53q60*Sp53*Sm60", "jq53q60*Sm53*Sp60", "omegad0*X1||U0", "omegad1*X2||U1", "omegad2*X3||U2", "omegad15*X4||U5", "omegad5*X4||U4", "omegad3*X4||U3", "omegad7*X6||U7", "omegad5*X6||U6", "omegad8*X7||U8", "omegad9*X8||U9", "omegad9*X10||U10", "omegad11*X10||U11", "omegad12*X11||U12", "omegad17*X12||U13", "omegad12*X13||U14", "omegad0*X14||U15", "omegad18*X14||U16", "omegad22*X15||U17", "omegad26*X16||U19", "omegad8*X16||U18", "omegad30*X17||U20", "omegad19*X18||U21", "omegad19*X20||U22", "omegad33*X20||U23", "omegad22*X21||U25", "omegad20*X21||U24", "omegad23*X22||U26", "omegad34*X24||U28", "omegad23*X24||U27", "omegad24*X25||U29", "omegad25*X26||U30", "omegad26*X27||U31", "omegad29*X28||U33", "omegad27*X28||U32", "omegad35*X28||U34", "omegad31*X30||U36", "omegad29*X30||U35", "omegad32*X31||U37", "omegad36*X32||U38", "omegad39*X33||U39", "omegad43*X34||U40", "omegad47*X35||U41", "omegad51*X36||U42", "omegad38*X37||U43", "omegad38*X39||U44", "omegad41*X40||U46", "omegad39*X40||U45", "omegad53*X41||U47", "omegad43*X42||U49", "omegad41*X42||U48", "omegad44*X43||U50", "omegad45*X44||U51", "omegad47*X46||U53", "omegad45*X46||U52", "omegad47*X48||U54", "omegad49*X48||U55", "omegad49*X50||U56", "omegad51*X50||U57", "omegad56*X52||U59", "omegad37*X52||U58", "omegad60*X53||U60", "omegad64*X54||U62", "omegad45*X54||U61", "omegad68*X55||U64", "omegad49*X55||U63", "omegad57*X56||U65", "omegad58*X57||U66", "omegad59*X58||U67", "omegad71*X58||U68", "omegad60*X59||U69", "omegad61*X60||U70", "omegad63*X62||U72", "omegad72*X62||U73", "omegad61*X62||U71", "omegad64*X63||U74", "omegad66*X65||U76", "omegad64*X65||U75", "omegad68*X67||U78", "omegad66*X67||U77", "omegad68*X69||U79", "omegad70*X69||U80", "omegad66*X73||U81", "omegad89*X74||U83", "omegad70*X74||U82", "omegad90*X75||U84", "omegad75*X76||U85", "omegad71*X77||U86", "omegad78*X77||U88", "omegad76*X77||U87", "omegad80*X79||U90", "omegad78*X79||U89", "omegad81*X80||U91", "omegad82*X81||U93", "omegad72*X81||U92", "omegad83*X82||U94", "omegad92*X83||U95", "omegad83*X84||U96", "omegad73*X85||U97", "omegad86*X85||U99", "omegad84*X85||U98", "omegad87*X86||U100", "omegad88*X87||U101", "omegad89*X88||U102", "omegad79*X91||U103", "omegad102*X92||U104", "omegad87*X93||U105", "omegad106*X93||U106", "omegad90*X94||U107", "omegad95*X94||U108", "omegad96*X95||U109", "omegad98*X97||U111", "omegad96*X97||U110", "omegad91*X98||U112", "omegad98*X99||U113", "omegad99*X100||U114", "omegad110*X100||U115", "omegad102*X101||U117", "omegad100*X101||U116", "omegad103*X102||U118", "omegad103*X104||U119", "omegad106*X105||U121", "omegad104*X105||U120", "omegad106*X107||U122", "omegad107*X108||U123", "omegad112*X108||U124", "omegad96*X109||U125", "omegad118*X110||U126", "omegad104*X111||U127", "omegad126*X112||U128", "omegad114*X113||U129", "omegad109*X114||U130", "omegad115*X114||U131", "omegad117*X116||U133", "omegad115*X116||U132", "omegad118*X117||U134", "omegad119*X118||U135", "omegad119*X120||U136", "omegad120*X121||U137", "omegad123*X122||U140", "omegad111*X122||U138", "omegad121*X122||U139", "omegad123*X124||U141", "omegad124*X125||U142", "omegad126*X125||U143"], "osc": {}, "qub": {"0": 3, "1": 3, "2": 3, "3": 3, "4": 3, "5": 3, "6": 3, "7": 3, "8": 3, "9": 3, "10": 3, "11": 3, "12": 3, "13": 3, "14": 3, "15": 3, "16": 3, "17": 3, "18": 3, "19": 3, "20": 3, "21": 3, "22": 3, "23": 3, "24": 3, "25": 3, "26": 3, "27": 3, "28": 3, "29": 3, "30": 3, "31": 3, "32": 3, "33": 3, "34": 3, "35": 3, "36": 3, "37": 3, "38": 3, "39": 3, "40": 3, "41": 3, "42": 3, "43": 3, "44": 3, "45": 3, "46": 3, "47": 3, "48": 3, "49": 3, "50": 3, "51": 3, "52": 3, "53": 3, "54": 3, "55": 3, "56": 3, "57": 3, "58": 3, "59": 3, "60": 3, "61": 3, "62": 3, "63": 3, "64": 3, "65": 3, "66": 3, "67": 3, "68": 3, "69": 3, "70": 3, "71": 3, "72": 3, "73": 3, "74": 3, "75": 3, "76": 3, "77": 3, "78": 3, "79": 3, "80": 3, "81": 3, "82": 3, "83": 3, "84": 3, "85": 3, "86": 3, "87": 3, "88": 3, "89": 3, "90": 3, 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119, 120, 121, 122, 123, 124, 125, 126]}]}, {"name": "measure", "qubits": [111], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m111", "label": "M_m111", "pulse_shape": "gaussian_square", "parameters": {"amp": [0.06113681804468876, -0.2305309946175798], "duration": 1440, "sigma": 32, "width": 1312}}, {"name": "delay", "t0": 1440, "ch": "m111", "duration": 6560}, {"name": "acquire", "t0": 0, "duration": 1440, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 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47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]}]}, {"name": "measure", "qubits": [115], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m115", "label": "M_m115", "pulse_shape": "gaussian_square", "parameters": {"amp": [-0.26037443015772666, -0.04929661367719992], "duration": 1440, "sigma": 32, "width": 1312}}, {"name": "delay", "t0": 1440, "ch": "m115", "duration": 6560}, {"name": "acquire", "t0": 0, "duration": 1440, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 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64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]}]}, {"name": "measure", "qubits": [117], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m117", "label": "M_m117", "pulse_shape": "gaussian_square", "parameters": 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"beta": 0.6515433326348544, "duration": 120, "sigma": 30}}]}, {"name": "x", "qubits": [126], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "d126", "label": "Xp_d126", "pulse_shape": "drag", "parameters": {"amp": [0.18501959563248155, 0.0], "beta": 0.09988096426150478, "duration": 120, "sigma": 30}}]}], "meas_kernel": {"name": "hw_qmfk", "params": {}}, "discriminator": {"name": "hw_qmfk", "params": {}}, "_data": {}} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/brisbane/fake_brisbane.py b/qiskit_ibm_runtime/fake_provider/backends/brisbane/fake_brisbane.py new file mode 100644 index 000000000..35c3c0c86 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/brisbane/fake_brisbane.py @@ -0,0 +1,28 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Brisbane device (127 qubit). +""" + +import os +from qiskit_ibm_runtime.fake_provider import fake_backend + + +class FakeBrisbane(fake_backend.FakeBackendV2): + """A fake 127 qubit backend.""" + + dirname = os.path.dirname(__file__) # type: ignore + conf_filename = "conf_brisbane.json" # type: ignore + props_filename = "props_brisbane.json" # type: ignore + defs_filename = "defs_brisbane.json" # type: ignore + backend_name = "fake_brisbane" # type: ignore diff --git a/qiskit_ibm_runtime/fake_provider/backends/brisbane/props_brisbane.json b/qiskit_ibm_runtime/fake_provider/backends/brisbane/props_brisbane.json new file mode 100644 index 000000000..1f99794ec --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/brisbane/props_brisbane.json @@ -0,0 +1 @@ +{"backend_name": "ibm_brisbane", "backend_version": "1.1.17", "last_update_date": "2024-02-28T10:39:17-05:00", "qubits": [[{"date": "2024-02-28T01:02:15-05:00", "name": "T1", "unit": "us", "value": 344.18066688647605}, {"date": "2024-02-28T01:14:21-05:00", "name": "T2", "unit": "us", "value": 75.64288203206611}, {"date": "2024-02-28T10:39:17-05:00", "name": "frequency", "unit": "GHz", "value": 4.721862452373812}, {"date": "2024-02-28T10:39:17-05:00", "name": "anharmonicity", "unit": "GHz", "value": -0.31197865973435573}, {"date": "2024-02-28T00:40:32-05:00", "name": "readout_error", "unit": "", "value": 0.0252}, {"date": "2024-02-28T00:40:32-05:00", "name": "prob_meas0_prep1", "unit": "", "value": 0.0242}, {"date": "2024-02-28T00:40:32-05:00", "name": "prob_meas1_prep0", "unit": "", "value": 0.0262}, {"date": "2024-02-28T00:40:32-05:00", 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"lf_100", "qubits": [37, 52, 56, 57, 58, 71, 77, 76, 75, 90, 94, 95, 96, 109, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 112, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 91, 79, 80, 81, 72, 62, 61, 60, 53, 41, 42, 43, 44, 45, 54, 64, 65, 66, 73, 85, 86, 87, 88, 89, 74, 70, 69, 68, 55, 49, 50, 51, 36, 32, 31, 30, 17, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 14, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]}]} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/cusco/__init__.py b/qiskit_ibm_runtime/fake_provider/backends/cusco/__init__.py new file mode 100644 index 000000000..5cc8f2be7 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/cusco/__init__.py @@ -0,0 +1,17 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Cusco backend (127 qubit). +""" + +from .fake_cusco import FakeCusco diff --git a/qiskit_ibm_runtime/fake_provider/backends/cusco/conf_cusco.json b/qiskit_ibm_runtime/fake_provider/backends/cusco/conf_cusco.json new file mode 100644 index 000000000..662e2542a --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/cusco/conf_cusco.json @@ -0,0 +1 @@ +{"backend_name": "ibm_cusco", "backend_version": "1.0.25", "n_qubits": 127, "basis_gates": ["ecr", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], 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7.336261915000001], [6.347548077000001, 7.347548077000001], [6.7474181060000005, 7.7474181060000005], [6.35228292, 7.35228292], [6.864970799000001, 7.864970799000001], [6.285414044, 7.285414044], [6.4686048650000005, 7.4686048650000005], [6.351149322, 7.351149322], [6.283080439000001, 7.283080439000001], [6.734382546000001, 7.734382546000001], [6.799128833, 7.799128833], [6.4101281320000005, 7.4101281320000005], [6.875480069000001, 7.875480069000001], [6.290410240000001, 7.290410240000001], [6.478646376, 7.478646376], [6.350425125, 7.350425125], [6.423009702000001, 7.423009702000001], [6.474662901, 7.474662901]], "meas_kernels": ["hw_qmfk"], "discriminators": ["quadratic_discriminator", "hw_qmfk", "linear_discriminator"], "rep_times": [1000.0], "meas_map": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]], "acquisition_latency": [], "conditional_latency": [], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{126}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{62,72}(\\sigma_{62}^{+}\\sigma_{72}^{-}+\\sigma_{62}^{-}\\sigma_{72}^{+}) + J_{67,68}(\\sigma_{67}^{+}\\sigma_{68}^{-}+\\sigma_{67}^{-}\\sigma_{68}^{+}) + J_{44,45}(\\sigma_{44}^{+}\\sigma_{45}^{-}+\\sigma_{44}^{-}\\sigma_{45}^{+}) + J_{99,100}(\\sigma_{99}^{+}\\sigma_{100}^{-}+\\sigma_{99}^{-}\\sigma_{100}^{+}) \\\\ & + J_{108,112}(\\sigma_{108}^{+}\\sigma_{112}^{-}+\\sigma_{108}^{-}\\sigma_{112}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{40,41}(\\sigma_{40}^{+}\\sigma_{41}^{-}+\\sigma_{40}^{-}\\sigma_{41}^{+}) + J_{0,14}(\\sigma_{0}^{+}\\sigma_{14}^{-}+\\sigma_{0}^{-}\\sigma_{14}^{+}) \\\\ & + J_{17,30}(\\sigma_{17}^{+}\\sigma_{30}^{-}+\\sigma_{17}^{-}\\sigma_{30}^{+}) + J_{100,101}(\\sigma_{100}^{+}\\sigma_{101}^{-}+\\sigma_{100}^{-}\\sigma_{101}^{+}) + J_{91,98}(\\sigma_{91}^{+}\\sigma_{98}^{-}+\\sigma_{91}^{-}\\sigma_{98}^{+}) + J_{100,110}(\\sigma_{100}^{+}\\sigma_{110}^{-}+\\sigma_{100}^{-}\\sigma_{110}^{+}) \\\\ & + J_{75,90}(\\sigma_{75}^{+}\\sigma_{90}^{-}+\\sigma_{75}^{-}\\sigma_{90}^{+}) + J_{96,97}(\\sigma_{96}^{+}\\sigma_{97}^{-}+\\sigma_{96}^{-}\\sigma_{97}^{+}) + J_{41,42}(\\sigma_{41}^{+}\\sigma_{42}^{-}+\\sigma_{41}^{-}\\sigma_{42}^{+}) + J_{18,19}(\\sigma_{18}^{+}\\sigma_{19}^{-}+\\sigma_{18}^{-}\\sigma_{19}^{+}) \\\\ & + J_{55,68}(\\sigma_{55}^{+}\\sigma_{68}^{-}+\\sigma_{55}^{-}\\sigma_{68}^{+}) + J_{9,10}(\\sigma_{9}^{+}\\sigma_{10}^{-}+\\sigma_{9}^{-}\\sigma_{10}^{+}) + J_{49,55}(\\sigma_{49}^{+}\\sigma_{55}^{-}+\\sigma_{49}^{-}\\sigma_{55}^{+}) + J_{106,107}(\\sigma_{106}^{+}\\sigma_{107}^{-}+\\sigma_{106}^{-}\\sigma_{107}^{+}) \\\\ & + J_{47,48}(\\sigma_{47}^{+}\\sigma_{48}^{-}+\\sigma_{47}^{-}\\sigma_{48}^{+}) + J_{42,43}(\\sigma_{42}^{+}\\sigma_{43}^{-}+\\sigma_{42}^{-}\\sigma_{43}^{+}) + J_{107,108}(\\sigma_{107}^{+}\\sigma_{108}^{-}+\\sigma_{107}^{-}\\sigma_{108}^{+}) + J_{73,85}(\\sigma_{73}^{+}\\sigma_{85}^{-}+\\sigma_{73}^{-}\\sigma_{85}^{+}) \\\\ & + J_{38,39}(\\sigma_{38}^{+}\\sigma_{39}^{-}+\\sigma_{38}^{-}\\sigma_{39}^{+}) + J_{20,33}(\\sigma_{20}^{+}\\sigma_{33}^{-}+\\sigma_{20}^{-}\\sigma_{33}^{+}) + J_{48,49}(\\sigma_{48}^{+}\\sigma_{49}^{-}+\\sigma_{48}^{-}\\sigma_{49}^{+}) + J_{103,104}(\\sigma_{103}^{+}\\sigma_{104}^{-}+\\sigma_{103}^{-}\\sigma_{104}^{+}) \\\\ & + J_{80,81}(\\sigma_{80}^{+}\\sigma_{81}^{-}+\\sigma_{80}^{-}\\sigma_{81}^{+}) + J_{75,76}(\\sigma_{75}^{+}\\sigma_{76}^{-}+\\sigma_{75}^{-}\\sigma_{76}^{+}) + J_{66,73}(\\sigma_{66}^{+}\\sigma_{73}^{-}+\\sigma_{66}^{-}\\sigma_{73}^{+}) + J_{85,86}(\\sigma_{85}^{+}\\sigma_{86}^{-}+\\sigma_{85}^{-}\\sigma_{86}^{+}) \\\\ & + J_{81,82}(\\sigma_{81}^{+}\\sigma_{82}^{-}+\\sigma_{81}^{-}\\sigma_{82}^{+}) + J_{110,118}(\\sigma_{110}^{+}\\sigma_{118}^{-}+\\sigma_{110}^{-}\\sigma_{118}^{+}) + J_{16,26}(\\sigma_{16}^{+}\\sigma_{26}^{-}+\\sigma_{16}^{-}\\sigma_{26}^{+}) + J_{90,94}(\\sigma_{90}^{+}\\sigma_{94}^{-}+\\sigma_{90}^{-}\\sigma_{94}^{+}) \\\\ & + J_{118,119}(\\sigma_{118}^{+}\\sigma_{119}^{-}+\\sigma_{118}^{-}\\sigma_{119}^{+}) + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{77,78}(\\sigma_{77}^{+}\\sigma_{78}^{-}+\\sigma_{77}^{-}\\sigma_{78}^{+}) + J_{22,23}(\\sigma_{22}^{+}\\sigma_{23}^{-}+\\sigma_{22}^{-}\\sigma_{23}^{+}) \\\\ & + J_{49,50}(\\sigma_{49}^{+}\\sigma_{50}^{-}+\\sigma_{49}^{-}\\sigma_{50}^{+}) + J_{104,105}(\\sigma_{104}^{+}\\sigma_{105}^{-}+\\sigma_{104}^{-}\\sigma_{105}^{+}) + J_{114,115}(\\sigma_{114}^{+}\\sigma_{115}^{-}+\\sigma_{114}^{-}\\sigma_{115}^{+}) + J_{45,46}(\\sigma_{45}^{+}\\sigma_{46}^{-}+\\sigma_{45}^{-}\\sigma_{46}^{+}) \\\\ & + J_{50,51}(\\sigma_{50}^{+}\\sigma_{51}^{-}+\\sigma_{50}^{-}\\sigma_{51}^{+}) + J_{105,106}(\\sigma_{105}^{+}\\sigma_{106}^{-}+\\sigma_{105}^{-}\\sigma_{106}^{+}) + J_{72,81}(\\sigma_{72}^{+}\\sigma_{81}^{-}+\\sigma_{72}^{-}\\sigma_{81}^{+}) + J_{82,83}(\\sigma_{82}^{+}\\sigma_{83}^{-}+\\sigma_{82}^{-}\\sigma_{83}^{+}) \\\\ & + J_{46,47}(\\sigma_{46}^{+}\\sigma_{47}^{-}+\\sigma_{46}^{-}\\sigma_{47}^{+}) + J_{78,79}(\\sigma_{78}^{+}\\sigma_{79}^{-}+\\sigma_{78}^{-}\\sigma_{79}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) + J_{83,84}(\\sigma_{83}^{+}\\sigma_{84}^{-}+\\sigma_{83}^{-}\\sigma_{84}^{+}) \\\\ & + J_{115,116}(\\sigma_{115}^{+}\\sigma_{116}^{-}+\\sigma_{115}^{-}\\sigma_{116}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) + J_{79,80}(\\sigma_{79}^{+}\\sigma_{80}^{-}+\\sigma_{79}^{-}\\sigma_{80}^{+}) \\\\ & + J_{56,57}(\\sigma_{56}^{+}\\sigma_{57}^{-}+\\sigma_{56}^{-}\\sigma_{57}^{+}) + J_{93,106}(\\sigma_{93}^{+}\\sigma_{106}^{-}+\\sigma_{93}^{-}\\sigma_{106}^{+}) + J_{116,117}(\\sigma_{116}^{+}\\sigma_{117}^{-}+\\sigma_{116}^{-}\\sigma_{117}^{+}) + J_{20,21}(\\sigma_{20}^{+}\\sigma_{21}^{-}+\\sigma_{20}^{-}\\sigma_{21}^{+}) \\\\ & + J_{41,53}(\\sigma_{41}^{+}\\sigma_{53}^{-}+\\sigma_{41}^{-}\\sigma_{53}^{+}) + J_{12,17}(\\sigma_{12}^{+}\\sigma_{17}^{-}+\\sigma_{12}^{-}\\sigma_{17}^{+}) + J_{57,58}(\\sigma_{57}^{+}\\sigma_{58}^{-}+\\sigma_{57}^{-}\\sigma_{58}^{+}) + J_{87,93}(\\sigma_{87}^{+}\\sigma_{93}^{-}+\\sigma_{87}^{-}\\sigma_{93}^{+}) \\\\ & + J_{30,31}(\\sigma_{30}^{+}\\sigma_{31}^{-}+\\sigma_{30}^{-}\\sigma_{31}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) + J_{79,91}(\\sigma_{79}^{+}\\sigma_{91}^{-}+\\sigma_{79}^{-}\\sigma_{91}^{+}) + J_{26,27}(\\sigma_{26}^{+}\\sigma_{27}^{-}+\\sigma_{26}^{-}\\sigma_{27}^{+}) \\\\ & + J_{21,22}(\\sigma_{21}^{+}\\sigma_{22}^{-}+\\sigma_{21}^{-}\\sigma_{22}^{+}) + J_{58,71}(\\sigma_{58}^{+}\\sigma_{71}^{-}+\\sigma_{58}^{-}\\sigma_{71}^{+}) + J_{31,32}(\\sigma_{31}^{+}\\sigma_{32}^{-}+\\sigma_{31}^{-}\\sigma_{32}^{+}) + J_{4,15}(\\sigma_{4}^{+}\\sigma_{15}^{-}+\\sigma_{4}^{-}\\sigma_{15}^{+}) \\\\ & + J_{86,87}(\\sigma_{86}^{+}\\sigma_{87}^{-}+\\sigma_{86}^{-}\\sigma_{87}^{+}) + J_{113,114}(\\sigma_{113}^{+}\\sigma_{114}^{-}+\\sigma_{113}^{-}\\sigma_{114}^{+}) + J_{104,111}(\\sigma_{104}^{+}\\sigma_{111}^{-}+\\sigma_{104}^{-}\\sigma_{111}^{+}) + J_{123,124}(\\sigma_{123}^{+}\\sigma_{124}^{-}+\\sigma_{123}^{-}\\sigma_{124}^{+}) \\\\ & + J_{27,28}(\\sigma_{27}^{+}\\sigma_{28}^{-}+\\sigma_{27}^{-}\\sigma_{28}^{+}) + J_{34,43}(\\sigma_{34}^{+}\\sigma_{43}^{-}+\\sigma_{34}^{-}\\sigma_{43}^{+}) + J_{119,120}(\\sigma_{119}^{+}\\sigma_{120}^{-}+\\sigma_{119}^{-}\\sigma_{120}^{+}) + J_{64,65}(\\sigma_{64}^{+}\\sigma_{65}^{-}+\\sigma_{64}^{-}\\sigma_{65}^{+}) \\\\ & + J_{54,64}(\\sigma_{54}^{+}\\sigma_{64}^{-}+\\sigma_{54}^{-}\\sigma_{64}^{+}) + J_{32,36}(\\sigma_{32}^{+}\\sigma_{36}^{-}+\\sigma_{32}^{-}\\sigma_{36}^{+}) + J_{5,6}(\\sigma_{5}^{+}\\sigma_{6}^{-}+\\sigma_{5}^{-}\\sigma_{6}^{+}) + J_{60,61}(\\sigma_{60}^{+}\\sigma_{61}^{-}+\\sigma_{60}^{-}\\sigma_{61}^{+}) \\\\ & + J_{14,18}(\\sigma_{14}^{+}\\sigma_{18}^{-}+\\sigma_{14}^{-}\\sigma_{18}^{+}) + J_{87,88}(\\sigma_{87}^{+}\\sigma_{88}^{-}+\\sigma_{87}^{-}\\sigma_{88}^{+}) + J_{97,98}(\\sigma_{97}^{+}\\sigma_{98}^{-}+\\sigma_{97}^{-}\\sigma_{98}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) \\\\ & + J_{112,126}(\\sigma_{112}^{+}\\sigma_{126}^{-}+\\sigma_{112}^{-}\\sigma_{126}^{+}) + J_{28,29}(\\sigma_{28}^{+}\\sigma_{29}^{-}+\\sigma_{28}^{-}\\sigma_{29}^{+}) + J_{45,54}(\\sigma_{45}^{+}\\sigma_{54}^{-}+\\sigma_{45}^{-}\\sigma_{54}^{+}) + J_{36,51}(\\sigma_{36}^{+}\\sigma_{51}^{-}+\\sigma_{36}^{-}\\sigma_{51}^{+}) \\\\ & + J_{88,89}(\\sigma_{88}^{+}\\sigma_{89}^{-}+\\sigma_{88}^{-}\\sigma_{89}^{+}) + J_{120,121}(\\sigma_{120}^{+}\\sigma_{121}^{-}+\\sigma_{120}^{-}\\sigma_{121}^{+}) + J_{15,22}(\\sigma_{15}^{+}\\sigma_{22}^{-}+\\sigma_{15}^{-}\\sigma_{22}^{+}) + J_{24,34}(\\sigma_{24}^{+}\\sigma_{34}^{-}+\\sigma_{24}^{-}\\sigma_{34}^{+}) \\\\ & + J_{84,85}(\\sigma_{84}^{+}\\sigma_{85}^{-}+\\sigma_{84}^{-}\\sigma_{85}^{+}) + J_{29,30}(\\sigma_{29}^{+}\\sigma_{30}^{-}+\\sigma_{29}^{-}\\sigma_{30}^{+}) + J_{61,62}(\\sigma_{61}^{+}\\sigma_{62}^{-}+\\sigma_{61}^{-}\\sigma_{62}^{+}) + J_{70,74}(\\sigma_{70}^{+}\\sigma_{74}^{-}+\\sigma_{70}^{-}\\sigma_{74}^{+}) \\\\ & + J_{121,122}(\\sigma_{121}^{+}\\sigma_{122}^{-}+\\sigma_{121}^{-}\\sigma_{122}^{+}) + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{122,123}(\\sigma_{122}^{+}\\sigma_{123}^{-}+\\sigma_{122}^{-}\\sigma_{123}^{+}) + J_{62,63}(\\sigma_{62}^{+}\\sigma_{63}^{-}+\\sigma_{62}^{-}\\sigma_{63}^{+}) \\\\ & + J_{117,118}(\\sigma_{117}^{+}\\sigma_{118}^{-}+\\sigma_{117}^{-}\\sigma_{118}^{+}) + J_{94,95}(\\sigma_{94}^{+}\\sigma_{95}^{-}+\\sigma_{94}^{-}\\sigma_{95}^{+}) + J_{109,114}(\\sigma_{109}^{+}\\sigma_{114}^{-}+\\sigma_{109}^{-}\\sigma_{114}^{+}) + J_{37,52}(\\sigma_{37}^{+}\\sigma_{52}^{-}+\\sigma_{37}^{-}\\sigma_{52}^{+}) \\\\ & + J_{58,59}(\\sigma_{58}^{+}\\sigma_{59}^{-}+\\sigma_{58}^{-}\\sigma_{59}^{+}) + J_{3,4}(\\sigma_{3}^{+}\\sigma_{4}^{-}+\\sigma_{3}^{-}\\sigma_{4}^{+}) + J_{33,39}(\\sigma_{33}^{+}\\sigma_{39}^{-}+\\sigma_{33}^{-}\\sigma_{39}^{+}) + J_{95,96}(\\sigma_{95}^{+}\\sigma_{96}^{-}+\\sigma_{95}^{-}\\sigma_{96}^{+}) \\\\ & + J_{68,69}(\\sigma_{68}^{+}\\sigma_{69}^{-}+\\sigma_{68}^{-}\\sigma_{69}^{+}) + J_{63,64}(\\sigma_{63}^{+}\\sigma_{64}^{-}+\\sigma_{63}^{-}\\sigma_{64}^{+}) + J_{71,77}(\\sigma_{71}^{+}\\sigma_{77}^{-}+\\sigma_{71}^{-}\\sigma_{77}^{+}) + J_{111,122}(\\sigma_{111}^{+}\\sigma_{122}^{-}+\\sigma_{111}^{-}\\sigma_{122}^{+}) \\\\ & + J_{4,5}(\\sigma_{4}^{+}\\sigma_{5}^{-}+\\sigma_{4}^{-}\\sigma_{5}^{+}) + J_{59,60}(\\sigma_{59}^{+}\\sigma_{60}^{-}+\\sigma_{59}^{-}\\sigma_{60}^{+}) + J_{96,109}(\\sigma_{96}^{+}\\sigma_{109}^{-}+\\sigma_{96}^{-}\\sigma_{109}^{+}) + J_{124,125}(\\sigma_{124}^{+}\\sigma_{125}^{-}+\\sigma_{124}^{-}\\sigma_{125}^{+}) \\\\ & + J_{69,70}(\\sigma_{69}^{+}\\sigma_{70}^{-}+\\sigma_{69}^{-}\\sigma_{70}^{+}) + J_{101,102}(\\sigma_{101}^{+}\\sigma_{102}^{-}+\\sigma_{101}^{-}\\sigma_{102}^{+}) + J_{35,47}(\\sigma_{35}^{+}\\sigma_{47}^{-}+\\sigma_{35}^{-}\\sigma_{47}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) \\\\ & + J_{65,66}(\\sigma_{65}^{+}\\sigma_{66}^{-}+\\sigma_{65}^{-}\\sigma_{66}^{+}) + J_{10,11}(\\sigma_{10}^{+}\\sigma_{11}^{-}+\\sigma_{10}^{-}\\sigma_{11}^{+}) + J_{37,38}(\\sigma_{37}^{+}\\sigma_{38}^{-}+\\sigma_{37}^{-}\\sigma_{38}^{+}) + J_{28,35}(\\sigma_{28}^{+}\\sigma_{35}^{-}+\\sigma_{28}^{-}\\sigma_{35}^{+}) \\\\ & + J_{102,103}(\\sigma_{102}^{+}\\sigma_{103}^{-}+\\sigma_{102}^{-}\\sigma_{103}^{+}) + J_{92,102}(\\sigma_{92}^{+}\\sigma_{102}^{-}+\\sigma_{92}^{-}\\sigma_{102}^{+}) + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{98,99}(\\sigma_{98}^{+}\\sigma_{99}^{-}+\\sigma_{98}^{-}\\sigma_{99}^{+}) \\\\ & + J_{43,44}(\\sigma_{43}^{+}\\sigma_{44}^{-}+\\sigma_{43}^{-}\\sigma_{44}^{+}) + J_{52,56}(\\sigma_{52}^{+}\\sigma_{56}^{-}+\\sigma_{52}^{-}\\sigma_{56}^{+}) + J_{125,126}(\\sigma_{125}^{+}\\sigma_{126}^{-}+\\sigma_{125}^{-}\\sigma_{126}^{+}) + J_{39,40}(\\sigma_{39}^{+}\\sigma_{40}^{-}+\\sigma_{39}^{-}\\sigma_{40}^{+}) \\\\ & + J_{8,16}(\\sigma_{8}^{+}\\sigma_{16}^{-}+\\sigma_{8}^{-}\\sigma_{16}^{+}) + J_{66,67}(\\sigma_{66}^{+}\\sigma_{67}^{-}+\\sigma_{66}^{-}\\sigma_{67}^{+}) + J_{11,12}(\\sigma_{11}^{+}\\sigma_{12}^{-}+\\sigma_{11}^{-}\\sigma_{12}^{+}) + J_{76,77}(\\sigma_{76}^{+}\\sigma_{77}^{-}+\\sigma_{76}^{-}\\sigma_{77}^{+}) \\\\ & + J_{83,92}(\\sigma_{83}^{+}\\sigma_{92}^{-}+\\sigma_{83}^{-}\\sigma_{92}^{+}) + J_{74,89}(\\sigma_{74}^{+}\\sigma_{89}^{-}+\\sigma_{74}^{-}\\sigma_{89}^{+}) + J_{7,8}(\\sigma_{7}^{+}\\sigma_{8}^{-}+\\sigma_{7}^{-}\\sigma_{8}^{+}) + J_{53,60}(\\sigma_{53}^{+}\\sigma_{60}^{-}+\\sigma_{53}^{-}\\sigma_{60}^{+}) \\\\ & + \\Omega_{d,0}(U_{0}^{(0,1)}(t))\\sigma_{0}^{X} + \\Omega_{d,2}(U_{1}^{(2,1)}(t))\\sigma_{2}^{X} \\\\ & + \\Omega_{d,3}(U_{2}^{(3,2)}(t))\\sigma_{3}^{X} + \\Omega_{d,4}(U_{4}^{(4,15)}(t)+U_{3}^{(4,3)}(t))\\sigma_{4}^{X} \\\\ & + \\Omega_{d,5}(U_{6}^{(5,6)}(t)+U_{5}^{(5,4)}(t))\\sigma_{5}^{X} + \\Omega_{d,7}(U_{7}^{(7,6)}(t))\\sigma_{7}^{X} \\\\ & + \\Omega_{d,8}(U_{8}^{(8,7)}(t))\\sigma_{8}^{X} + \\Omega_{d,9}(U_{9}^{(9,8)}(t))\\sigma_{9}^{X} \\\\ & + \\Omega_{d,10}(U_{10}^{(10,9)}(t))\\sigma_{10}^{X} + \\Omega_{d,11}(U_{12}^{(11,12)}(t)+U_{11}^{(11,10)}(t))\\sigma_{11}^{X} \\\\ & + \\Omega_{d,12}(U_{13}^{(12,17)}(t))\\sigma_{12}^{X} + \\Omega_{d,13}(U_{14}^{(13,12)}(t))\\sigma_{13}^{X} \\\\ & + \\Omega_{d,14}(U_{15}^{(14,0)}(t))\\sigma_{14}^{X} + \\Omega_{d,16}(U_{16}^{(16,8)}(t))\\sigma_{16}^{X} \\\\ & + \\Omega_{d,17}(U_{17}^{(17,30)}(t))\\sigma_{17}^{X} + \\Omega_{d,18}(U_{19}^{(18,19)}(t)+U_{18}^{(18,14)}(t))\\sigma_{18}^{X} \\\\ & + \\Omega_{d,20}(U_{20}^{(20,19)}(t)+U_{21}^{(20,33)}(t))\\sigma_{20}^{X} + \\Omega_{d,21}(U_{23}^{(21,22)}(t)+U_{22}^{(21,20)}(t))\\sigma_{21}^{X} \\\\ & + \\Omega_{d,22}(U_{24}^{(22,15)}(t))\\sigma_{22}^{X} + \\Omega_{d,23}(U_{25}^{(23,22)}(t)+U_{26}^{(23,24)}(t))\\sigma_{23}^{X} \\\\ & + \\Omega_{d,25}(U_{27}^{(25,24)}(t))\\sigma_{25}^{X} + \\Omega_{d,26}(U_{28}^{(26,16)}(t)+U_{30}^{(26,27)}(t)+U_{29}^{(26,25)}(t))\\sigma_{26}^{X} \\\\ & + \\Omega_{d,28}(U_{31}^{(28,27)}(t))\\sigma_{28}^{X} + \\Omega_{d,29}(U_{33}^{(29,30)}(t)+U_{32}^{(29,28)}(t))\\sigma_{29}^{X} \\\\ & + \\Omega_{d,30}(U_{34}^{(30,31)}(t))\\sigma_{30}^{X} + \\Omega_{d,31}(U_{35}^{(31,32)}(t))\\sigma_{31}^{X} \\\\ & + \\Omega_{d,32}(U_{36}^{(32,36)}(t))\\sigma_{32}^{X} + \\Omega_{d,33}(U_{37}^{(33,39)}(t))\\sigma_{33}^{X} \\\\ & + \\Omega_{d,34}(U_{38}^{(34,24)}(t))\\sigma_{34}^{X} + \\Omega_{d,35}(U_{39}^{(35,28)}(t)+U_{40}^{(35,47)}(t))\\sigma_{35}^{X} \\\\ & + \\Omega_{d,36}(U_{41}^{(36,51)}(t))\\sigma_{36}^{X} + \\Omega_{d,37}(U_{42}^{(37,38)}(t))\\sigma_{37}^{X} \\\\ & + \\Omega_{d,38}(U_{43}^{(38,39)}(t))\\sigma_{38}^{X} + \\Omega_{d,40}(U_{45}^{(40,41)}(t)+U_{44}^{(40,39)}(t))\\sigma_{40}^{X} \\\\ & + \\Omega_{d,42}(U_{46}^{(42,41)}(t)+U_{47}^{(42,43)}(t))\\sigma_{42}^{X} + \\Omega_{d,43}(U_{48}^{(43,34)}(t)+U_{49}^{(43,44)}(t))\\sigma_{43}^{X} \\\\ & + \\Omega_{d,44}(U_{50}^{(44,45)}(t))\\sigma_{44}^{X} + \\Omega_{d,46}(U_{52}^{(46,47)}(t)+U_{51}^{(46,45)}(t))\\sigma_{46}^{X} \\\\ & + \\Omega_{d,48}(U_{54}^{(48,49)}(t)+U_{53}^{(48,47)}(t))\\sigma_{48}^{X} + \\Omega_{d,50}(U_{55}^{(50,49)}(t))\\sigma_{50}^{X} \\\\ & + \\Omega_{d,51}(U_{56}^{(51,50)}(t))\\sigma_{51}^{X} + \\Omega_{d,52}(U_{58}^{(52,56)}(t)+U_{57}^{(52,37)}(t))\\sigma_{52}^{X} \\\\ & + \\Omega_{d,53}(U_{59}^{(53,41)}(t))\\sigma_{53}^{X} + \\Omega_{d,54}(U_{61}^{(54,64)}(t)+U_{60}^{(54,45)}(t))\\sigma_{54}^{X} \\\\ & + \\Omega_{d,55}(U_{63}^{(55,68)}(t)+U_{62}^{(55,49)}(t))\\sigma_{55}^{X} + \\Omega_{d,56}(U_{64}^{(56,57)}(t))\\sigma_{56}^{X} \\\\ & + \\Omega_{d,57}(U_{65}^{(57,58)}(t))\\sigma_{57}^{X} + \\Omega_{d,58}(U_{67}^{(58,71)}(t)+U_{66}^{(58,59)}(t))\\sigma_{58}^{X} \\\\ & + \\Omega_{d,60}(U_{68}^{(60,53)}(t)+U_{70}^{(60,61)}(t)+U_{69}^{(60,59)}(t))\\sigma_{60}^{X} + \\Omega_{d,62}(U_{72}^{(62,63)}(t)+U_{71}^{(62,61)}(t))\\sigma_{62}^{X} \\\\ & + \\Omega_{d,64}(U_{73}^{(64,63)}(t))\\sigma_{64}^{X} + \\Omega_{d,65}(U_{75}^{(65,66)}(t)+U_{74}^{(65,64)}(t))\\sigma_{65}^{X} \\\\ & + \\Omega_{d,66}(U_{76}^{(66,73)}(t))\\sigma_{66}^{X} + \\Omega_{d,67}(U_{78}^{(67,68)}(t)+U_{77}^{(67,66)}(t))\\sigma_{67}^{X} \\\\ & + \\Omega_{d,68}(U_{79}^{(68,69)}(t))\\sigma_{68}^{X} + \\Omega_{d,70}(U_{80}^{(70,69)}(t)+U_{81}^{(70,74)}(t))\\sigma_{70}^{X} \\\\ & + \\Omega_{d,72}(U_{82}^{(72,62)}(t)+U_{83}^{(72,81)}(t))\\sigma_{72}^{X} + \\Omega_{d,73}(U_{84}^{(73,85)}(t))\\sigma_{73}^{X} \\\\ & + \\Omega_{d,74}(U_{85}^{(74,89)}(t))\\sigma_{74}^{X} + \\Omega_{d,76}(U_{87}^{(76,77)}(t)+U_{86}^{(76,75)}(t))\\sigma_{76}^{X} \\\\ & + \\Omega_{d,77}(U_{88}^{(77,71)}(t))\\sigma_{77}^{X} + \\Omega_{d,78}(U_{89}^{(78,77)}(t))\\sigma_{78}^{X} \\\\ & + \\Omega_{d,79}(U_{90}^{(79,78)}(t))\\sigma_{79}^{X} + \\Omega_{d,80}(U_{92}^{(80,81)}(t)+U_{91}^{(80,79)}(t))\\sigma_{80}^{X} \\\\ & + \\Omega_{d,81}(U_{93}^{(81,82)}(t))\\sigma_{81}^{X} + \\Omega_{d,83}(U_{94}^{(83,82)}(t)+U_{95}^{(83,92)}(t))\\sigma_{83}^{X} \\\\ & + \\Omega_{d,84}(U_{96}^{(84,83)}(t))\\sigma_{84}^{X} + \\Omega_{d,85}(U_{98}^{(85,86)}(t)+U_{97}^{(85,84)}(t))\\sigma_{85}^{X} \\\\ & + \\Omega_{d,87}(U_{100}^{(87,88)}(t)+U_{99}^{(87,86)}(t))\\sigma_{87}^{X} + \\Omega_{d,88}(U_{101}^{(88,89)}(t))\\sigma_{88}^{X} \\\\ & + \\Omega_{d,90}(U_{102}^{(90,75)}(t))\\sigma_{90}^{X} + \\Omega_{d,91}(U_{103}^{(91,79)}(t))\\sigma_{91}^{X} \\\\ & + \\Omega_{d,92}(U_{104}^{(92,102)}(t))\\sigma_{92}^{X} + \\Omega_{d,93}(U_{105}^{(93,87)}(t)+U_{106}^{(93,106)}(t))\\sigma_{93}^{X} \\\\ & + \\Omega_{d,94}(U_{107}^{(94,90)}(t)+U_{108}^{(94,95)}(t))\\sigma_{94}^{X} + \\Omega_{d,96}(U_{111}^{(96,109)}(t)+U_{110}^{(96,97)}(t)+U_{109}^{(96,95)}(t))\\sigma_{96}^{X} \\\\ & + \\Omega_{d,97}(U_{112}^{(97,98)}(t))\\sigma_{97}^{X} + \\Omega_{d,98}(U_{113}^{(98,91)}(t))\\sigma_{98}^{X} \\\\ & + \\Omega_{d,99}(U_{114}^{(99,98)}(t))\\sigma_{99}^{X} + \\Omega_{d,100}(U_{116}^{(100,110)}(t)+U_{115}^{(100,99)}(t))\\sigma_{100}^{X} \\\\ & + \\Omega_{d,101}(U_{117}^{(101,100)}(t))\\sigma_{101}^{X} + \\Omega_{d,102}(U_{118}^{(102,101)}(t))\\sigma_{102}^{X} \\\\ & + \\Omega_{d,103}(U_{120}^{(103,104)}(t)+U_{119}^{(103,102)}(t))\\sigma_{103}^{X} + \\Omega_{d,104}(U_{121}^{(104,105)}(t)+U_{122}^{(104,111)}(t))\\sigma_{104}^{X} \\\\ & + \\Omega_{d,105}(U_{123}^{(105,106)}(t))\\sigma_{105}^{X} + \\Omega_{d,106}(U_{124}^{(106,107)}(t))\\sigma_{106}^{X} \\\\ & + \\Omega_{d,107}(U_{125}^{(107,108)}(t))\\sigma_{107}^{X} + \\Omega_{d,108}(U_{126}^{(108,112)}(t))\\sigma_{108}^{X} \\\\ & + \\Omega_{d,109}(U_{127}^{(109,114)}(t))\\sigma_{109}^{X} + \\Omega_{d,111}(U_{128}^{(111,122)}(t))\\sigma_{111}^{X} \\\\ & + \\Omega_{d,112}(U_{129}^{(112,126)}(t))\\sigma_{112}^{X} + \\Omega_{d,113}(U_{130}^{(113,114)}(t))\\sigma_{113}^{X} \\\\ & + \\Omega_{d,115}(U_{131}^{(115,114)}(t))\\sigma_{115}^{X} + \\Omega_{d,116}(U_{133}^{(116,117)}(t)+U_{132}^{(116,115)}(t))\\sigma_{116}^{X} \\\\ & + \\Omega_{d,117}(U_{134}^{(117,118)}(t))\\sigma_{117}^{X} + \\Omega_{d,118}(U_{135}^{(118,110)}(t)+U_{136}^{(118,119)}(t))\\sigma_{118}^{X} \\\\ & + \\Omega_{d,119}(U_{137}^{(119,120)}(t))\\sigma_{119}^{X} + \\Omega_{d,121}(U_{138}^{(121,120)}(t)+U_{139}^{(121,122)}(t))\\sigma_{121}^{X} \\\\ & + \\Omega_{d,123}(U_{140}^{(123,122)}(t)+U_{141}^{(123,124)}(t))\\sigma_{123}^{X} + \\Omega_{d,125}(U_{142}^{(125,124)}(t))\\sigma_{125}^{X} \\\\ & + \\Omega_{d,126}(U_{143}^{(126,125)}(t))\\sigma_{126}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,126,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,126,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,126,-delta{i}/2*O{i}]", "_SUM[i,0,126,omegad{i}*X{i}||D{i}]", "jq62q72*Sp62*Sm72", "jq62q72*Sm62*Sp72", "jq67q68*Sp67*Sm68", "jq67q68*Sm67*Sp68", "jq44q45*Sp44*Sm45", "jq44q45*Sm44*Sp45", "jq99q100*Sp99*Sm100", "jq99q100*Sm99*Sp100", "jq108q112*Sp108*Sm112", "jq108q112*Sm108*Sp112", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq40q41*Sp40*Sm41", "jq40q41*Sm40*Sp41", "jq0q14*Sp0*Sm14", "jq0q14*Sm0*Sp14", "jq17q30*Sp17*Sm30", "jq17q30*Sm17*Sp30", "jq100q101*Sp100*Sm101", "jq100q101*Sm100*Sp101", "jq91q98*Sp91*Sm98", "jq91q98*Sm91*Sp98", "jq100q110*Sp100*Sm110", "jq100q110*Sm100*Sp110", "jq75q90*Sp75*Sm90", "jq75q90*Sm75*Sp90", "jq96q97*Sp96*Sm97", "jq96q97*Sm96*Sp97", "jq41q42*Sp41*Sm42", "jq41q42*Sm41*Sp42", "jq18q19*Sp18*Sm19", "jq18q19*Sm18*Sp19", "jq55q68*Sp55*Sm68", "jq55q68*Sm55*Sp68", "jq9q10*Sp9*Sm10", "jq9q10*Sm9*Sp10", "jq49q55*Sp49*Sm55", "jq49q55*Sm49*Sp55", "jq106q107*Sp106*Sm107", "jq106q107*Sm106*Sp107", "jq47q48*Sp47*Sm48", "jq47q48*Sm47*Sp48", "jq42q43*Sp42*Sm43", "jq42q43*Sm42*Sp43", "jq107q108*Sp107*Sm108", "jq107q108*Sm107*Sp108", "jq73q85*Sp73*Sm85", "jq73q85*Sm73*Sp85", "jq38q39*Sp38*Sm39", "jq38q39*Sm38*Sp39", "jq20q33*Sp20*Sm33", "jq20q33*Sm20*Sp33", "jq48q49*Sp48*Sm49", "jq48q49*Sm48*Sp49", "jq103q104*Sp103*Sm104", "jq103q104*Sm103*Sp104", "jq80q81*Sp80*Sm81", "jq80q81*Sm80*Sp81", "jq75q76*Sp75*Sm76", "jq75q76*Sm75*Sp76", "jq66q73*Sp66*Sm73", "jq66q73*Sm66*Sp73", "jq85q86*Sp85*Sm86", "jq85q86*Sm85*Sp86", "jq81q82*Sp81*Sm82", "jq81q82*Sm81*Sp82", "jq110q118*Sp110*Sm118", "jq110q118*Sm110*Sp118", "jq16q26*Sp16*Sm26", "jq16q26*Sm16*Sp26", "jq90q94*Sp90*Sm94", "jq90q94*Sm90*Sp94", "jq118q119*Sp118*Sm119", "jq118q119*Sm118*Sp119", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq77q78*Sp77*Sm78", "jq77q78*Sm77*Sp78", "jq22q23*Sp22*Sm23", "jq22q23*Sm22*Sp23", "jq49q50*Sp49*Sm50", "jq49q50*Sm49*Sp50", "jq104q105*Sp104*Sm105", "jq104q105*Sm104*Sp105", "jq114q115*Sp114*Sm115", "jq114q115*Sm114*Sp115", "jq45q46*Sp45*Sm46", "jq45q46*Sm45*Sp46", "jq50q51*Sp50*Sm51", "jq50q51*Sm50*Sp51", "jq105q106*Sp105*Sm106", "jq105q106*Sm105*Sp106", "jq72q81*Sp72*Sm81", "jq72q81*Sm72*Sp81", "jq82q83*Sp82*Sm83", "jq82q83*Sm82*Sp83", "jq46q47*Sp46*Sm47", "jq46q47*Sm46*Sp47", "jq78q79*Sp78*Sm79", "jq78q79*Sm78*Sp79", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq83q84*Sp83*Sm84", "jq83q84*Sm83*Sp84", "jq115q116*Sp115*Sm116", "jq115q116*Sm115*Sp116", "jq19q20*Sp19*Sm20", "jq19q20*Sm19*Sp20", "jq24q25*Sp24*Sm25", "jq24q25*Sm24*Sp25", "jq79q80*Sp79*Sm80", "jq79q80*Sm79*Sp80", "jq56q57*Sp56*Sm57", "jq56q57*Sm56*Sp57", "jq93q106*Sp93*Sm106", "jq93q106*Sm93*Sp106", "jq116q117*Sp116*Sm117", "jq116q117*Sm116*Sp117", "jq20q21*Sp20*Sm21", "jq20q21*Sm20*Sp21", "jq41q53*Sp41*Sm53", "jq41q53*Sm41*Sp53", "jq12q17*Sp12*Sm17", "jq12q17*Sm12*Sp17", "jq57q58*Sp57*Sm58", "jq57q58*Sm57*Sp58", "jq87q93*Sp87*Sm93", "jq87q93*Sm87*Sp93", "jq30q31*Sp30*Sm31", "jq30q31*Sm30*Sp31", "jq25q26*Sp25*Sm26", "jq25q26*Sm25*Sp26", "jq79q91*Sp79*Sm91", "jq79q91*Sm79*Sp91", "jq26q27*Sp26*Sm27", "jq26q27*Sm26*Sp27", "jq21q22*Sp21*Sm22", "jq21q22*Sm21*Sp22", "jq58q71*Sp58*Sm71", "jq58q71*Sm58*Sp71", "jq31q32*Sp31*Sm32", "jq31q32*Sm31*Sp32", "jq4q15*Sp4*Sm15", "jq4q15*Sm4*Sp15", "jq86q87*Sp86*Sm87", "jq86q87*Sm86*Sp87", "jq113q114*Sp113*Sm114", "jq113q114*Sm113*Sp114", "jq104q111*Sp104*Sm111", "jq104q111*Sm104*Sp111", "jq123q124*Sp123*Sm124", "jq123q124*Sm123*Sp124", "jq27q28*Sp27*Sm28", "jq27q28*Sm27*Sp28", "jq34q43*Sp34*Sm43", "jq34q43*Sm34*Sp43", "jq119q120*Sp119*Sm120", "jq119q120*Sm119*Sp120", "jq64q65*Sp64*Sm65", "jq64q65*Sm64*Sp65", "jq54q64*Sp54*Sm64", "jq54q64*Sm54*Sp64", "jq32q36*Sp32*Sm36", "jq32q36*Sm32*Sp36", "jq5q6*Sp5*Sm6", "jq5q6*Sm5*Sp6", "jq60q61*Sp60*Sm61", "jq60q61*Sm60*Sp61", "jq14q18*Sp14*Sm18", "jq14q18*Sm14*Sp18", "jq87q88*Sp87*Sm88", "jq87q88*Sm87*Sp88", "jq97q98*Sp97*Sm98", "jq97q98*Sm97*Sp98", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq112q126*Sp112*Sm126", "jq112q126*Sm112*Sp126", "jq28q29*Sp28*Sm29", "jq28q29*Sm28*Sp29", "jq45q54*Sp45*Sm54", "jq45q54*Sm45*Sp54", "jq36q51*Sp36*Sm51", "jq36q51*Sm36*Sp51", "jq88q89*Sp88*Sm89", "jq88q89*Sm88*Sp89", "jq120q121*Sp120*Sm121", "jq120q121*Sm120*Sp121", "jq15q22*Sp15*Sm22", "jq15q22*Sm15*Sp22", "jq24q34*Sp24*Sm34", "jq24q34*Sm24*Sp34", "jq84q85*Sp84*Sm85", "jq84q85*Sm84*Sp85", "jq29q30*Sp29*Sm30", "jq29q30*Sm29*Sp30", "jq61q62*Sp61*Sm62", "jq61q62*Sm61*Sp62", "jq70q74*Sp70*Sm74", "jq70q74*Sm70*Sp74", "jq121q122*Sp121*Sm122", "jq121q122*Sm121*Sp122", "jq2q3*Sp2*Sm3", "jq2q3*Sm2*Sp3", "jq122q123*Sp122*Sm123", "jq122q123*Sm122*Sp123", "jq62q63*Sp62*Sm63", "jq62q63*Sm62*Sp63", "jq117q118*Sp117*Sm118", "jq117q118*Sm117*Sp118", "jq94q95*Sp94*Sm95", "jq94q95*Sm94*Sp95", "jq109q114*Sp109*Sm114", "jq109q114*Sm109*Sp114", "jq37q52*Sp37*Sm52", "jq37q52*Sm37*Sp52", "jq58q59*Sp58*Sm59", "jq58q59*Sm58*Sp59", "jq3q4*Sp3*Sm4", "jq3q4*Sm3*Sp4", "jq33q39*Sp33*Sm39", "jq33q39*Sm33*Sp39", "jq95q96*Sp95*Sm96", "jq95q96*Sm95*Sp96", "jq68q69*Sp68*Sm69", "jq68q69*Sm68*Sp69", "jq63q64*Sp63*Sm64", "jq63q64*Sm63*Sp64", "jq71q77*Sp71*Sm77", "jq71q77*Sm71*Sp77", "jq111q122*Sp111*Sm122", "jq111q122*Sm111*Sp122", "jq4q5*Sp4*Sm5", "jq4q5*Sm4*Sp5", "jq59q60*Sp59*Sm60", "jq59q60*Sm59*Sp60", "jq96q109*Sp96*Sm109", "jq96q109*Sm96*Sp109", "jq124q125*Sp124*Sm125", "jq124q125*Sm124*Sp125", "jq69q70*Sp69*Sm70", "jq69q70*Sm69*Sp70", "jq101q102*Sp101*Sm102", "jq101q102*Sm101*Sp102", "jq35q47*Sp35*Sm47", "jq35q47*Sm35*Sp47", "jq0q1*Sp0*Sm1", "jq0q1*Sm0*Sp1", "jq65q66*Sp65*Sm66", "jq65q66*Sm65*Sp66", "jq10q11*Sp10*Sm11", "jq10q11*Sm10*Sp11", "jq37q38*Sp37*Sm38", "jq37q38*Sm37*Sp38", "jq28q35*Sp28*Sm35", "jq28q35*Sm28*Sp35", "jq102q103*Sp102*Sm103", "jq102q103*Sm102*Sp103", "jq92q102*Sp92*Sm102", "jq92q102*Sm92*Sp102", "jq6q7*Sp6*Sm7", "jq6q7*Sm6*Sp7", "jq98q99*Sp98*Sm99", "jq98q99*Sm98*Sp99", "jq43q44*Sp43*Sm44", "jq43q44*Sm43*Sp44", "jq52q56*Sp52*Sm56", "jq52q56*Sm52*Sp56", "jq125q126*Sp125*Sm126", "jq125q126*Sm125*Sp126", "jq39q40*Sp39*Sm40", "jq39q40*Sm39*Sp40", "jq8q16*Sp8*Sm16", "jq8q16*Sm8*Sp16", "jq66q67*Sp66*Sm67", "jq66q67*Sm66*Sp67", "jq11q12*Sp11*Sm12", "jq11q12*Sm11*Sp12", "jq76q77*Sp76*Sm77", "jq76q77*Sm76*Sp77", "jq83q92*Sp83*Sm92", "jq83q92*Sm83*Sp92", "jq74q89*Sp74*Sm89", "jq74q89*Sm74*Sp89", "jq7q8*Sp7*Sm8", "jq7q8*Sm7*Sp8", "jq53q60*Sp53*Sm60", "jq53q60*Sm53*Sp60", "omegad1*X0||U0", "omegad1*X2||U1", "omegad2*X3||U2", "omegad15*X4||U4", "omegad3*X4||U3", "omegad6*X5||U6", "omegad4*X5||U5", "omegad6*X7||U7", "omegad7*X8||U8", "omegad8*X9||U9", "omegad9*X10||U10", "omegad12*X11||U12", "omegad10*X11||U11", "omegad17*X12||U13", "omegad12*X13||U14", "omegad0*X14||U15", "omegad8*X16||U16", "omegad30*X17||U17", "omegad19*X18||U19", "omegad14*X18||U18", "omegad19*X20||U20", "omegad33*X20||U21", "omegad22*X21||U23", "omegad20*X21||U22", "omegad15*X22||U24", "omegad22*X23||U25", "omegad24*X23||U26", "omegad24*X25||U27", "omegad16*X26||U28", "omegad27*X26||U30", "omegad25*X26||U29", "omegad27*X28||U31", "omegad30*X29||U33", "omegad28*X29||U32", "omegad31*X30||U34", "omegad32*X31||U35", "omegad36*X32||U36", "omegad39*X33||U37", "omegad24*X34||U38", "omegad28*X35||U39", "omegad47*X35||U40", "omegad51*X36||U41", "omegad38*X37||U42", "omegad39*X38||U43", "omegad41*X40||U45", "omegad39*X40||U44", "omegad41*X42||U46", "omegad43*X42||U47", "omegad34*X43||U48", "omegad44*X43||U49", "omegad45*X44||U50", "omegad47*X46||U52", "omegad45*X46||U51", "omegad49*X48||U54", "omegad47*X48||U53", "omegad49*X50||U55", "omegad50*X51||U56", "omegad56*X52||U58", "omegad37*X52||U57", "omegad41*X53||U59", "omegad64*X54||U61", "omegad45*X54||U60", "omegad68*X55||U63", "omegad49*X55||U62", "omegad57*X56||U64", "omegad58*X57||U65", "omegad71*X58||U67", "omegad59*X58||U66", "omegad53*X60||U68", "omegad61*X60||U70", "omegad59*X60||U69", "omegad63*X62||U72", "omegad61*X62||U71", "omegad63*X64||U73", "omegad66*X65||U75", "omegad64*X65||U74", "omegad73*X66||U76", "omegad68*X67||U78", "omegad66*X67||U77", "omegad69*X68||U79", "omegad69*X70||U80", "omegad74*X70||U81", "omegad62*X72||U82", "omegad81*X72||U83", "omegad85*X73||U84", "omegad89*X74||U85", "omegad77*X76||U87", "omegad75*X76||U86", "omegad71*X77||U88", "omegad77*X78||U89", "omegad78*X79||U90", "omegad81*X80||U92", "omegad79*X80||U91", "omegad82*X81||U93", "omegad82*X83||U94", "omegad92*X83||U95", "omegad83*X84||U96", "omegad86*X85||U98", "omegad84*X85||U97", "omegad88*X87||U100", "omegad86*X87||U99", "omegad89*X88||U101", "omegad75*X90||U102", "omegad79*X91||U103", "omegad102*X92||U104", "omegad87*X93||U105", "omegad106*X93||U106", "omegad90*X94||U107", "omegad95*X94||U108", "omegad109*X96||U111", "omegad97*X96||U110", "omegad95*X96||U109", "omegad98*X97||U112", "omegad91*X98||U113", "omegad98*X99||U114", "omegad110*X100||U116", "omegad99*X100||U115", "omegad100*X101||U117", "omegad101*X102||U118", "omegad104*X103||U120", "omegad102*X103||U119", "omegad105*X104||U121", "omegad111*X104||U122", "omegad106*X105||U123", "omegad107*X106||U124", "omegad108*X107||U125", "omegad112*X108||U126", "omegad114*X109||U127", "omegad122*X111||U128", "omegad126*X112||U129", "omegad114*X113||U130", "omegad114*X115||U131", "omegad117*X116||U133", "omegad115*X116||U132", "omegad118*X117||U134", "omegad110*X118||U135", "omegad119*X118||U136", 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a/qiskit_ibm_runtime/fake_provider/backends/cusco/defs_cusco.json b/qiskit_ibm_runtime/fake_provider/backends/cusco/defs_cusco.json new file mode 100644 index 000000000..01d9a97e8 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/cusco/defs_cusco.json @@ -0,0 +1 @@ +{"qubit_freq_est": [5.014982481627551, 4.955775039370185, 4.806657095434795, 5.232281694879282, 5.138287218428989, 4.987996280681617, 4.898880000121953, 5.022901315552583, 5.111744531189483, 5.153249514271878, 4.997062830388116, 5.1745234525219574, 4.935404588645414, 5.168663032681165, 4.930107305547402, 5.014957716509449, 5.279193979224664, 5.3955156818179075, 5.058583493511433, 4.958157690314698, 5.044085630836211, 5.159928091691546, 5.28231190358602, 5.162786301014468, 5.079754218129248, 5.137418895164864, 5.213551323640222, 5.033182503475799, 5.20831383515457, 5.117361117144152, 5.030238193637969, 5.187523071341145, 5.06768007385507, 5.143072121011085, 5.110029551726926, 5.265690769954216, 4.987782623511454, 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"drag", "parameters": {"amp": [0.2631452350018387, 0.0], "beta": -2.314529601667271, "duration": 88, "sigma": 22}}]}], "meas_kernel": {"name": "hw_qmfk", "params": {}}, "discriminator": {"name": "hw_qmfk", "params": {}}, "_data": {}} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/cusco/fake_cusco.py b/qiskit_ibm_runtime/fake_provider/backends/cusco/fake_cusco.py new file mode 100644 index 000000000..bcca7ce02 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/cusco/fake_cusco.py @@ -0,0 +1,28 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Cusco device (127 qubit). +""" + +import os +from qiskit_ibm_runtime.fake_provider import fake_backend + + +class FakeCusco(fake_backend.FakeBackendV2): + """A fake 127 qubit backend.""" + + dirname = os.path.dirname(__file__) # type: ignore + conf_filename = "conf_cusco.json" # type: ignore + props_filename = "props_cusco.json" # type: ignore + defs_filename = "defs_cusco.json" # type: ignore + backend_name = "fake_cusco" # type: ignore diff --git a/qiskit_ibm_runtime/fake_provider/backends/cusco/props_cusco.json b/qiskit_ibm_runtime/fake_provider/backends/cusco/props_cusco.json new file mode 100644 index 000000000..b014a1628 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/cusco/props_cusco.json @@ -0,0 +1 @@ +{"backend_name": "ibm_cusco", "backend_version": "1.0.25", "last_update_date": "2024-02-28T09:05:57-05:00", "qubits": [[{"date": "2024-02-27T01:59:18-05:00", "name": "T1", "unit": "us", "value": 223.7036813728529}, {"date": "2024-02-28T01:37:21-05:00", "name": "T2", "unit": "us", "value": 51.22543662294568}, {"date": "2024-02-28T09:05:57-05:00", "name": "frequency", "unit": "GHz", "value": 5.014982481627551}, {"date": "2024-02-28T09:05:57-05:00", "name": "anharmonicity", "unit": "GHz", "value": -0.3073897230302147}, {"date": "2024-02-28T01:07:28-05:00", "name": "readout_error", "unit": "", "value": 0.06030000000000002}, {"date": "2024-02-28T01:07:28-05:00", "name": "prob_meas0_prep1", "unit": "", "value": 0.0262}, {"date": "2024-02-28T01:07:28-05:00", "name": "prob_meas1_prep0", "unit": "", "value": 0.0944}, {"date": "2024-02-28T01:07:28-05:00", "name": 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0.0025067300896623604}, {"date": "2023-06-25T00:00:00-04:00", "name": "lf_100", "unit": "", "value": 0.0024171318694243293}], "general_qlists": [{"name": "lf_100", "qubits": [2, 1, 0, 14, 18, 19, 20, 33, 39, 38, 37, 52, 56, 57, 58, 71, 77, 76, 75, 90, 94, 95, 96, 109, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 112, 108, 107, 106, 105, 104, 103, 102, 101, 100, 99, 98, 91, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 74, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 53, 41, 42, 43, 34, 24, 23, 22, 15, 4, 5, 6, 7, 8, 16, 26, 27, 28, 29, 30, 31, 32, 36, 51, 50, 49, 48]}]} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/kawasaki/__init__.py b/qiskit_ibm_runtime/fake_provider/backends/kawasaki/__init__.py new file mode 100644 index 000000000..c6cfa94c3 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kawasaki/__init__.py @@ -0,0 +1,17 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Kawasaki backend (127 qubit). +""" + +from .fake_kawasaki import FakeKawasaki diff --git a/qiskit_ibm_runtime/fake_provider/backends/kawasaki/conf_kawasaki.json b/qiskit_ibm_runtime/fake_provider/backends/kawasaki/conf_kawasaki.json new file mode 100644 index 000000000..69e405732 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kawasaki/conf_kawasaki.json @@ -0,0 +1 @@ +{"backend_name": "alt_kawasaki", "backend_version": "2.0.0", "n_qubits": 127, "basis_gates": ["ecr", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], 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72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]], "acquisition_latency": [], "conditional_latency": [], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{126}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{62,72}(\\sigma_{62}^{+}\\sigma_{72}^{-}+\\sigma_{62}^{-}\\sigma_{72}^{+}) + J_{67,68}(\\sigma_{67}^{+}\\sigma_{68}^{-}+\\sigma_{67}^{-}\\sigma_{68}^{+}) + J_{44,45}(\\sigma_{44}^{+}\\sigma_{45}^{-}+\\sigma_{44}^{-}\\sigma_{45}^{+}) + J_{99,100}(\\sigma_{99}^{+}\\sigma_{100}^{-}+\\sigma_{99}^{-}\\sigma_{100}^{+}) \\\\ & + J_{108,112}(\\sigma_{108}^{+}\\sigma_{112}^{-}+\\sigma_{108}^{-}\\sigma_{112}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{40,41}(\\sigma_{40}^{+}\\sigma_{41}^{-}+\\sigma_{40}^{-}\\sigma_{41}^{+}) + J_{0,14}(\\sigma_{0}^{+}\\sigma_{14}^{-}+\\sigma_{0}^{-}\\sigma_{14}^{+}) \\\\ & + J_{17,30}(\\sigma_{17}^{+}\\sigma_{30}^{-}+\\sigma_{17}^{-}\\sigma_{30}^{+}) + J_{100,101}(\\sigma_{100}^{+}\\sigma_{101}^{-}+\\sigma_{100}^{-}\\sigma_{101}^{+}) + J_{91,98}(\\sigma_{91}^{+}\\sigma_{98}^{-}+\\sigma_{91}^{-}\\sigma_{98}^{+}) + J_{100,110}(\\sigma_{100}^{+}\\sigma_{110}^{-}+\\sigma_{100}^{-}\\sigma_{110}^{+}) \\\\ & + J_{75,90}(\\sigma_{75}^{+}\\sigma_{90}^{-}+\\sigma_{75}^{-}\\sigma_{90}^{+}) + J_{41,42}(\\sigma_{41}^{+}\\sigma_{42}^{-}+\\sigma_{41}^{-}\\sigma_{42}^{+}) + J_{96,97}(\\sigma_{96}^{+}\\sigma_{97}^{-}+\\sigma_{96}^{-}\\sigma_{97}^{+}) + J_{18,19}(\\sigma_{18}^{+}\\sigma_{19}^{-}+\\sigma_{18}^{-}\\sigma_{19}^{+}) \\\\ & + J_{55,68}(\\sigma_{55}^{+}\\sigma_{68}^{-}+\\sigma_{55}^{-}\\sigma_{68}^{+}) + J_{9,10}(\\sigma_{9}^{+}\\sigma_{10}^{-}+\\sigma_{9}^{-}\\sigma_{10}^{+}) + J_{49,55}(\\sigma_{49}^{+}\\sigma_{55}^{-}+\\sigma_{49}^{-}\\sigma_{55}^{+}) + J_{106,107}(\\sigma_{106}^{+}\\sigma_{107}^{-}+\\sigma_{106}^{-}\\sigma_{107}^{+}) \\\\ & + J_{47,48}(\\sigma_{47}^{+}\\sigma_{48}^{-}+\\sigma_{47}^{-}\\sigma_{48}^{+}) + J_{42,43}(\\sigma_{42}^{+}\\sigma_{43}^{-}+\\sigma_{42}^{-}\\sigma_{43}^{+}) + J_{107,108}(\\sigma_{107}^{+}\\sigma_{108}^{-}+\\sigma_{107}^{-}\\sigma_{108}^{+}) + J_{73,85}(\\sigma_{73}^{+}\\sigma_{85}^{-}+\\sigma_{73}^{-}\\sigma_{85}^{+}) \\\\ & + J_{38,39}(\\sigma_{38}^{+}\\sigma_{39}^{-}+\\sigma_{38}^{-}\\sigma_{39}^{+}) + J_{20,33}(\\sigma_{20}^{+}\\sigma_{33}^{-}+\\sigma_{20}^{-}\\sigma_{33}^{+}) + J_{48,49}(\\sigma_{48}^{+}\\sigma_{49}^{-}+\\sigma_{48}^{-}\\sigma_{49}^{+}) + J_{103,104}(\\sigma_{103}^{+}\\sigma_{104}^{-}+\\sigma_{103}^{-}\\sigma_{104}^{+}) \\\\ & + J_{80,81}(\\sigma_{80}^{+}\\sigma_{81}^{-}+\\sigma_{80}^{-}\\sigma_{81}^{+}) + J_{75,76}(\\sigma_{75}^{+}\\sigma_{76}^{-}+\\sigma_{75}^{-}\\sigma_{76}^{+}) + J_{66,73}(\\sigma_{66}^{+}\\sigma_{73}^{-}+\\sigma_{66}^{-}\\sigma_{73}^{+}) + J_{85,86}(\\sigma_{85}^{+}\\sigma_{86}^{-}+\\sigma_{85}^{-}\\sigma_{86}^{+}) \\\\ & + J_{81,82}(\\sigma_{81}^{+}\\sigma_{82}^{-}+\\sigma_{81}^{-}\\sigma_{82}^{+}) + J_{110,118}(\\sigma_{110}^{+}\\sigma_{118}^{-}+\\sigma_{110}^{-}\\sigma_{118}^{+}) + J_{16,26}(\\sigma_{16}^{+}\\sigma_{26}^{-}+\\sigma_{16}^{-}\\sigma_{26}^{+}) + J_{90,94}(\\sigma_{90}^{+}\\sigma_{94}^{-}+\\sigma_{90}^{-}\\sigma_{94}^{+}) \\\\ & + J_{118,119}(\\sigma_{118}^{+}\\sigma_{119}^{-}+\\sigma_{118}^{-}\\sigma_{119}^{+}) + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{77,78}(\\sigma_{77}^{+}\\sigma_{78}^{-}+\\sigma_{77}^{-}\\sigma_{78}^{+}) + J_{22,23}(\\sigma_{22}^{+}\\sigma_{23}^{-}+\\sigma_{22}^{-}\\sigma_{23}^{+}) \\\\ & + J_{49,50}(\\sigma_{49}^{+}\\sigma_{50}^{-}+\\sigma_{49}^{-}\\sigma_{50}^{+}) + J_{104,105}(\\sigma_{104}^{+}\\sigma_{105}^{-}+\\sigma_{104}^{-}\\sigma_{105}^{+}) + J_{114,115}(\\sigma_{114}^{+}\\sigma_{115}^{-}+\\sigma_{114}^{-}\\sigma_{115}^{+}) + J_{45,46}(\\sigma_{45}^{+}\\sigma_{46}^{-}+\\sigma_{45}^{-}\\sigma_{46}^{+}) \\\\ & + J_{50,51}(\\sigma_{50}^{+}\\sigma_{51}^{-}+\\sigma_{50}^{-}\\sigma_{51}^{+}) + J_{105,106}(\\sigma_{105}^{+}\\sigma_{106}^{-}+\\sigma_{105}^{-}\\sigma_{106}^{+}) + J_{72,81}(\\sigma_{72}^{+}\\sigma_{81}^{-}+\\sigma_{72}^{-}\\sigma_{81}^{+}) + J_{82,83}(\\sigma_{82}^{+}\\sigma_{83}^{-}+\\sigma_{82}^{-}\\sigma_{83}^{+}) \\\\ & + J_{46,47}(\\sigma_{46}^{+}\\sigma_{47}^{-}+\\sigma_{46}^{-}\\sigma_{47}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) + J_{78,79}(\\sigma_{78}^{+}\\sigma_{79}^{-}+\\sigma_{78}^{-}\\sigma_{79}^{+}) + J_{83,84}(\\sigma_{83}^{+}\\sigma_{84}^{-}+\\sigma_{83}^{-}\\sigma_{84}^{+}) \\\\ & + J_{115,116}(\\sigma_{115}^{+}\\sigma_{116}^{-}+\\sigma_{115}^{-}\\sigma_{116}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) + J_{79,80}(\\sigma_{79}^{+}\\sigma_{80}^{-}+\\sigma_{79}^{-}\\sigma_{80}^{+}) \\\\ & + J_{56,57}(\\sigma_{56}^{+}\\sigma_{57}^{-}+\\sigma_{56}^{-}\\sigma_{57}^{+}) + J_{93,106}(\\sigma_{93}^{+}\\sigma_{106}^{-}+\\sigma_{93}^{-}\\sigma_{106}^{+}) + J_{116,117}(\\sigma_{116}^{+}\\sigma_{117}^{-}+\\sigma_{116}^{-}\\sigma_{117}^{+}) + J_{20,21}(\\sigma_{20}^{+}\\sigma_{21}^{-}+\\sigma_{20}^{-}\\sigma_{21}^{+}) \\\\ & + J_{12,17}(\\sigma_{12}^{+}\\sigma_{17}^{-}+\\sigma_{12}^{-}\\sigma_{17}^{+}) + J_{41,53}(\\sigma_{41}^{+}\\sigma_{53}^{-}+\\sigma_{41}^{-}\\sigma_{53}^{+}) + J_{57,58}(\\sigma_{57}^{+}\\sigma_{58}^{-}+\\sigma_{57}^{-}\\sigma_{58}^{+}) + J_{87,93}(\\sigma_{87}^{+}\\sigma_{93}^{-}+\\sigma_{87}^{-}\\sigma_{93}^{+}) \\\\ & + J_{30,31}(\\sigma_{30}^{+}\\sigma_{31}^{-}+\\sigma_{30}^{-}\\sigma_{31}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) + J_{79,91}(\\sigma_{79}^{+}\\sigma_{91}^{-}+\\sigma_{79}^{-}\\sigma_{91}^{+}) + J_{26,27}(\\sigma_{26}^{+}\\sigma_{27}^{-}+\\sigma_{26}^{-}\\sigma_{27}^{+}) \\\\ & + J_{21,22}(\\sigma_{21}^{+}\\sigma_{22}^{-}+\\sigma_{21}^{-}\\sigma_{22}^{+}) + J_{58,71}(\\sigma_{58}^{+}\\sigma_{71}^{-}+\\sigma_{58}^{-}\\sigma_{71}^{+}) + J_{86,87}(\\sigma_{86}^{+}\\sigma_{87}^{-}+\\sigma_{86}^{-}\\sigma_{87}^{+}) + J_{4,15}(\\sigma_{4}^{+}\\sigma_{15}^{-}+\\sigma_{4}^{-}\\sigma_{15}^{+}) \\\\ & + J_{31,32}(\\sigma_{31}^{+}\\sigma_{32}^{-}+\\sigma_{31}^{-}\\sigma_{32}^{+}) + J_{113,114}(\\sigma_{113}^{+}\\sigma_{114}^{-}+\\sigma_{113}^{-}\\sigma_{114}^{+}) + J_{104,111}(\\sigma_{104}^{+}\\sigma_{111}^{-}+\\sigma_{104}^{-}\\sigma_{111}^{+}) + J_{123,124}(\\sigma_{123}^{+}\\sigma_{124}^{-}+\\sigma_{123}^{-}\\sigma_{124}^{+}) \\\\ & + J_{27,28}(\\sigma_{27}^{+}\\sigma_{28}^{-}+\\sigma_{27}^{-}\\sigma_{28}^{+}) + J_{34,43}(\\sigma_{34}^{+}\\sigma_{43}^{-}+\\sigma_{34}^{-}\\sigma_{43}^{+}) + J_{64,65}(\\sigma_{64}^{+}\\sigma_{65}^{-}+\\sigma_{64}^{-}\\sigma_{65}^{+}) + J_{119,120}(\\sigma_{119}^{+}\\sigma_{120}^{-}+\\sigma_{119}^{-}\\sigma_{120}^{+}) \\\\ & + J_{54,64}(\\sigma_{54}^{+}\\sigma_{64}^{-}+\\sigma_{54}^{-}\\sigma_{64}^{+}) + J_{32,36}(\\sigma_{32}^{+}\\sigma_{36}^{-}+\\sigma_{32}^{-}\\sigma_{36}^{+}) + J_{60,61}(\\sigma_{60}^{+}\\sigma_{61}^{-}+\\sigma_{60}^{-}\\sigma_{61}^{+}) + J_{5,6}(\\sigma_{5}^{+}\\sigma_{6}^{-}+\\sigma_{5}^{-}\\sigma_{6}^{+}) \\\\ & + J_{14,18}(\\sigma_{14}^{+}\\sigma_{18}^{-}+\\sigma_{14}^{-}\\sigma_{18}^{+}) + J_{87,88}(\\sigma_{87}^{+}\\sigma_{88}^{-}+\\sigma_{87}^{-}\\sigma_{88}^{+}) + J_{97,98}(\\sigma_{97}^{+}\\sigma_{98}^{-}+\\sigma_{97}^{-}\\sigma_{98}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) \\\\ & + J_{112,126}(\\sigma_{112}^{+}\\sigma_{126}^{-}+\\sigma_{112}^{-}\\sigma_{126}^{+}) + J_{28,29}(\\sigma_{28}^{+}\\sigma_{29}^{-}+\\sigma_{28}^{-}\\sigma_{29}^{+}) + J_{45,54}(\\sigma_{45}^{+}\\sigma_{54}^{-}+\\sigma_{45}^{-}\\sigma_{54}^{+}) + J_{36,51}(\\sigma_{36}^{+}\\sigma_{51}^{-}+\\sigma_{36}^{-}\\sigma_{51}^{+}) \\\\ & + J_{88,89}(\\sigma_{88}^{+}\\sigma_{89}^{-}+\\sigma_{88}^{-}\\sigma_{89}^{+}) + J_{120,121}(\\sigma_{120}^{+}\\sigma_{121}^{-}+\\sigma_{120}^{-}\\sigma_{121}^{+}) + J_{15,22}(\\sigma_{15}^{+}\\sigma_{22}^{-}+\\sigma_{15}^{-}\\sigma_{22}^{+}) + J_{24,34}(\\sigma_{24}^{+}\\sigma_{34}^{-}+\\sigma_{24}^{-}\\sigma_{34}^{+}) \\\\ & + J_{84,85}(\\sigma_{84}^{+}\\sigma_{85}^{-}+\\sigma_{84}^{-}\\sigma_{85}^{+}) + J_{61,62}(\\sigma_{61}^{+}\\sigma_{62}^{-}+\\sigma_{61}^{-}\\sigma_{62}^{+}) + J_{70,74}(\\sigma_{70}^{+}\\sigma_{74}^{-}+\\sigma_{70}^{-}\\sigma_{74}^{+}) + J_{121,122}(\\sigma_{121}^{+}\\sigma_{122}^{-}+\\sigma_{121}^{-}\\sigma_{122}^{+}) \\\\ & + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{122,123}(\\sigma_{122}^{+}\\sigma_{123}^{-}+\\sigma_{122}^{-}\\sigma_{123}^{+}) + J_{117,118}(\\sigma_{117}^{+}\\sigma_{118}^{-}+\\sigma_{117}^{-}\\sigma_{118}^{+}) + J_{62,63}(\\sigma_{62}^{+}\\sigma_{63}^{-}+\\sigma_{62}^{-}\\sigma_{63}^{+}) \\\\ & + J_{109,114}(\\sigma_{109}^{+}\\sigma_{114}^{-}+\\sigma_{109}^{-}\\sigma_{114}^{+}) + J_{94,95}(\\sigma_{94}^{+}\\sigma_{95}^{-}+\\sigma_{94}^{-}\\sigma_{95}^{+}) + J_{37,52}(\\sigma_{37}^{+}\\sigma_{52}^{-}+\\sigma_{37}^{-}\\sigma_{52}^{+}) + J_{3,4}(\\sigma_{3}^{+}\\sigma_{4}^{-}+\\sigma_{3}^{-}\\sigma_{4}^{+}) \\\\ & + J_{58,59}(\\sigma_{58}^{+}\\sigma_{59}^{-}+\\sigma_{58}^{-}\\sigma_{59}^{+}) + J_{33,39}(\\sigma_{33}^{+}\\sigma_{39}^{-}+\\sigma_{33}^{-}\\sigma_{39}^{+}) + J_{95,96}(\\sigma_{95}^{+}\\sigma_{96}^{-}+\\sigma_{95}^{-}\\sigma_{96}^{+}) + J_{68,69}(\\sigma_{68}^{+}\\sigma_{69}^{-}+\\sigma_{68}^{-}\\sigma_{69}^{+}) \\\\ & + J_{63,64}(\\sigma_{63}^{+}\\sigma_{64}^{-}+\\sigma_{63}^{-}\\sigma_{64}^{+}) + J_{71,77}(\\sigma_{71}^{+}\\sigma_{77}^{-}+\\sigma_{71}^{-}\\sigma_{77}^{+}) + J_{111,122}(\\sigma_{111}^{+}\\sigma_{122}^{-}+\\sigma_{111}^{-}\\sigma_{122}^{+}) + J_{4,5}(\\sigma_{4}^{+}\\sigma_{5}^{-}+\\sigma_{4}^{-}\\sigma_{5}^{+}) \\\\ & + J_{59,60}(\\sigma_{59}^{+}\\sigma_{60}^{-}+\\sigma_{59}^{-}\\sigma_{60}^{+}) + J_{96,109}(\\sigma_{96}^{+}\\sigma_{109}^{-}+\\sigma_{96}^{-}\\sigma_{109}^{+}) + J_{69,70}(\\sigma_{69}^{+}\\sigma_{70}^{-}+\\sigma_{69}^{-}\\sigma_{70}^{+}) + J_{124,125}(\\sigma_{124}^{+}\\sigma_{125}^{-}+\\sigma_{124}^{-}\\sigma_{125}^{+}) \\\\ & + J_{35,47}(\\sigma_{35}^{+}\\sigma_{47}^{-}+\\sigma_{35}^{-}\\sigma_{47}^{+}) + J_{101,102}(\\sigma_{101}^{+}\\sigma_{102}^{-}+\\sigma_{101}^{-}\\sigma_{102}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) + J_{65,66}(\\sigma_{65}^{+}\\sigma_{66}^{-}+\\sigma_{65}^{-}\\sigma_{66}^{+}) \\\\ & + J_{10,11}(\\sigma_{10}^{+}\\sigma_{11}^{-}+\\sigma_{10}^{-}\\sigma_{11}^{+}) + J_{37,38}(\\sigma_{37}^{+}\\sigma_{38}^{-}+\\sigma_{37}^{-}\\sigma_{38}^{+}) + J_{28,35}(\\sigma_{28}^{+}\\sigma_{35}^{-}+\\sigma_{28}^{-}\\sigma_{35}^{+}) + J_{102,103}(\\sigma_{102}^{+}\\sigma_{103}^{-}+\\sigma_{102}^{-}\\sigma_{103}^{+}) \\\\ & + J_{92,102}(\\sigma_{92}^{+}\\sigma_{102}^{-}+\\sigma_{92}^{-}\\sigma_{102}^{+}) + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{98,99}(\\sigma_{98}^{+}\\sigma_{99}^{-}+\\sigma_{98}^{-}\\sigma_{99}^{+}) + J_{43,44}(\\sigma_{43}^{+}\\sigma_{44}^{-}+\\sigma_{43}^{-}\\sigma_{44}^{+}) \\\\ & + J_{52,56}(\\sigma_{52}^{+}\\sigma_{56}^{-}+\\sigma_{52}^{-}\\sigma_{56}^{+}) + J_{125,126}(\\sigma_{125}^{+}\\sigma_{126}^{-}+\\sigma_{125}^{-}\\sigma_{126}^{+}) + J_{39,40}(\\sigma_{39}^{+}\\sigma_{40}^{-}+\\sigma_{39}^{-}\\sigma_{40}^{+}) + J_{8,16}(\\sigma_{8}^{+}\\sigma_{16}^{-}+\\sigma_{8}^{-}\\sigma_{16}^{+}) \\\\ & + J_{11,12}(\\sigma_{11}^{+}\\sigma_{12}^{-}+\\sigma_{11}^{-}\\sigma_{12}^{+}) + J_{66,67}(\\sigma_{66}^{+}\\sigma_{67}^{-}+\\sigma_{66}^{-}\\sigma_{67}^{+}) + J_{76,77}(\\sigma_{76}^{+}\\sigma_{77}^{-}+\\sigma_{76}^{-}\\sigma_{77}^{+}) + J_{83,92}(\\sigma_{83}^{+}\\sigma_{92}^{-}+\\sigma_{83}^{-}\\sigma_{92}^{+}) \\\\ & + J_{74,89}(\\sigma_{74}^{+}\\sigma_{89}^{-}+\\sigma_{74}^{-}\\sigma_{89}^{+}) + J_{7,8}(\\sigma_{7}^{+}\\sigma_{8}^{-}+\\sigma_{7}^{-}\\sigma_{8}^{+}) + J_{53,60}(\\sigma_{53}^{+}\\sigma_{60}^{-}+\\sigma_{53}^{-}\\sigma_{60}^{+}) \\\\ & + \\Omega_{d,0}(U_{0}^{(0,1)}(t)+U_{1}^{(0,14)}(t))\\sigma_{0}^{X} + \\Omega_{d,1}(U_{2}^{(1,2)}(t))\\sigma_{1}^{X} \\\\ & + \\Omega_{d,2}(U_{3}^{(2,3)}(t))\\sigma_{2}^{X} + \\Omega_{d,4}(U_{5}^{(4,5)}(t)+U_{6}^{(4,15)}(t)+U_{4}^{(4,3)}(t))\\sigma_{4}^{X} \\\\ & + \\Omega_{d,6}(U_{8}^{(6,7)}(t)+U_{7}^{(6,5)}(t))\\sigma_{6}^{X} + \\Omega_{d,7}(U_{9}^{(7,8)}(t))\\sigma_{7}^{X} \\\\ & + \\Omega_{d,8}(U_{10}^{(8,9)}(t))\\sigma_{8}^{X} + \\Omega_{d,10}(U_{11}^{(10,9)}(t))\\sigma_{10}^{X} \\\\ & + \\Omega_{d,11}(U_{12}^{(11,10)}(t)+U_{13}^{(11,12)}(t))\\sigma_{11}^{X} + \\Omega_{d,13}(U_{14}^{(13,12)}(t))\\sigma_{13}^{X} \\\\ & + \\Omega_{d,15}(U_{15}^{(15,22)}(t))\\sigma_{15}^{X} + \\Omega_{d,16}(U_{16}^{(16,8)}(t))\\sigma_{16}^{X} \\\\ & + \\Omega_{d,17}(U_{17}^{(17,12)}(t)+U_{18}^{(17,30)}(t))\\sigma_{17}^{X} + \\Omega_{d,18}(U_{19}^{(18,14)}(t)+U_{20}^{(18,19)}(t))\\sigma_{18}^{X} \\\\ & + \\Omega_{d,19}(U_{21}^{(19,20)}(t))\\sigma_{19}^{X} + \\Omega_{d,21}(U_{22}^{(21,20)}(t))\\sigma_{21}^{X} \\\\ & + \\Omega_{d,22}(U_{23}^{(22,21)}(t)+U_{24}^{(22,23)}(t))\\sigma_{22}^{X} + \\Omega_{d,23}(U_{25}^{(23,24)}(t))\\sigma_{23}^{X} \\\\ & + \\Omega_{d,24}(U_{26}^{(24,25)}(t))\\sigma_{24}^{X} + \\Omega_{d,25}(U_{27}^{(25,26)}(t))\\sigma_{25}^{X} \\\\ & + \\Omega_{d,26}(U_{28}^{(26,16)}(t))\\sigma_{26}^{X} + \\Omega_{d,27}(U_{29}^{(27,26)}(t))\\sigma_{27}^{X} \\\\ & + \\Omega_{d,28}(U_{30}^{(28,27)}(t))\\sigma_{28}^{X} + \\Omega_{d,29}(U_{31}^{(29,28)}(t))\\sigma_{29}^{X} \\\\ & + \\Omega_{d,31}(U_{32}^{(31,30)}(t))\\sigma_{31}^{X} + \\Omega_{d,32}(U_{33}^{(32,31)}(t))\\sigma_{32}^{X} \\\\ & + \\Omega_{d,33}(U_{34}^{(33,20)}(t))\\sigma_{33}^{X} + \\Omega_{d,34}(U_{35}^{(34,24)}(t))\\sigma_{34}^{X} \\\\ & + \\Omega_{d,35}(U_{36}^{(35,28)}(t)+U_{37}^{(35,47)}(t))\\sigma_{35}^{X} + \\Omega_{d,36}(U_{38}^{(36,32)}(t))\\sigma_{36}^{X} \\\\ & + \\Omega_{d,38}(U_{40}^{(38,39)}(t)+U_{39}^{(38,37)}(t))\\sigma_{38}^{X} + \\Omega_{d,39}(U_{42}^{(39,40)}(t)+U_{41}^{(39,33)}(t))\\sigma_{39}^{X} \\\\ & + \\Omega_{d,41}(U_{44}^{(41,42)}(t)+U_{43}^{(41,40)}(t))\\sigma_{41}^{X} + \\Omega_{d,43}(U_{46}^{(43,42)}(t)+U_{45}^{(43,34)}(t))\\sigma_{43}^{X} \\\\ & + \\Omega_{d,44}(U_{48}^{(44,45)}(t)+U_{47}^{(44,43)}(t))\\sigma_{44}^{X} + \\Omega_{d,46}(U_{49}^{(46,45)}(t))\\sigma_{46}^{X} \\\\ & + \\Omega_{d,47}(U_{50}^{(47,46)}(t))\\sigma_{47}^{X} + \\Omega_{d,48}(U_{52}^{(48,49)}(t)+U_{51}^{(48,47)}(t))\\sigma_{48}^{X} \\\\ & + \\Omega_{d,49}(U_{53}^{(49,50)}(t))\\sigma_{49}^{X} + \\Omega_{d,51}(U_{54}^{(51,36)}(t)+U_{55}^{(51,50)}(t))\\sigma_{51}^{X} \\\\ & + \\Omega_{d,52}(U_{56}^{(52,37)}(t))\\sigma_{52}^{X} + \\Omega_{d,53}(U_{57}^{(53,41)}(t)+U_{58}^{(53,60)}(t))\\sigma_{53}^{X} \\\\ & + \\Omega_{d,54}(U_{59}^{(54,45)}(t))\\sigma_{54}^{X} + \\Omega_{d,55}(U_{60}^{(55,49)}(t))\\sigma_{55}^{X} \\\\ & + \\Omega_{d,56}(U_{61}^{(56,52)}(t)+U_{62}^{(56,57)}(t))\\sigma_{56}^{X} + \\Omega_{d,57}(U_{63}^{(57,58)}(t))\\sigma_{57}^{X} \\\\ & + \\Omega_{d,58}(U_{64}^{(58,71)}(t))\\sigma_{58}^{X} + \\Omega_{d,59}(U_{65}^{(59,58)}(t)+U_{66}^{(59,60)}(t))\\sigma_{59}^{X} \\\\ & + \\Omega_{d,60}(U_{67}^{(60,61)}(t))\\sigma_{60}^{X} + \\Omega_{d,61}(U_{68}^{(61,62)}(t))\\sigma_{61}^{X} \\\\ & + \\Omega_{d,63}(U_{70}^{(63,64)}(t)+U_{69}^{(63,62)}(t))\\sigma_{63}^{X} + \\Omega_{d,64}(U_{71}^{(64,54)}(t)+U_{72}^{(64,65)}(t))\\sigma_{64}^{X} \\\\ & + \\Omega_{d,65}(U_{73}^{(65,66)}(t))\\sigma_{65}^{X} + \\Omega_{d,66}(U_{75}^{(66,73)}(t)+U_{74}^{(66,67)}(t))\\sigma_{66}^{X} \\\\ & + \\Omega_{d,67}(U_{76}^{(67,68)}(t))\\sigma_{67}^{X} + \\Omega_{d,68}(U_{77}^{(68,55)}(t))\\sigma_{68}^{X} \\\\ & + \\Omega_{d,69}(U_{79}^{(69,70)}(t)+U_{78}^{(69,68)}(t))\\sigma_{69}^{X} + \\Omega_{d,71}(U_{80}^{(71,77)}(t))\\sigma_{71}^{X} \\\\ & + \\Omega_{d,72}(U_{81}^{(72,62)}(t))\\sigma_{72}^{X} + \\Omega_{d,74}(U_{83}^{(74,89)}(t)+U_{82}^{(74,70)}(t))\\sigma_{74}^{X} \\\\ & + \\Omega_{d,75}(U_{84}^{(75,76)}(t))\\sigma_{75}^{X} + \\Omega_{d,77}(U_{85}^{(77,76)}(t))\\sigma_{77}^{X} \\\\ & + \\Omega_{d,78}(U_{86}^{(78,77)}(t)+U_{87}^{(78,79)}(t))\\sigma_{78}^{X} + \\Omega_{d,79}(U_{88}^{(79,91)}(t))\\sigma_{79}^{X} \\\\ & + \\Omega_{d,80}(U_{90}^{(80,81)}(t)+U_{89}^{(80,79)}(t))\\sigma_{80}^{X} + \\Omega_{d,81}(U_{91}^{(81,72)}(t))\\sigma_{81}^{X} \\\\ & + \\Omega_{d,82}(U_{92}^{(82,81)}(t))\\sigma_{82}^{X} + \\Omega_{d,83}(U_{93}^{(83,82)}(t))\\sigma_{83}^{X} \\\\ & + \\Omega_{d,84}(U_{94}^{(84,83)}(t)+U_{95}^{(84,85)}(t))\\sigma_{84}^{X} + \\Omega_{d,85}(U_{96}^{(85,73)}(t))\\sigma_{85}^{X} \\\\ & + \\Omega_{d,86}(U_{98}^{(86,87)}(t)+U_{97}^{(86,85)}(t))\\sigma_{86}^{X} + \\Omega_{d,87}(U_{99}^{(87,93)}(t))\\sigma_{87}^{X} \\\\ & + \\Omega_{d,88}(U_{100}^{(88,87)}(t)+U_{101}^{(88,89)}(t))\\sigma_{88}^{X} + \\Omega_{d,90}(U_{103}^{(90,94)}(t)+U_{102}^{(90,75)}(t))\\sigma_{90}^{X} \\\\ & + \\Omega_{d,92}(U_{105}^{(92,102)}(t)+U_{104}^{(92,83)}(t))\\sigma_{92}^{X} + \\Omega_{d,95}(U_{107}^{(95,96)}(t)+U_{106}^{(95,94)}(t))\\sigma_{95}^{X} \\\\ & + \\Omega_{d,96}(U_{108}^{(96,109)}(t))\\sigma_{96}^{X} + \\Omega_{d,97}(U_{109}^{(97,96)}(t)+U_{110}^{(97,98)}(t))\\sigma_{97}^{X} \\\\ & + \\Omega_{d,98}(U_{112}^{(98,99)}(t)+U_{111}^{(98,91)}(t))\\sigma_{98}^{X} + \\Omega_{d,100}(U_{113}^{(100,99)}(t)+U_{114}^{(100,101)}(t))\\sigma_{100}^{X} \\\\ & + \\Omega_{d,101}(U_{115}^{(101,102)}(t))\\sigma_{101}^{X} + \\Omega_{d,102}(U_{116}^{(102,103)}(t))\\sigma_{102}^{X} \\\\ & + \\Omega_{d,104}(U_{117}^{(104,103)}(t)+U_{119}^{(104,111)}(t)+U_{118}^{(104,105)}(t))\\sigma_{104}^{X} + \\Omega_{d,106}(U_{121}^{(106,105)}(t)+U_{120}^{(106,93)}(t)+U_{122}^{(106,107)}(t))\\sigma_{106}^{X} \\\\ & + \\Omega_{d,107}(U_{123}^{(107,108)}(t))\\sigma_{107}^{X} + \\Omega_{d,108}(U_{124}^{(108,112)}(t))\\sigma_{108}^{X} \\\\ & + \\Omega_{d,110}(U_{125}^{(110,100)}(t))\\sigma_{110}^{X} + \\Omega_{d,112}(U_{126}^{(112,126)}(t))\\sigma_{112}^{X} \\\\ & + \\Omega_{d,114}(U_{128}^{(114,113)}(t)+U_{129}^{(114,115)}(t)+U_{127}^{(114,109)}(t))\\sigma_{114}^{X} + \\Omega_{d,116}(U_{130}^{(116,115)}(t)+U_{131}^{(116,117)}(t))\\sigma_{116}^{X} \\\\ & + \\Omega_{d,118}(U_{132}^{(118,110)}(t)+U_{133}^{(118,117)}(t))\\sigma_{118}^{X} + \\Omega_{d,119}(U_{134}^{(119,118)}(t)+U_{135}^{(119,120)}(t))\\sigma_{119}^{X} \\\\ & + \\Omega_{d,120}(U_{136}^{(120,121)}(t))\\sigma_{120}^{X} + \\Omega_{d,121}(U_{137}^{(121,122)}(t))\\sigma_{121}^{X} \\\\ & + \\Omega_{d,122}(U_{138}^{(122,111)}(t)+U_{139}^{(122,123)}(t))\\sigma_{122}^{X} + \\Omega_{d,123}(U_{140}^{(123,124)}(t))\\sigma_{123}^{X} \\\\ & + \\Omega_{d,124}(U_{141}^{(124,125)}(t))\\sigma_{124}^{X} + \\Omega_{d,126}(U_{142}^{(126,125)}(t))\\sigma_{126}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,126,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,126,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,126,-delta{i}/2*O{i}]", "_SUM[i,0,126,omegad{i}*X{i}||D{i}]", "jq62q72*Sp62*Sm72", "jq62q72*Sm62*Sp72", "jq67q68*Sp67*Sm68", "jq67q68*Sm67*Sp68", "jq44q45*Sp44*Sm45", "jq44q45*Sm44*Sp45", "jq99q100*Sp99*Sm100", "jq99q100*Sm99*Sp100", "jq108q112*Sp108*Sm112", "jq108q112*Sm108*Sp112", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq40q41*Sp40*Sm41", "jq40q41*Sm40*Sp41", "jq0q14*Sp0*Sm14", "jq0q14*Sm0*Sp14", "jq17q30*Sp17*Sm30", "jq17q30*Sm17*Sp30", "jq100q101*Sp100*Sm101", "jq100q101*Sm100*Sp101", "jq91q98*Sp91*Sm98", "jq91q98*Sm91*Sp98", "jq100q110*Sp100*Sm110", "jq100q110*Sm100*Sp110", "jq75q90*Sp75*Sm90", "jq75q90*Sm75*Sp90", "jq41q42*Sp41*Sm42", "jq41q42*Sm41*Sp42", "jq96q97*Sp96*Sm97", "jq96q97*Sm96*Sp97", "jq18q19*Sp18*Sm19", "jq18q19*Sm18*Sp19", "jq55q68*Sp55*Sm68", "jq55q68*Sm55*Sp68", "jq9q10*Sp9*Sm10", "jq9q10*Sm9*Sp10", "jq49q55*Sp49*Sm55", "jq49q55*Sm49*Sp55", "jq106q107*Sp106*Sm107", "jq106q107*Sm106*Sp107", "jq47q48*Sp47*Sm48", "jq47q48*Sm47*Sp48", "jq42q43*Sp42*Sm43", "jq42q43*Sm42*Sp43", "jq107q108*Sp107*Sm108", "jq107q108*Sm107*Sp108", "jq73q85*Sp73*Sm85", "jq73q85*Sm73*Sp85", "jq38q39*Sp38*Sm39", "jq38q39*Sm38*Sp39", "jq20q33*Sp20*Sm33", "jq20q33*Sm20*Sp33", "jq48q49*Sp48*Sm49", "jq48q49*Sm48*Sp49", "jq103q104*Sp103*Sm104", "jq103q104*Sm103*Sp104", "jq80q81*Sp80*Sm81", "jq80q81*Sm80*Sp81", "jq75q76*Sp75*Sm76", "jq75q76*Sm75*Sp76", "jq66q73*Sp66*Sm73", "jq66q73*Sm66*Sp73", "jq85q86*Sp85*Sm86", "jq85q86*Sm85*Sp86", "jq81q82*Sp81*Sm82", "jq81q82*Sm81*Sp82", "jq110q118*Sp110*Sm118", "jq110q118*Sm110*Sp118", "jq16q26*Sp16*Sm26", "jq16q26*Sm16*Sp26", "jq90q94*Sp90*Sm94", "jq90q94*Sm90*Sp94", "jq118q119*Sp118*Sm119", "jq118q119*Sm118*Sp119", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq77q78*Sp77*Sm78", "jq77q78*Sm77*Sp78", "jq22q23*Sp22*Sm23", "jq22q23*Sm22*Sp23", "jq49q50*Sp49*Sm50", "jq49q50*Sm49*Sp50", "jq104q105*Sp104*Sm105", "jq104q105*Sm104*Sp105", "jq114q115*Sp114*Sm115", "jq114q115*Sm114*Sp115", "jq45q46*Sp45*Sm46", "jq45q46*Sm45*Sp46", "jq50q51*Sp50*Sm51", "jq50q51*Sm50*Sp51", "jq105q106*Sp105*Sm106", "jq105q106*Sm105*Sp106", "jq72q81*Sp72*Sm81", "jq72q81*Sm72*Sp81", "jq82q83*Sp82*Sm83", "jq82q83*Sm82*Sp83", "jq46q47*Sp46*Sm47", "jq46q47*Sm46*Sp47", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq78q79*Sp78*Sm79", "jq78q79*Sm78*Sp79", "jq83q84*Sp83*Sm84", "jq83q84*Sm83*Sp84", "jq115q116*Sp115*Sm116", "jq115q116*Sm115*Sp116", "jq19q20*Sp19*Sm20", "jq19q20*Sm19*Sp20", "jq24q25*Sp24*Sm25", "jq24q25*Sm24*Sp25", "jq79q80*Sp79*Sm80", "jq79q80*Sm79*Sp80", "jq56q57*Sp56*Sm57", "jq56q57*Sm56*Sp57", "jq93q106*Sp93*Sm106", "jq93q106*Sm93*Sp106", "jq116q117*Sp116*Sm117", "jq116q117*Sm116*Sp117", "jq20q21*Sp20*Sm21", "jq20q21*Sm20*Sp21", "jq12q17*Sp12*Sm17", "jq12q17*Sm12*Sp17", "jq41q53*Sp41*Sm53", "jq41q53*Sm41*Sp53", "jq57q58*Sp57*Sm58", "jq57q58*Sm57*Sp58", "jq87q93*Sp87*Sm93", "jq87q93*Sm87*Sp93", "jq30q31*Sp30*Sm31", "jq30q31*Sm30*Sp31", "jq25q26*Sp25*Sm26", "jq25q26*Sm25*Sp26", "jq79q91*Sp79*Sm91", "jq79q91*Sm79*Sp91", "jq26q27*Sp26*Sm27", "jq26q27*Sm26*Sp27", "jq21q22*Sp21*Sm22", "jq21q22*Sm21*Sp22", "jq58q71*Sp58*Sm71", "jq58q71*Sm58*Sp71", "jq86q87*Sp86*Sm87", "jq86q87*Sm86*Sp87", "jq4q15*Sp4*Sm15", "jq4q15*Sm4*Sp15", "jq31q32*Sp31*Sm32", "jq31q32*Sm31*Sp32", "jq113q114*Sp113*Sm114", "jq113q114*Sm113*Sp114", "jq104q111*Sp104*Sm111", "jq104q111*Sm104*Sp111", "jq123q124*Sp123*Sm124", "jq123q124*Sm123*Sp124", "jq27q28*Sp27*Sm28", "jq27q28*Sm27*Sp28", "jq34q43*Sp34*Sm43", "jq34q43*Sm34*Sp43", "jq64q65*Sp64*Sm65", "jq64q65*Sm64*Sp65", "jq119q120*Sp119*Sm120", "jq119q120*Sm119*Sp120", "jq54q64*Sp54*Sm64", "jq54q64*Sm54*Sp64", "jq32q36*Sp32*Sm36", "jq32q36*Sm32*Sp36", "jq60q61*Sp60*Sm61", "jq60q61*Sm60*Sp61", "jq5q6*Sp5*Sm6", "jq5q6*Sm5*Sp6", "jq14q18*Sp14*Sm18", "jq14q18*Sm14*Sp18", "jq87q88*Sp87*Sm88", "jq87q88*Sm87*Sp88", "jq97q98*Sp97*Sm98", "jq97q98*Sm97*Sp98", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq112q126*Sp112*Sm126", "jq112q126*Sm112*Sp126", "jq28q29*Sp28*Sm29", "jq28q29*Sm28*Sp29", "jq45q54*Sp45*Sm54", "jq45q54*Sm45*Sp54", "jq36q51*Sp36*Sm51", "jq36q51*Sm36*Sp51", "jq88q89*Sp88*Sm89", "jq88q89*Sm88*Sp89", "jq120q121*Sp120*Sm121", "jq120q121*Sm120*Sp121", "jq15q22*Sp15*Sm22", "jq15q22*Sm15*Sp22", "jq24q34*Sp24*Sm34", "jq24q34*Sm24*Sp34", "jq84q85*Sp84*Sm85", "jq84q85*Sm84*Sp85", "jq61q62*Sp61*Sm62", "jq61q62*Sm61*Sp62", "jq70q74*Sp70*Sm74", "jq70q74*Sm70*Sp74", "jq121q122*Sp121*Sm122", "jq121q122*Sm121*Sp122", "jq2q3*Sp2*Sm3", "jq2q3*Sm2*Sp3", "jq122q123*Sp122*Sm123", "jq122q123*Sm122*Sp123", "jq117q118*Sp117*Sm118", "jq117q118*Sm117*Sp118", "jq62q63*Sp62*Sm63", "jq62q63*Sm62*Sp63", "jq109q114*Sp109*Sm114", "jq109q114*Sm109*Sp114", "jq94q95*Sp94*Sm95", "jq94q95*Sm94*Sp95", "jq37q52*Sp37*Sm52", "jq37q52*Sm37*Sp52", "jq3q4*Sp3*Sm4", "jq3q4*Sm3*Sp4", "jq58q59*Sp58*Sm59", "jq58q59*Sm58*Sp59", "jq33q39*Sp33*Sm39", "jq33q39*Sm33*Sp39", "jq95q96*Sp95*Sm96", "jq95q96*Sm95*Sp96", "jq68q69*Sp68*Sm69", "jq68q69*Sm68*Sp69", "jq63q64*Sp63*Sm64", "jq63q64*Sm63*Sp64", "jq71q77*Sp71*Sm77", "jq71q77*Sm71*Sp77", "jq111q122*Sp111*Sm122", "jq111q122*Sm111*Sp122", "jq4q5*Sp4*Sm5", "jq4q5*Sm4*Sp5", "jq59q60*Sp59*Sm60", "jq59q60*Sm59*Sp60", "jq96q109*Sp96*Sm109", "jq96q109*Sm96*Sp109", "jq69q70*Sp69*Sm70", "jq69q70*Sm69*Sp70", "jq124q125*Sp124*Sm125", "jq124q125*Sm124*Sp125", "jq35q47*Sp35*Sm47", "jq35q47*Sm35*Sp47", "jq101q102*Sp101*Sm102", "jq101q102*Sm101*Sp102", "jq0q1*Sp0*Sm1", "jq0q1*Sm0*Sp1", "jq65q66*Sp65*Sm66", "jq65q66*Sm65*Sp66", "jq10q11*Sp10*Sm11", "jq10q11*Sm10*Sp11", "jq37q38*Sp37*Sm38", "jq37q38*Sm37*Sp38", "jq28q35*Sp28*Sm35", "jq28q35*Sm28*Sp35", "jq102q103*Sp102*Sm103", "jq102q103*Sm102*Sp103", "jq92q102*Sp92*Sm102", "jq92q102*Sm92*Sp102", "jq6q7*Sp6*Sm7", "jq6q7*Sm6*Sp7", "jq98q99*Sp98*Sm99", "jq98q99*Sm98*Sp99", "jq43q44*Sp43*Sm44", "jq43q44*Sm43*Sp44", "jq52q56*Sp52*Sm56", "jq52q56*Sm52*Sp56", "jq125q126*Sp125*Sm126", "jq125q126*Sm125*Sp126", "jq39q40*Sp39*Sm40", "jq39q40*Sm39*Sp40", "jq8q16*Sp8*Sm16", "jq8q16*Sm8*Sp16", "jq11q12*Sp11*Sm12", "jq11q12*Sm11*Sp12", "jq66q67*Sp66*Sm67", "jq66q67*Sm66*Sp67", "jq76q77*Sp76*Sm77", "jq76q77*Sm76*Sp77", "jq83q92*Sp83*Sm92", "jq83q92*Sm83*Sp92", "jq74q89*Sp74*Sm89", "jq74q89*Sm74*Sp89", "jq7q8*Sp7*Sm8", "jq7q8*Sm7*Sp8", "jq53q60*Sp53*Sm60", "jq53q60*Sm53*Sp60", "omegad1*X0||U0", "omegad14*X0||U1", "omegad2*X1||U2", "omegad3*X2||U3", "omegad5*X4||U5", "omegad15*X4||U6", "omegad3*X4||U4", "omegad7*X6||U8", "omegad5*X6||U7", "omegad8*X7||U9", "omegad9*X8||U10", "omegad9*X10||U11", "omegad10*X11||U12", "omegad12*X11||U13", "omegad12*X13||U14", "omegad22*X15||U15", "omegad8*X16||U16", "omegad12*X17||U17", "omegad30*X17||U18", "omegad14*X18||U19", "omegad19*X18||U20", "omegad20*X19||U21", "omegad20*X21||U22", "omegad21*X22||U23", "omegad23*X22||U24", "omegad24*X23||U25", "omegad25*X24||U26", "omegad26*X25||U27", "omegad16*X26||U28", "omegad26*X27||U29", "omegad27*X28||U30", "omegad28*X29||U31", "omegad30*X31||U32", "omegad31*X32||U33", "omegad20*X33||U34", "omegad24*X34||U35", "omegad28*X35||U36", "omegad47*X35||U37", "omegad32*X36||U38", "omegad39*X38||U40", "omegad37*X38||U39", "omegad40*X39||U42", "omegad33*X39||U41", "omegad42*X41||U44", "omegad40*X41||U43", "omegad42*X43||U46", "omegad34*X43||U45", "omegad45*X44||U48", "omegad43*X44||U47", "omegad45*X46||U49", "omegad46*X47||U50", "omegad49*X48||U52", "omegad47*X48||U51", "omegad50*X49||U53", "omegad36*X51||U54", "omegad50*X51||U55", "omegad37*X52||U56", "omegad41*X53||U57", "omegad60*X53||U58", "omegad45*X54||U59", "omegad49*X55||U60", "omegad52*X56||U61", "omegad57*X56||U62", "omegad58*X57||U63", "omegad71*X58||U64", "omegad58*X59||U65", "omegad60*X59||U66", "omegad61*X60||U67", "omegad62*X61||U68", "omegad64*X63||U70", "omegad62*X63||U69", "omegad54*X64||U71", "omegad65*X64||U72", "omegad66*X65||U73", "omegad73*X66||U75", "omegad67*X66||U74", "omegad68*X67||U76", "omegad55*X68||U77", "omegad70*X69||U79", "omegad68*X69||U78", "omegad77*X71||U80", "omegad62*X72||U81", "omegad89*X74||U83", "omegad70*X74||U82", "omegad76*X75||U84", "omegad76*X77||U85", "omegad77*X78||U86", "omegad79*X78||U87", "omegad91*X79||U88", "omegad81*X80||U90", "omegad79*X80||U89", "omegad72*X81||U91", "omegad81*X82||U92", "omegad82*X83||U93", "omegad83*X84||U94", "omegad85*X84||U95", "omegad73*X85||U96", "omegad87*X86||U98", "omegad85*X86||U97", "omegad93*X87||U99", "omegad87*X88||U100", "omegad89*X88||U101", "omegad94*X90||U103", "omegad75*X90||U102", "omegad102*X92||U105", "omegad83*X92||U104", "omegad96*X95||U107", "omegad94*X95||U106", "omegad109*X96||U108", "omegad96*X97||U109", "omegad98*X97||U110", "omegad99*X98||U112", "omegad91*X98||U111", "omegad99*X100||U113", "omegad101*X100||U114", "omegad102*X101||U115", "omegad103*X102||U116", "omegad103*X104||U117", "omegad111*X104||U119", "omegad105*X104||U118", "omegad105*X106||U121", "omegad93*X106||U120", "omegad107*X106||U122", "omegad108*X107||U123", "omegad112*X108||U124", "omegad100*X110||U125", "omegad126*X112||U126", "omegad113*X114||U128", "omegad115*X114||U129", "omegad109*X114||U127", "omegad115*X116||U130", "omegad117*X116||U131", "omegad110*X118||U132", "omegad117*X118||U133", "omegad118*X119||U134", "omegad120*X119||U135", "omegad121*X120||U136", "omegad122*X121||U137", "omegad111*X122||U138", "omegad123*X122||U139", "omegad124*X123||U140", "omegad125*X124||U141", "omegad125*X126||U142"], "osc": {}, "qub": {"0": 3, "1": 3, "2": 3, "3": 3, "4": 3, "5": 3, "6": 3, "7": 3, "8": 3, "9": 3, "10": 3, "11": 3, "12": 3, "13": 3, "14": 3, "15": 3, "16": 3, "17": 3, "18": 3, "19": 3, "20": 3, "21": 3, "22": 3, "23": 3, "24": 3, "25": 3, "26": 3, "27": 3, "28": 3, "29": 3, "30": 3, "31": 3, "32": 3, "33": 3, "34": 3, "35": 3, "36": 3, "37": 3, "38": 3, "39": 3, "40": 3, "41": 3, "42": 3, "43": 3, "44": 3, "45": 3, "46": 3, "47": 3, "48": 3, "49": 3, "50": 3, "51": 3, "52": 3, "53": 3, "54": 3, "55": 3, "56": 3, "57": 3, "58": 3, "59": 3, "60": 3, "61": 3, "62": 3, "63": 3, "64": 3, "65": 3, "66": 3, "67": 3, "68": 3, "69": 3, "70": 3, "71": 3, "72": 3, "73": 3, "74": 3, "75": 3, "76": 3, "77": 3, "78": 3, "79": 3, "80": 3, "81": 3, "82": 3, "83": 3, "84": 3, "85": 3, "86": 3, "87": 3, "88": 3, "89": 3, "90": 3, "91": 3, "92": 3, "93": 3, "94": 3, "95": 3, "96": 3, "97": 3, "98": 3, "99": 3, "100": 3, "101": 3, "102": 3, "103": 3, "104": 3, "105": 3, "106": 3, "107": 3, "108": 3, "109": 3, "110": 3, "111": 3, "112": 3, "113": 3, "114": 3, "115": 3, "116": 3, "117": 3, "118": 3, "119": 3, "120": 3, "121": 3, "122": 3, 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117, 118, 119, 120, 121, 122, 123, 124, 125, 126]}]}, {"name": "measure", "qubits": [25], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m25", "label": "M_m25", "pulse_shape": "gaussian_square", "parameters": {"amp": [0.16071757708873166, -0.1013403197879679], "duration": 3840, "sigma": 64, "width": 3584}}, {"name": "acquire", "t0": 0, "duration": 3840, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 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125, 126]}]}, {"name": "measure", "qubits": [40], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m40", "label": "M_m40", "pulse_shape": "gaussian_square", "parameters": {"amp": [-0.4387708943823796, 0.33163248068138124], "duration": 3840, "sigma": 64, "width": 3584}}, {"name": "acquire", "t0": 0, "duration": 3840, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 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125, 126]}]}, {"name": "measure", "qubits": [45], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m45", "label": "M_m45", "pulse_shape": "gaussian_square", "parameters": {"amp": [-0.22971459535038322, 0.22278062007950714], "duration": 3840, "sigma": 64, "width": 3584}}, {"name": "acquire", "t0": 0, "duration": 3840, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]}]}, {"name": "measure", "qubits": [46], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m46", "label": "M_m46", "pulse_shape": "gaussian_square", "parameters": {"amp": [-0.16149611640267547, 0.22873347893750384], "duration": 3840, "sigma": 64, "width": 3584}}, {"name": "acquire", "t0": 0, "duration": 3840, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 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110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]}]}, {"name": "measure", "qubits": [108], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m108", "label": "M_m108", "pulse_shape": "gaussian_square", "parameters": {"amp": [0.15175207875344873, -0.05070805255585247], "duration": 3840, "sigma": 64, "width": 3584}}, {"name": "acquire", "t0": 0, "duration": 3840, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 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110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]}]}, {"name": "measure", "qubits": [113], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m113", "label": "M_m113", "pulse_shape": "gaussian_square", "parameters": {"amp": [-0.17218131768815725, 0.10175261096979218], "duration": 3840, "sigma": 64, "width": 3584}}, {"name": "acquire", "t0": 0, "duration": 3840, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 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110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]}]}, {"name": "measure", "qubits": [123], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m123", "label": "M_m123", "pulse_shape": "gaussian_square", "parameters": {"amp": [0.08615178268702867, 0.3081847990083985], "duration": 3840, "sigma": 64, "width": 3584}}, {"name": "acquire", "t0": 0, "duration": 3840, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 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"t0": 0, "ch": "d124", "label": "Xp_d124", "pulse_shape": "drag", "parameters": {"amp": [0.1965402187373356, 0.0], "beta": 5.400701310831489, "duration": 240, "sigma": 60}}]}, {"name": "x", "qubits": [125], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "d125", "label": "Xp_d125", "pulse_shape": "drag", "parameters": {"amp": [0.1921259499640045, 0.0], "beta": -2.99891761828057, "duration": 240, "sigma": 60}}]}, {"name": "x", "qubits": [126], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "d126", "label": "Xp_d126", "pulse_shape": "drag", "parameters": {"amp": [0.19243556618176838, 0.0], "beta": -2.8523315322449125, "duration": 240, "sigma": 60}}]}], "meas_kernel": {"name": "hw_qmfk", "params": {}}, "discriminator": {"name": "hw_qmfk", "params": {}}, "_data": {}} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/kawasaki/fake_kawasaki.py b/qiskit_ibm_runtime/fake_provider/backends/kawasaki/fake_kawasaki.py new file mode 100644 index 000000000..f4303e647 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kawasaki/fake_kawasaki.py @@ -0,0 +1,28 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Kawasaki device (127 qubit). +""" + +import os +from qiskit_ibm_runtime.fake_provider import fake_backend + + +class FakeKawasaki(fake_backend.FakeBackendV2): + """A fake 127 qubit backend.""" + + dirname = os.path.dirname(__file__) # type: ignore + conf_filename = "conf_kawasaki.json" # type: ignore + props_filename = "props_kawasaki.json" # type: ignore + defs_filename = "defs_kawasaki.json" # type: ignore + backend_name = "fake_kawasaki" # type: ignore diff --git a/qiskit_ibm_runtime/fake_provider/backends/kawasaki/props_kawasaki.json b/qiskit_ibm_runtime/fake_provider/backends/kawasaki/props_kawasaki.json new file mode 100644 index 000000000..d66a68164 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kawasaki/props_kawasaki.json @@ -0,0 +1 @@ +{"backend_name": "alt_kawasaki", "backend_version": "2.0.0", "last_update_date": "2023-09-29T22:15:53-04:00", "qubits": [[{"date": "2023-09-28T11:37:44-04:00", "name": "T1", "unit": "us", "value": 107.35433366527712}, {"date": "2023-09-28T11:40:40-04:00", "name": "T2", "unit": "us", "value": 116.59885507295891}, {"date": "2023-09-29T22:15:53-04:00", "name": "frequency", "unit": "GHz", "value": 5.243555626134729}, {"date": "2023-09-29T22:15:53-04:00", "name": "anharmonicity", "unit": "GHz", "value": -0.20640003780600244}, {"date": "2023-09-28T11:32:15-04:00", "name": "readout_error", "unit": "", "value": 0.03370000000000006}, {"date": "2023-09-28T11:32:15-04:00", "name": "prob_meas0_prep1", "unit": "", "value": 0.03500000000000003}, {"date": "2023-09-28T11:32:15-04:00", "name": "prob_meas1_prep0", "unit": "", "value": 0.0324}, {"date": 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@@ -0,0 +1,17 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Kyiv backend (127 qubit). +""" + +from .fake_kyiv import FakeKyiv diff --git a/qiskit_ibm_runtime/fake_provider/backends/kyiv/conf_kyiv.json b/qiskit_ibm_runtime/fake_provider/backends/kyiv/conf_kyiv.json new file mode 100644 index 000000000..8b4c12c9d --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kyiv/conf_kyiv.json @@ -0,0 +1 @@ +{"backend_name": "ibm_kyiv", "backend_version": "1.20.2", "n_qubits": 127, "basis_gates": ["ecr", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], 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"acquisition_latency": [], "conditional_latency": [], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{126}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{62,72}(\\sigma_{62}^{+}\\sigma_{72}^{-}+\\sigma_{62}^{-}\\sigma_{72}^{+}) + J_{67,68}(\\sigma_{67}^{+}\\sigma_{68}^{-}+\\sigma_{67}^{-}\\sigma_{68}^{+}) + J_{99,100}(\\sigma_{99}^{+}\\sigma_{100}^{-}+\\sigma_{99}^{-}\\sigma_{100}^{+}) + J_{44,45}(\\sigma_{44}^{+}\\sigma_{45}^{-}+\\sigma_{44}^{-}\\sigma_{45}^{+}) \\\\ & + J_{108,112}(\\sigma_{108}^{+}\\sigma_{112}^{-}+\\sigma_{108}^{-}\\sigma_{112}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{40,41}(\\sigma_{40}^{+}\\sigma_{41}^{-}+\\sigma_{40}^{-}\\sigma_{41}^{+}) + J_{0,14}(\\sigma_{0}^{+}\\sigma_{14}^{-}+\\sigma_{0}^{-}\\sigma_{14}^{+}) \\\\ & + J_{17,30}(\\sigma_{17}^{+}\\sigma_{30}^{-}+\\sigma_{17}^{-}\\sigma_{30}^{+}) + J_{100,101}(\\sigma_{100}^{+}\\sigma_{101}^{-}+\\sigma_{100}^{-}\\sigma_{101}^{+}) + J_{91,98}(\\sigma_{91}^{+}\\sigma_{98}^{-}+\\sigma_{91}^{-}\\sigma_{98}^{+}) + J_{100,110}(\\sigma_{100}^{+}\\sigma_{110}^{-}+\\sigma_{100}^{-}\\sigma_{110}^{+}) \\\\ & + J_{75,90}(\\sigma_{75}^{+}\\sigma_{90}^{-}+\\sigma_{75}^{-}\\sigma_{90}^{+}) + J_{96,97}(\\sigma_{96}^{+}\\sigma_{97}^{-}+\\sigma_{96}^{-}\\sigma_{97}^{+}) + J_{41,42}(\\sigma_{41}^{+}\\sigma_{42}^{-}+\\sigma_{41}^{-}\\sigma_{42}^{+}) + J_{18,19}(\\sigma_{18}^{+}\\sigma_{19}^{-}+\\sigma_{18}^{-}\\sigma_{19}^{+}) \\\\ & + J_{55,68}(\\sigma_{55}^{+}\\sigma_{68}^{-}+\\sigma_{55}^{-}\\sigma_{68}^{+}) + J_{9,10}(\\sigma_{9}^{+}\\sigma_{10}^{-}+\\sigma_{9}^{-}\\sigma_{10}^{+}) + J_{49,55}(\\sigma_{49}^{+}\\sigma_{55}^{-}+\\sigma_{49}^{-}\\sigma_{55}^{+}) + J_{106,107}(\\sigma_{106}^{+}\\sigma_{107}^{-}+\\sigma_{106}^{-}\\sigma_{107}^{+}) \\\\ & + J_{47,48}(\\sigma_{47}^{+}\\sigma_{48}^{-}+\\sigma_{47}^{-}\\sigma_{48}^{+}) + J_{42,43}(\\sigma_{42}^{+}\\sigma_{43}^{-}+\\sigma_{42}^{-}\\sigma_{43}^{+}) + J_{107,108}(\\sigma_{107}^{+}\\sigma_{108}^{-}+\\sigma_{107}^{-}\\sigma_{108}^{+}) + J_{73,85}(\\sigma_{73}^{+}\\sigma_{85}^{-}+\\sigma_{73}^{-}\\sigma_{85}^{+}) \\\\ & + J_{38,39}(\\sigma_{38}^{+}\\sigma_{39}^{-}+\\sigma_{38}^{-}\\sigma_{39}^{+}) + J_{20,33}(\\sigma_{20}^{+}\\sigma_{33}^{-}+\\sigma_{20}^{-}\\sigma_{33}^{+}) + J_{103,104}(\\sigma_{103}^{+}\\sigma_{104}^{-}+\\sigma_{103}^{-}\\sigma_{104}^{+}) + J_{48,49}(\\sigma_{48}^{+}\\sigma_{49}^{-}+\\sigma_{48}^{-}\\sigma_{49}^{+}) \\\\ & + J_{80,81}(\\sigma_{80}^{+}\\sigma_{81}^{-}+\\sigma_{80}^{-}\\sigma_{81}^{+}) + J_{75,76}(\\sigma_{75}^{+}\\sigma_{76}^{-}+\\sigma_{75}^{-}\\sigma_{76}^{+}) + J_{66,73}(\\sigma_{66}^{+}\\sigma_{73}^{-}+\\sigma_{66}^{-}\\sigma_{73}^{+}) + J_{85,86}(\\sigma_{85}^{+}\\sigma_{86}^{-}+\\sigma_{85}^{-}\\sigma_{86}^{+}) \\\\ & + J_{110,118}(\\sigma_{110}^{+}\\sigma_{118}^{-}+\\sigma_{110}^{-}\\sigma_{118}^{+}) + J_{81,82}(\\sigma_{81}^{+}\\sigma_{82}^{-}+\\sigma_{81}^{-}\\sigma_{82}^{+}) + J_{16,26}(\\sigma_{16}^{+}\\sigma_{26}^{-}+\\sigma_{16}^{-}\\sigma_{26}^{+}) + J_{90,94}(\\sigma_{90}^{+}\\sigma_{94}^{-}+\\sigma_{90}^{-}\\sigma_{94}^{+}) \\\\ & + J_{118,119}(\\sigma_{118}^{+}\\sigma_{119}^{-}+\\sigma_{118}^{-}\\sigma_{119}^{+}) + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{22,23}(\\sigma_{22}^{+}\\sigma_{23}^{-}+\\sigma_{22}^{-}\\sigma_{23}^{+}) + J_{77,78}(\\sigma_{77}^{+}\\sigma_{78}^{-}+\\sigma_{77}^{-}\\sigma_{78}^{+}) \\\\ & + J_{49,50}(\\sigma_{49}^{+}\\sigma_{50}^{-}+\\sigma_{49}^{-}\\sigma_{50}^{+}) + J_{104,105}(\\sigma_{104}^{+}\\sigma_{105}^{-}+\\sigma_{104}^{-}\\sigma_{105}^{+}) + J_{114,115}(\\sigma_{114}^{+}\\sigma_{115}^{-}+\\sigma_{114}^{-}\\sigma_{115}^{+}) + J_{45,46}(\\sigma_{45}^{+}\\sigma_{46}^{-}+\\sigma_{45}^{-}\\sigma_{46}^{+}) \\\\ & + J_{105,106}(\\sigma_{105}^{+}\\sigma_{106}^{-}+\\sigma_{105}^{-}\\sigma_{106}^{+}) + J_{50,51}(\\sigma_{50}^{+}\\sigma_{51}^{-}+\\sigma_{50}^{-}\\sigma_{51}^{+}) + J_{72,81}(\\sigma_{72}^{+}\\sigma_{81}^{-}+\\sigma_{72}^{-}\\sigma_{81}^{+}) + J_{82,83}(\\sigma_{82}^{+}\\sigma_{83}^{-}+\\sigma_{82}^{-}\\sigma_{83}^{+}) \\\\ & + J_{46,47}(\\sigma_{46}^{+}\\sigma_{47}^{-}+\\sigma_{46}^{-}\\sigma_{47}^{+}) + J_{78,79}(\\sigma_{78}^{+}\\sigma_{79}^{-}+\\sigma_{78}^{-}\\sigma_{79}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) + J_{83,84}(\\sigma_{83}^{+}\\sigma_{84}^{-}+\\sigma_{83}^{-}\\sigma_{84}^{+}) \\\\ & + J_{115,116}(\\sigma_{115}^{+}\\sigma_{116}^{-}+\\sigma_{115}^{-}\\sigma_{116}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) + J_{79,80}(\\sigma_{79}^{+}\\sigma_{80}^{-}+\\sigma_{79}^{-}\\sigma_{80}^{+}) \\\\ & + J_{56,57}(\\sigma_{56}^{+}\\sigma_{57}^{-}+\\sigma_{56}^{-}\\sigma_{57}^{+}) + J_{93,106}(\\sigma_{93}^{+}\\sigma_{106}^{-}+\\sigma_{93}^{-}\\sigma_{106}^{+}) + J_{116,117}(\\sigma_{116}^{+}\\sigma_{117}^{-}+\\sigma_{116}^{-}\\sigma_{117}^{+}) + J_{20,21}(\\sigma_{20}^{+}\\sigma_{21}^{-}+\\sigma_{20}^{-}\\sigma_{21}^{+}) \\\\ & + J_{12,17}(\\sigma_{12}^{+}\\sigma_{17}^{-}+\\sigma_{12}^{-}\\sigma_{17}^{+}) + J_{41,53}(\\sigma_{41}^{+}\\sigma_{53}^{-}+\\sigma_{41}^{-}\\sigma_{53}^{+}) + J_{57,58}(\\sigma_{57}^{+}\\sigma_{58}^{-}+\\sigma_{57}^{-}\\sigma_{58}^{+}) + J_{87,93}(\\sigma_{87}^{+}\\sigma_{93}^{-}+\\sigma_{87}^{-}\\sigma_{93}^{+}) \\\\ & + J_{30,31}(\\sigma_{30}^{+}\\sigma_{31}^{-}+\\sigma_{30}^{-}\\sigma_{31}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) + J_{79,91}(\\sigma_{79}^{+}\\sigma_{91}^{-}+\\sigma_{79}^{-}\\sigma_{91}^{+}) + J_{26,27}(\\sigma_{26}^{+}\\sigma_{27}^{-}+\\sigma_{26}^{-}\\sigma_{27}^{+}) \\\\ & + J_{21,22}(\\sigma_{21}^{+}\\sigma_{22}^{-}+\\sigma_{21}^{-}\\sigma_{22}^{+}) + J_{58,71}(\\sigma_{58}^{+}\\sigma_{71}^{-}+\\sigma_{58}^{-}\\sigma_{71}^{+}) + J_{31,32}(\\sigma_{31}^{+}\\sigma_{32}^{-}+\\sigma_{31}^{-}\\sigma_{32}^{+}) + J_{4,15}(\\sigma_{4}^{+}\\sigma_{15}^{-}+\\sigma_{4}^{-}\\sigma_{15}^{+}) \\\\ & + J_{86,87}(\\sigma_{86}^{+}\\sigma_{87}^{-}+\\sigma_{86}^{-}\\sigma_{87}^{+}) + J_{113,114}(\\sigma_{113}^{+}\\sigma_{114}^{-}+\\sigma_{113}^{-}\\sigma_{114}^{+}) + J_{104,111}(\\sigma_{104}^{+}\\sigma_{111}^{-}+\\sigma_{104}^{-}\\sigma_{111}^{+}) + J_{123,124}(\\sigma_{123}^{+}\\sigma_{124}^{-}+\\sigma_{123}^{-}\\sigma_{124}^{+}) \\\\ & + J_{27,28}(\\sigma_{27}^{+}\\sigma_{28}^{-}+\\sigma_{27}^{-}\\sigma_{28}^{+}) + J_{34,43}(\\sigma_{34}^{+}\\sigma_{43}^{-}+\\sigma_{34}^{-}\\sigma_{43}^{+}) + J_{64,65}(\\sigma_{64}^{+}\\sigma_{65}^{-}+\\sigma_{64}^{-}\\sigma_{65}^{+}) + J_{119,120}(\\sigma_{119}^{+}\\sigma_{120}^{-}+\\sigma_{119}^{-}\\sigma_{120}^{+}) \\\\ & + J_{54,64}(\\sigma_{54}^{+}\\sigma_{64}^{-}+\\sigma_{54}^{-}\\sigma_{64}^{+}) + J_{32,36}(\\sigma_{32}^{+}\\sigma_{36}^{-}+\\sigma_{32}^{-}\\sigma_{36}^{+}) + J_{60,61}(\\sigma_{60}^{+}\\sigma_{61}^{-}+\\sigma_{60}^{-}\\sigma_{61}^{+}) + J_{5,6}(\\sigma_{5}^{+}\\sigma_{6}^{-}+\\sigma_{5}^{-}\\sigma_{6}^{+}) \\\\ & + J_{14,18}(\\sigma_{14}^{+}\\sigma_{18}^{-}+\\sigma_{14}^{-}\\sigma_{18}^{+}) + J_{87,88}(\\sigma_{87}^{+}\\sigma_{88}^{-}+\\sigma_{87}^{-}\\sigma_{88}^{+}) + J_{97,98}(\\sigma_{97}^{+}\\sigma_{98}^{-}+\\sigma_{97}^{-}\\sigma_{98}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) \\\\ & + J_{112,126}(\\sigma_{112}^{+}\\sigma_{126}^{-}+\\sigma_{112}^{-}\\sigma_{126}^{+}) + J_{28,29}(\\sigma_{28}^{+}\\sigma_{29}^{-}+\\sigma_{28}^{-}\\sigma_{29}^{+}) + J_{45,54}(\\sigma_{45}^{+}\\sigma_{54}^{-}+\\sigma_{45}^{-}\\sigma_{54}^{+}) + J_{36,51}(\\sigma_{36}^{+}\\sigma_{51}^{-}+\\sigma_{36}^{-}\\sigma_{51}^{+}) \\\\ & + J_{88,89}(\\sigma_{88}^{+}\\sigma_{89}^{-}+\\sigma_{88}^{-}\\sigma_{89}^{+}) + J_{120,121}(\\sigma_{120}^{+}\\sigma_{121}^{-}+\\sigma_{120}^{-}\\sigma_{121}^{+}) + J_{15,22}(\\sigma_{15}^{+}\\sigma_{22}^{-}+\\sigma_{15}^{-}\\sigma_{22}^{+}) + J_{24,34}(\\sigma_{24}^{+}\\sigma_{34}^{-}+\\sigma_{24}^{-}\\sigma_{34}^{+}) \\\\ & + J_{84,85}(\\sigma_{84}^{+}\\sigma_{85}^{-}+\\sigma_{84}^{-}\\sigma_{85}^{+}) + J_{29,30}(\\sigma_{29}^{+}\\sigma_{30}^{-}+\\sigma_{29}^{-}\\sigma_{30}^{+}) + J_{61,62}(\\sigma_{61}^{+}\\sigma_{62}^{-}+\\sigma_{61}^{-}\\sigma_{62}^{+}) + J_{70,74}(\\sigma_{70}^{+}\\sigma_{74}^{-}+\\sigma_{70}^{-}\\sigma_{74}^{+}) \\\\ & + J_{121,122}(\\sigma_{121}^{+}\\sigma_{122}^{-}+\\sigma_{121}^{-}\\sigma_{122}^{+}) + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{122,123}(\\sigma_{122}^{+}\\sigma_{123}^{-}+\\sigma_{122}^{-}\\sigma_{123}^{+}) + J_{117,118}(\\sigma_{117}^{+}\\sigma_{118}^{-}+\\sigma_{117}^{-}\\sigma_{118}^{+}) \\\\ & + J_{62,63}(\\sigma_{62}^{+}\\sigma_{63}^{-}+\\sigma_{62}^{-}\\sigma_{63}^{+}) + J_{94,95}(\\sigma_{94}^{+}\\sigma_{95}^{-}+\\sigma_{94}^{-}\\sigma_{95}^{+}) + J_{109,114}(\\sigma_{109}^{+}\\sigma_{114}^{-}+\\sigma_{109}^{-}\\sigma_{114}^{+}) + J_{37,52}(\\sigma_{37}^{+}\\sigma_{52}^{-}+\\sigma_{37}^{-}\\sigma_{52}^{+}) \\\\ & + J_{58,59}(\\sigma_{58}^{+}\\sigma_{59}^{-}+\\sigma_{58}^{-}\\sigma_{59}^{+}) + J_{3,4}(\\sigma_{3}^{+}\\sigma_{4}^{-}+\\sigma_{3}^{-}\\sigma_{4}^{+}) + J_{33,39}(\\sigma_{33}^{+}\\sigma_{39}^{-}+\\sigma_{33}^{-}\\sigma_{39}^{+}) + J_{95,96}(\\sigma_{95}^{+}\\sigma_{96}^{-}+\\sigma_{95}^{-}\\sigma_{96}^{+}) \\\\ & + J_{68,69}(\\sigma_{68}^{+}\\sigma_{69}^{-}+\\sigma_{68}^{-}\\sigma_{69}^{+}) + J_{63,64}(\\sigma_{63}^{+}\\sigma_{64}^{-}+\\sigma_{63}^{-}\\sigma_{64}^{+}) + J_{71,77}(\\sigma_{71}^{+}\\sigma_{77}^{-}+\\sigma_{71}^{-}\\sigma_{77}^{+}) + J_{111,122}(\\sigma_{111}^{+}\\sigma_{122}^{-}+\\sigma_{111}^{-}\\sigma_{122}^{+}) \\\\ & + J_{4,5}(\\sigma_{4}^{+}\\sigma_{5}^{-}+\\sigma_{4}^{-}\\sigma_{5}^{+}) + J_{59,60}(\\sigma_{59}^{+}\\sigma_{60}^{-}+\\sigma_{59}^{-}\\sigma_{60}^{+}) + J_{96,109}(\\sigma_{96}^{+}\\sigma_{109}^{-}+\\sigma_{96}^{-}\\sigma_{109}^{+}) + J_{124,125}(\\sigma_{124}^{+}\\sigma_{125}^{-}+\\sigma_{124}^{-}\\sigma_{125}^{+}) \\\\ & + J_{69,70}(\\sigma_{69}^{+}\\sigma_{70}^{-}+\\sigma_{69}^{-}\\sigma_{70}^{+}) + J_{35,47}(\\sigma_{35}^{+}\\sigma_{47}^{-}+\\sigma_{35}^{-}\\sigma_{47}^{+}) + J_{101,102}(\\sigma_{101}^{+}\\sigma_{102}^{-}+\\sigma_{101}^{-}\\sigma_{102}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) \\\\ & + J_{10,11}(\\sigma_{10}^{+}\\sigma_{11}^{-}+\\sigma_{10}^{-}\\sigma_{11}^{+}) + J_{65,66}(\\sigma_{65}^{+}\\sigma_{66}^{-}+\\sigma_{65}^{-}\\sigma_{66}^{+}) + J_{37,38}(\\sigma_{37}^{+}\\sigma_{38}^{-}+\\sigma_{37}^{-}\\sigma_{38}^{+}) + J_{28,35}(\\sigma_{28}^{+}\\sigma_{35}^{-}+\\sigma_{28}^{-}\\sigma_{35}^{+}) \\\\ & + J_{102,103}(\\sigma_{102}^{+}\\sigma_{103}^{-}+\\sigma_{102}^{-}\\sigma_{103}^{+}) + J_{92,102}(\\sigma_{92}^{+}\\sigma_{102}^{-}+\\sigma_{92}^{-}\\sigma_{102}^{+}) + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{98,99}(\\sigma_{98}^{+}\\sigma_{99}^{-}+\\sigma_{98}^{-}\\sigma_{99}^{+}) \\\\ & + J_{43,44}(\\sigma_{43}^{+}\\sigma_{44}^{-}+\\sigma_{43}^{-}\\sigma_{44}^{+}) + J_{52,56}(\\sigma_{52}^{+}\\sigma_{56}^{-}+\\sigma_{52}^{-}\\sigma_{56}^{+}) + J_{125,126}(\\sigma_{125}^{+}\\sigma_{126}^{-}+\\sigma_{125}^{-}\\sigma_{126}^{+}) + J_{39,40}(\\sigma_{39}^{+}\\sigma_{40}^{-}+\\sigma_{39}^{-}\\sigma_{40}^{+}) \\\\ & + J_{8,16}(\\sigma_{8}^{+}\\sigma_{16}^{-}+\\sigma_{8}^{-}\\sigma_{16}^{+}) + J_{66,67}(\\sigma_{66}^{+}\\sigma_{67}^{-}+\\sigma_{66}^{-}\\sigma_{67}^{+}) + J_{11,12}(\\sigma_{11}^{+}\\sigma_{12}^{-}+\\sigma_{11}^{-}\\sigma_{12}^{+}) + J_{76,77}(\\sigma_{76}^{+}\\sigma_{77}^{-}+\\sigma_{76}^{-}\\sigma_{77}^{+}) \\\\ & + J_{83,92}(\\sigma_{83}^{+}\\sigma_{92}^{-}+\\sigma_{83}^{-}\\sigma_{92}^{+}) + J_{74,89}(\\sigma_{74}^{+}\\sigma_{89}^{-}+\\sigma_{74}^{-}\\sigma_{89}^{+}) + J_{7,8}(\\sigma_{7}^{+}\\sigma_{8}^{-}+\\sigma_{7}^{-}\\sigma_{8}^{+}) + J_{53,60}(\\sigma_{53}^{+}\\sigma_{60}^{-}+\\sigma_{53}^{-}\\sigma_{60}^{+}) \\\\ & + \\Omega_{d,0}(U_{0}^{(0,1)}(t)+U_{1}^{(0,14)}(t))\\sigma_{0}^{X} + \\Omega_{d,1}(U_{2}^{(1,2)}(t))\\sigma_{1}^{X} \\\\ & + \\Omega_{d,2}(U_{3}^{(2,3)}(t))\\sigma_{2}^{X} + \\Omega_{d,4}(U_{5}^{(4,15)}(t)+U_{4}^{(4,3)}(t))\\sigma_{4}^{X} \\\\ & + \\Omega_{d,5}(U_{6}^{(5,4)}(t))\\sigma_{5}^{X} + \\Omega_{d,6}(U_{7}^{(6,5)}(t))\\sigma_{6}^{X} \\\\ & + \\Omega_{d,7}(U_{9}^{(7,8)}(t)+U_{8}^{(7,6)}(t))\\sigma_{7}^{X} + \\Omega_{d,8}(U_{10}^{(8,9)}(t))\\sigma_{8}^{X} \\\\ & + \\Omega_{d,10}(U_{12}^{(10,11)}(t)+U_{11}^{(10,9)}(t))\\sigma_{10}^{X} + \\Omega_{d,11}(U_{13}^{(11,12)}(t))\\sigma_{11}^{X} \\\\ & + \\Omega_{d,13}(U_{14}^{(13,12)}(t))\\sigma_{13}^{X} + \\Omega_{d,14}(U_{15}^{(14,18)}(t))\\sigma_{14}^{X} \\\\ & + \\Omega_{d,16}(U_{16}^{(16,8)}(t))\\sigma_{16}^{X} + \\Omega_{d,17}(U_{17}^{(17,12)}(t)+U_{18}^{(17,30)}(t))\\sigma_{17}^{X} \\\\ & + \\Omega_{d,19}(U_{19}^{(19,18)}(t))\\sigma_{19}^{X} + \\Omega_{d,20}(U_{20}^{(20,19)}(t))\\sigma_{20}^{X} \\\\ & + \\Omega_{d,21}(U_{21}^{(21,20)}(t)+U_{22}^{(21,22)}(t))\\sigma_{21}^{X} + \\Omega_{d,22}(U_{24}^{(22,23)}(t)+U_{23}^{(22,15)}(t))\\sigma_{22}^{X} \\\\ & + \\Omega_{d,23}(U_{25}^{(23,24)}(t))\\sigma_{23}^{X} + \\Omega_{d,24}(U_{26}^{(24,25)}(t))\\sigma_{24}^{X} \\\\ & + \\Omega_{d,26}(U_{29}^{(26,27)}(t)+U_{27}^{(26,16)}(t)+U_{28}^{(26,25)}(t))\\sigma_{26}^{X} + \\Omega_{d,28}(U_{30}^{(28,27)}(t))\\sigma_{28}^{X} \\\\ & + \\Omega_{d,29}(U_{31}^{(29,28)}(t)+U_{32}^{(29,30)}(t))\\sigma_{29}^{X} + \\Omega_{d,31}(U_{34}^{(31,32)}(t)+U_{33}^{(31,30)}(t))\\sigma_{31}^{X} \\\\ & + \\Omega_{d,33}(U_{36}^{(33,39)}(t)+U_{35}^{(33,20)}(t))\\sigma_{33}^{X} + \\Omega_{d,34}(U_{37}^{(34,24)}(t))\\sigma_{34}^{X} \\\\ & + \\Omega_{d,35}(U_{39}^{(35,47)}(t)+U_{38}^{(35,28)}(t))\\sigma_{35}^{X} + \\Omega_{d,36}(U_{41}^{(36,51)}(t)+U_{40}^{(36,32)}(t))\\sigma_{36}^{X} \\\\ & + \\Omega_{d,37}(U_{42}^{(37,38)}(t)+U_{43}^{(37,52)}(t))\\sigma_{37}^{X} + \\Omega_{d,39}(U_{44}^{(39,38)}(t))\\sigma_{39}^{X} \\\\ & + \\Omega_{d,40}(U_{46}^{(40,41)}(t)+U_{45}^{(40,39)}(t))\\sigma_{40}^{X} + \\Omega_{d,42}(U_{48}^{(42,43)}(t)+U_{47}^{(42,41)}(t))\\sigma_{42}^{X} \\\\ & + \\Omega_{d,43}(U_{49}^{(43,34)}(t))\\sigma_{43}^{X} + \\Omega_{d,44}(U_{50}^{(44,43)}(t))\\sigma_{44}^{X} \\\\ & + \\Omega_{d,45}(U_{52}^{(45,46)}(t)+U_{51}^{(45,44)}(t))\\sigma_{45}^{X} + \\Omega_{d,46}(U_{53}^{(46,47)}(t))\\sigma_{46}^{X} \\\\ & + \\Omega_{d,48}(U_{54}^{(48,47)}(t)+U_{55}^{(48,49)}(t))\\sigma_{48}^{X} + \\Omega_{d,50}(U_{56}^{(50,49)}(t)+U_{57}^{(50,51)}(t))\\sigma_{50}^{X} \\\\ & + \\Omega_{d,53}(U_{59}^{(53,60)}(t)+U_{58}^{(53,41)}(t))\\sigma_{53}^{X} + \\Omega_{d,54}(U_{61}^{(54,64)}(t)+U_{60}^{(54,45)}(t))\\sigma_{54}^{X} \\\\ & + \\Omega_{d,55}(U_{62}^{(55,49)}(t))\\sigma_{55}^{X} + \\Omega_{d,56}(U_{63}^{(56,52)}(t))\\sigma_{56}^{X} \\\\ & + \\Omega_{d,57}(U_{65}^{(57,58)}(t)+U_{64}^{(57,56)}(t))\\sigma_{57}^{X} + \\Omega_{d,58}(U_{67}^{(58,71)}(t)+U_{66}^{(58,59)}(t))\\sigma_{58}^{X} \\\\ & + \\Omega_{d,59}(U_{68}^{(59,60)}(t))\\sigma_{59}^{X} + \\Omega_{d,60}(U_{69}^{(60,61)}(t))\\sigma_{60}^{X} \\\\ & + \\Omega_{d,61}(U_{70}^{(61,62)}(t))\\sigma_{61}^{X} + \\Omega_{d,63}(U_{71}^{(63,62)}(t)+U_{72}^{(63,64)}(t))\\sigma_{63}^{X} \\\\ & + \\Omega_{d,64}(U_{73}^{(64,65)}(t))\\sigma_{64}^{X} + \\Omega_{d,66}(U_{75}^{(66,67)}(t)+U_{74}^{(66,65)}(t))\\sigma_{66}^{X} \\\\ & + \\Omega_{d,67}(U_{76}^{(67,68)}(t))\\sigma_{67}^{X} + \\Omega_{d,68}(U_{78}^{(68,69)}(t)+U_{77}^{(68,55)}(t))\\sigma_{68}^{X} \\\\ & + \\Omega_{d,69}(U_{79}^{(69,70)}(t))\\sigma_{69}^{X} + \\Omega_{d,70}(U_{80}^{(70,74)}(t))\\sigma_{70}^{X} \\\\ & + \\Omega_{d,72}(U_{82}^{(72,81)}(t)+U_{81}^{(72,62)}(t))\\sigma_{72}^{X} + \\Omega_{d,73}(U_{83}^{(73,66)}(t)+U_{84}^{(73,85)}(t))\\sigma_{73}^{X} \\\\ & + \\Omega_{d,75}(U_{86}^{(75,90)}(t)+U_{85}^{(75,76)}(t))\\sigma_{75}^{X} + \\Omega_{d,76}(U_{87}^{(76,77)}(t))\\sigma_{76}^{X} \\\\ & + \\Omega_{d,77}(U_{89}^{(77,78)}(t)+U_{88}^{(77,71)}(t))\\sigma_{77}^{X} + \\Omega_{d,79}(U_{90}^{(79,78)}(t))\\sigma_{79}^{X} \\\\ & + \\Omega_{d,80}(U_{92}^{(80,81)}(t)+U_{91}^{(80,79)}(t))\\sigma_{80}^{X} + \\Omega_{d,82}(U_{94}^{(82,83)}(t)+U_{93}^{(82,81)}(t))\\sigma_{82}^{X} \\\\ & + \\Omega_{d,84}(U_{95}^{(84,83)}(t))\\sigma_{84}^{X} + \\Omega_{d,85}(U_{96}^{(85,84)}(t)+U_{97}^{(85,86)}(t))\\sigma_{85}^{X} \\\\ & + \\Omega_{d,87}(U_{98}^{(87,86)}(t)+U_{99}^{(87,93)}(t))\\sigma_{87}^{X} + \\Omega_{d,88}(U_{100}^{(88,87)}(t)+U_{101}^{(88,89)}(t))\\sigma_{88}^{X} \\\\ & + \\Omega_{d,89}(U_{102}^{(89,74)}(t))\\sigma_{89}^{X} + \\Omega_{d,91}(U_{104}^{(91,98)}(t)+U_{103}^{(91,79)}(t))\\sigma_{91}^{X} \\\\ & + \\Omega_{d,92}(U_{105}^{(92,83)}(t)+U_{106}^{(92,102)}(t))\\sigma_{92}^{X} + \\Omega_{d,93}(U_{107}^{(93,106)}(t))\\sigma_{93}^{X} \\\\ & + \\Omega_{d,94}(U_{108}^{(94,90)}(t)+U_{109}^{(94,95)}(t))\\sigma_{94}^{X} + \\Omega_{d,96}(U_{110}^{(96,95)}(t)+U_{112}^{(96,109)}(t)+U_{111}^{(96,97)}(t))\\sigma_{96}^{X} \\\\ & + \\Omega_{d,97}(U_{113}^{(97,98)}(t))\\sigma_{97}^{X} + \\Omega_{d,98}(U_{114}^{(98,99)}(t))\\sigma_{98}^{X} \\\\ & + \\Omega_{d,100}(U_{116}^{(100,110)}(t)+U_{115}^{(100,99)}(t))\\sigma_{100}^{X} + \\Omega_{d,101}(U_{118}^{(101,102)}(t)+U_{117}^{(101,100)}(t))\\sigma_{101}^{X} \\\\ & + \\Omega_{d,103}(U_{120}^{(103,104)}(t)+U_{119}^{(103,102)}(t))\\sigma_{103}^{X} + \\Omega_{d,105}(U_{122}^{(105,106)}(t)+U_{121}^{(105,104)}(t))\\sigma_{105}^{X} \\\\ & + \\Omega_{d,107}(U_{124}^{(107,108)}(t)+U_{123}^{(107,106)}(t))\\sigma_{107}^{X} + \\Omega_{d,108}(U_{125}^{(108,112)}(t))\\sigma_{108}^{X} \\\\ & + \\Omega_{d,109}(U_{126}^{(109,114)}(t))\\sigma_{109}^{X} + \\Omega_{d,110}(U_{127}^{(110,118)}(t))\\sigma_{110}^{X} \\\\ & + \\Omega_{d,111}(U_{129}^{(111,122)}(t)+U_{128}^{(111,104)}(t))\\sigma_{111}^{X} + \\Omega_{d,114}(U_{131}^{(114,115)}(t)+U_{130}^{(114,113)}(t))\\sigma_{114}^{X} \\\\ & + \\Omega_{d,116}(U_{133}^{(116,117)}(t)+U_{132}^{(116,115)}(t))\\sigma_{116}^{X} + \\Omega_{d,117}(U_{134}^{(117,118)}(t))\\sigma_{117}^{X} \\\\ & + \\Omega_{d,118}(U_{135}^{(118,119)}(t))\\sigma_{118}^{X} + \\Omega_{d,119}(U_{136}^{(119,120)}(t))\\sigma_{119}^{X} \\\\ & + \\Omega_{d,121}(U_{137}^{(121,120)}(t))\\sigma_{121}^{X} + \\Omega_{d,122}(U_{138}^{(122,121)}(t)+U_{139}^{(122,123)}(t))\\sigma_{122}^{X} \\\\ & + \\Omega_{d,123}(U_{140}^{(123,124)}(t))\\sigma_{123}^{X} + \\Omega_{d,125}(U_{142}^{(125,126)}(t)+U_{141}^{(125,124)}(t))\\sigma_{125}^{X} \\\\ & + \\Omega_{d,126}(U_{143}^{(126,112)}(t))\\sigma_{126}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,126,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,126,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,126,-delta{i}/2*O{i}]", "_SUM[i,0,126,omegad{i}*X{i}||D{i}]", "jq62q72*Sp62*Sm72", "jq62q72*Sm62*Sp72", "jq67q68*Sp67*Sm68", "jq67q68*Sm67*Sp68", "jq99q100*Sp99*Sm100", "jq99q100*Sm99*Sp100", "jq44q45*Sp44*Sm45", "jq44q45*Sm44*Sp45", "jq108q112*Sp108*Sm112", "jq108q112*Sm108*Sp112", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq40q41*Sp40*Sm41", "jq40q41*Sm40*Sp41", "jq0q14*Sp0*Sm14", "jq0q14*Sm0*Sp14", "jq17q30*Sp17*Sm30", "jq17q30*Sm17*Sp30", "jq100q101*Sp100*Sm101", "jq100q101*Sm100*Sp101", "jq91q98*Sp91*Sm98", "jq91q98*Sm91*Sp98", "jq100q110*Sp100*Sm110", "jq100q110*Sm100*Sp110", "jq75q90*Sp75*Sm90", "jq75q90*Sm75*Sp90", "jq96q97*Sp96*Sm97", "jq96q97*Sm96*Sp97", "jq41q42*Sp41*Sm42", "jq41q42*Sm41*Sp42", "jq18q19*Sp18*Sm19", "jq18q19*Sm18*Sp19", "jq55q68*Sp55*Sm68", "jq55q68*Sm55*Sp68", "jq9q10*Sp9*Sm10", "jq9q10*Sm9*Sp10", "jq49q55*Sp49*Sm55", "jq49q55*Sm49*Sp55", "jq106q107*Sp106*Sm107", "jq106q107*Sm106*Sp107", "jq47q48*Sp47*Sm48", "jq47q48*Sm47*Sp48", "jq42q43*Sp42*Sm43", "jq42q43*Sm42*Sp43", "jq107q108*Sp107*Sm108", "jq107q108*Sm107*Sp108", "jq73q85*Sp73*Sm85", "jq73q85*Sm73*Sp85", "jq38q39*Sp38*Sm39", "jq38q39*Sm38*Sp39", "jq20q33*Sp20*Sm33", "jq20q33*Sm20*Sp33", "jq103q104*Sp103*Sm104", "jq103q104*Sm103*Sp104", "jq48q49*Sp48*Sm49", "jq48q49*Sm48*Sp49", "jq80q81*Sp80*Sm81", "jq80q81*Sm80*Sp81", "jq75q76*Sp75*Sm76", "jq75q76*Sm75*Sp76", "jq66q73*Sp66*Sm73", "jq66q73*Sm66*Sp73", "jq85q86*Sp85*Sm86", "jq85q86*Sm85*Sp86", "jq110q118*Sp110*Sm118", "jq110q118*Sm110*Sp118", "jq81q82*Sp81*Sm82", "jq81q82*Sm81*Sp82", "jq16q26*Sp16*Sm26", "jq16q26*Sm16*Sp26", "jq90q94*Sp90*Sm94", "jq90q94*Sm90*Sp94", "jq118q119*Sp118*Sm119", "jq118q119*Sm118*Sp119", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq22q23*Sp22*Sm23", "jq22q23*Sm22*Sp23", "jq77q78*Sp77*Sm78", "jq77q78*Sm77*Sp78", "jq49q50*Sp49*Sm50", "jq49q50*Sm49*Sp50", "jq104q105*Sp104*Sm105", "jq104q105*Sm104*Sp105", "jq114q115*Sp114*Sm115", "jq114q115*Sm114*Sp115", "jq45q46*Sp45*Sm46", "jq45q46*Sm45*Sp46", "jq105q106*Sp105*Sm106", "jq105q106*Sm105*Sp106", "jq50q51*Sp50*Sm51", "jq50q51*Sm50*Sp51", "jq72q81*Sp72*Sm81", "jq72q81*Sm72*Sp81", "jq82q83*Sp82*Sm83", "jq82q83*Sm82*Sp83", "jq46q47*Sp46*Sm47", "jq46q47*Sm46*Sp47", "jq78q79*Sp78*Sm79", "jq78q79*Sm78*Sp79", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq83q84*Sp83*Sm84", "jq83q84*Sm83*Sp84", "jq115q116*Sp115*Sm116", "jq115q116*Sm115*Sp116", "jq19q20*Sp19*Sm20", "jq19q20*Sm19*Sp20", "jq24q25*Sp24*Sm25", "jq24q25*Sm24*Sp25", "jq79q80*Sp79*Sm80", "jq79q80*Sm79*Sp80", "jq56q57*Sp56*Sm57", "jq56q57*Sm56*Sp57", "jq93q106*Sp93*Sm106", "jq93q106*Sm93*Sp106", "jq116q117*Sp116*Sm117", "jq116q117*Sm116*Sp117", "jq20q21*Sp20*Sm21", "jq20q21*Sm20*Sp21", "jq12q17*Sp12*Sm17", "jq12q17*Sm12*Sp17", "jq41q53*Sp41*Sm53", "jq41q53*Sm41*Sp53", "jq57q58*Sp57*Sm58", "jq57q58*Sm57*Sp58", "jq87q93*Sp87*Sm93", "jq87q93*Sm87*Sp93", "jq30q31*Sp30*Sm31", "jq30q31*Sm30*Sp31", "jq25q26*Sp25*Sm26", "jq25q26*Sm25*Sp26", "jq79q91*Sp79*Sm91", "jq79q91*Sm79*Sp91", "jq26q27*Sp26*Sm27", "jq26q27*Sm26*Sp27", "jq21q22*Sp21*Sm22", "jq21q22*Sm21*Sp22", "jq58q71*Sp58*Sm71", "jq58q71*Sm58*Sp71", "jq31q32*Sp31*Sm32", "jq31q32*Sm31*Sp32", "jq4q15*Sp4*Sm15", "jq4q15*Sm4*Sp15", "jq86q87*Sp86*Sm87", "jq86q87*Sm86*Sp87", "jq113q114*Sp113*Sm114", "jq113q114*Sm113*Sp114", "jq104q111*Sp104*Sm111", "jq104q111*Sm104*Sp111", "jq123q124*Sp123*Sm124", "jq123q124*Sm123*Sp124", "jq27q28*Sp27*Sm28", "jq27q28*Sm27*Sp28", "jq34q43*Sp34*Sm43", "jq34q43*Sm34*Sp43", "jq64q65*Sp64*Sm65", "jq64q65*Sm64*Sp65", "jq119q120*Sp119*Sm120", "jq119q120*Sm119*Sp120", "jq54q64*Sp54*Sm64", "jq54q64*Sm54*Sp64", "jq32q36*Sp32*Sm36", "jq32q36*Sm32*Sp36", "jq60q61*Sp60*Sm61", "jq60q61*Sm60*Sp61", "jq5q6*Sp5*Sm6", "jq5q6*Sm5*Sp6", "jq14q18*Sp14*Sm18", "jq14q18*Sm14*Sp18", "jq87q88*Sp87*Sm88", "jq87q88*Sm87*Sp88", "jq97q98*Sp97*Sm98", "jq97q98*Sm97*Sp98", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq112q126*Sp112*Sm126", "jq112q126*Sm112*Sp126", "jq28q29*Sp28*Sm29", "jq28q29*Sm28*Sp29", "jq45q54*Sp45*Sm54", "jq45q54*Sm45*Sp54", "jq36q51*Sp36*Sm51", "jq36q51*Sm36*Sp51", "jq88q89*Sp88*Sm89", "jq88q89*Sm88*Sp89", "jq120q121*Sp120*Sm121", "jq120q121*Sm120*Sp121", "jq15q22*Sp15*Sm22", "jq15q22*Sm15*Sp22", "jq24q34*Sp24*Sm34", "jq24q34*Sm24*Sp34", "jq84q85*Sp84*Sm85", "jq84q85*Sm84*Sp85", "jq29q30*Sp29*Sm30", "jq29q30*Sm29*Sp30", "jq61q62*Sp61*Sm62", "jq61q62*Sm61*Sp62", "jq70q74*Sp70*Sm74", "jq70q74*Sm70*Sp74", "jq121q122*Sp121*Sm122", "jq121q122*Sm121*Sp122", "jq2q3*Sp2*Sm3", "jq2q3*Sm2*Sp3", "jq122q123*Sp122*Sm123", "jq122q123*Sm122*Sp123", "jq117q118*Sp117*Sm118", "jq117q118*Sm117*Sp118", "jq62q63*Sp62*Sm63", "jq62q63*Sm62*Sp63", "jq94q95*Sp94*Sm95", "jq94q95*Sm94*Sp95", "jq109q114*Sp109*Sm114", "jq109q114*Sm109*Sp114", "jq37q52*Sp37*Sm52", "jq37q52*Sm37*Sp52", "jq58q59*Sp58*Sm59", "jq58q59*Sm58*Sp59", "jq3q4*Sp3*Sm4", "jq3q4*Sm3*Sp4", "jq33q39*Sp33*Sm39", "jq33q39*Sm33*Sp39", "jq95q96*Sp95*Sm96", "jq95q96*Sm95*Sp96", "jq68q69*Sp68*Sm69", "jq68q69*Sm68*Sp69", "jq63q64*Sp63*Sm64", "jq63q64*Sm63*Sp64", "jq71q77*Sp71*Sm77", "jq71q77*Sm71*Sp77", "jq111q122*Sp111*Sm122", "jq111q122*Sm111*Sp122", "jq4q5*Sp4*Sm5", "jq4q5*Sm4*Sp5", "jq59q60*Sp59*Sm60", "jq59q60*Sm59*Sp60", "jq96q109*Sp96*Sm109", "jq96q109*Sm96*Sp109", "jq124q125*Sp124*Sm125", "jq124q125*Sm124*Sp125", "jq69q70*Sp69*Sm70", "jq69q70*Sm69*Sp70", "jq35q47*Sp35*Sm47", "jq35q47*Sm35*Sp47", "jq101q102*Sp101*Sm102", "jq101q102*Sm101*Sp102", "jq0q1*Sp0*Sm1", "jq0q1*Sm0*Sp1", "jq10q11*Sp10*Sm11", "jq10q11*Sm10*Sp11", "jq65q66*Sp65*Sm66", "jq65q66*Sm65*Sp66", "jq37q38*Sp37*Sm38", "jq37q38*Sm37*Sp38", "jq28q35*Sp28*Sm35", "jq28q35*Sm28*Sp35", "jq102q103*Sp102*Sm103", "jq102q103*Sm102*Sp103", "jq92q102*Sp92*Sm102", "jq92q102*Sm92*Sp102", "jq6q7*Sp6*Sm7", "jq6q7*Sm6*Sp7", "jq98q99*Sp98*Sm99", "jq98q99*Sm98*Sp99", "jq43q44*Sp43*Sm44", "jq43q44*Sm43*Sp44", "jq52q56*Sp52*Sm56", "jq52q56*Sm52*Sp56", "jq125q126*Sp125*Sm126", "jq125q126*Sm125*Sp126", "jq39q40*Sp39*Sm40", "jq39q40*Sm39*Sp40", "jq8q16*Sp8*Sm16", "jq8q16*Sm8*Sp16", "jq66q67*Sp66*Sm67", "jq66q67*Sm66*Sp67", "jq11q12*Sp11*Sm12", "jq11q12*Sm11*Sp12", "jq76q77*Sp76*Sm77", "jq76q77*Sm76*Sp77", "jq83q92*Sp83*Sm92", "jq83q92*Sm83*Sp92", "jq74q89*Sp74*Sm89", "jq74q89*Sm74*Sp89", "jq7q8*Sp7*Sm8", "jq7q8*Sm7*Sp8", "jq53q60*Sp53*Sm60", "jq53q60*Sm53*Sp60", "omegad1*X0||U0", "omegad14*X0||U1", "omegad2*X1||U2", "omegad3*X2||U3", "omegad15*X4||U5", "omegad3*X4||U4", "omegad4*X5||U6", "omegad5*X6||U7", "omegad8*X7||U9", "omegad6*X7||U8", "omegad9*X8||U10", "omegad11*X10||U12", "omegad9*X10||U11", "omegad12*X11||U13", "omegad12*X13||U14", "omegad18*X14||U15", "omegad8*X16||U16", "omegad12*X17||U17", "omegad30*X17||U18", "omegad18*X19||U19", "omegad19*X20||U20", "omegad20*X21||U21", "omegad22*X21||U22", "omegad23*X22||U24", "omegad15*X22||U23", "omegad24*X23||U25", "omegad25*X24||U26", "omegad27*X26||U29", "omegad16*X26||U27", "omegad25*X26||U28", "omegad27*X28||U30", "omegad28*X29||U31", "omegad30*X29||U32", "omegad32*X31||U34", "omegad30*X31||U33", "omegad39*X33||U36", "omegad20*X33||U35", "omegad24*X34||U37", "omegad47*X35||U39", "omegad28*X35||U38", "omegad51*X36||U41", "omegad32*X36||U40", "omegad38*X37||U42", "omegad52*X37||U43", "omegad38*X39||U44", "omegad41*X40||U46", "omegad39*X40||U45", "omegad43*X42||U48", "omegad41*X42||U47", "omegad34*X43||U49", "omegad43*X44||U50", "omegad46*X45||U52", "omegad44*X45||U51", "omegad47*X46||U53", "omegad47*X48||U54", "omegad49*X48||U55", "omegad49*X50||U56", "omegad51*X50||U57", "omegad60*X53||U59", "omegad41*X53||U58", "omegad64*X54||U61", "omegad45*X54||U60", "omegad49*X55||U62", "omegad52*X56||U63", "omegad58*X57||U65", "omegad56*X57||U64", "omegad71*X58||U67", "omegad59*X58||U66", "omegad60*X59||U68", "omegad61*X60||U69", "omegad62*X61||U70", "omegad62*X63||U71", "omegad64*X63||U72", "omegad65*X64||U73", "omegad67*X66||U75", "omegad65*X66||U74", "omegad68*X67||U76", "omegad69*X68||U78", "omegad55*X68||U77", "omegad70*X69||U79", "omegad74*X70||U80", "omegad81*X72||U82", "omegad62*X72||U81", "omegad66*X73||U83", "omegad85*X73||U84", "omegad90*X75||U86", "omegad76*X75||U85", "omegad77*X76||U87", "omegad78*X77||U89", "omegad71*X77||U88", "omegad78*X79||U90", "omegad81*X80||U92", "omegad79*X80||U91", "omegad83*X82||U94", "omegad81*X82||U93", "omegad83*X84||U95", "omegad84*X85||U96", "omegad86*X85||U97", "omegad86*X87||U98", "omegad93*X87||U99", "omegad87*X88||U100", "omegad89*X88||U101", "omegad74*X89||U102", "omegad98*X91||U104", "omegad79*X91||U103", "omegad83*X92||U105", "omegad102*X92||U106", "omegad106*X93||U107", "omegad90*X94||U108", "omegad95*X94||U109", "omegad95*X96||U110", "omegad109*X96||U112", "omegad97*X96||U111", "omegad98*X97||U113", "omegad99*X98||U114", "omegad110*X100||U116", "omegad99*X100||U115", "omegad102*X101||U118", "omegad100*X101||U117", "omegad104*X103||U120", "omegad102*X103||U119", "omegad106*X105||U122", "omegad104*X105||U121", "omegad108*X107||U124", "omegad106*X107||U123", "omegad112*X108||U125", "omegad114*X109||U126", "omegad118*X110||U127", "omegad122*X111||U129", "omegad104*X111||U128", "omegad115*X114||U131", "omegad113*X114||U130", "omegad117*X116||U133", "omegad115*X116||U132", "omegad118*X117||U134", "omegad119*X118||U135", "omegad120*X119||U136", "omegad120*X121||U137", "omegad121*X122||U138", "omegad123*X122||U139", "omegad124*X123||U140", "omegad126*X125||U142", "omegad124*X125||U141", "omegad112*X126||U143"], "osc": {}, "qub": {"0": 3, "1": 3, "2": 3, "3": 3, "4": 3, "5": 3, "6": 3, "7": 3, "8": 3, "9": 3, "10": 3, "11": 3, "12": 3, "13": 3, "14": 3, "15": 3, "16": 3, "17": 3, "18": 3, "19": 3, "20": 3, "21": 3, "22": 3, "23": 3, "24": 3, "25": 3, "26": 3, "27": 3, "28": 3, "29": 3, "30": 3, "31": 3, "32": 3, "33": 3, "34": 3, "35": 3, "36": 3, "37": 3, "38": 3, "39": 3, "40": 3, "41": 3, "42": 3, "43": 3, "44": 3, "45": 3, "46": 3, "47": 3, "48": 3, "49": 3, "50": 3, "51": 3, "52": 3, "53": 3, "54": 3, "55": 3, "56": 3, "57": 3, "58": 3, "59": 3, "60": 3, "61": 3, "62": 3, "63": 3, "64": 3, "65": 3, "66": 3, "67": 3, "68": 3, "69": 3, "70": 3, "71": 3, "72": 3, "73": 3, "74": 3, "75": 3, "76": 3, "77": 3, "78": 3, "79": 3, "80": 3, "81": 3, "82": 3, "83": 3, "84": 3, "85": 3, "86": 3, "87": 3, "88": 3, "89": 3, "90": 3, "91": 3, "92": 3, "93": 3, "94": 3, "95": 3, "96": 3, "97": 3, "98": 3, "99": 3, "100": 3, "101": 3, "102": 3, "103": 3, "104": 3, "105": 3, "106": 3, "107": 3, "108": 3, "109": 3, "110": 3, "111": 3, "112": 3, "113": 3, "114": 3, "115": 3, "116": 3, "117": 3, "118": 3, "119": 3, "120": 3, "121": 3, "122": 3, "123": 3, 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file diff --git a/qiskit_ibm_runtime/fake_provider/backends/kyiv/fake_kyiv.py b/qiskit_ibm_runtime/fake_provider/backends/kyiv/fake_kyiv.py new file mode 100644 index 000000000..31cd7c662 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kyiv/fake_kyiv.py @@ -0,0 +1,28 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Kyiv device (127 qubit). +""" + +import os +from qiskit_ibm_runtime.fake_provider import fake_backend + + +class FakeKyiv(fake_backend.FakeBackendV2): + """A fake 127 qubit backend.""" + + dirname = os.path.dirname(__file__) # type: ignore + conf_filename = "conf_kyiv.json" # type: ignore + props_filename = "props_kyiv.json" # type: ignore + defs_filename = "defs_kyiv.json" # type: ignore + backend_name = "fake_kyiv" # type: ignore diff --git a/qiskit_ibm_runtime/fake_provider/backends/kyiv/props_kyiv.json b/qiskit_ibm_runtime/fake_provider/backends/kyiv/props_kyiv.json new file mode 100644 index 000000000..ba22f07d9 --- 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"general_qlists": [{"name": "lf_100", "qubits": [89, 74, 70, 69, 68, 67, 66, 73, 85, 84, 83, 82, 81, 80, 79, 91, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 112, 126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 109, 96, 95, 94, 90, 75, 76, 77, 71, 58, 57, 56, 52, 37, 38, 39, 40, 41, 53, 60, 61, 62, 63, 64, 54, 45, 44, 43, 34, 24, 25, 26, 27, 28, 35, 47, 48, 49, 50, 51, 36, 32, 31, 30, 17, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 14]}]} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/kyoto/__init__.py b/qiskit_ibm_runtime/fake_provider/backends/kyoto/__init__.py new file mode 100644 index 000000000..3d7096225 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kyoto/__init__.py @@ -0,0 +1,17 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Kyoto backend (127 qubit). +""" + +from .fake_kyoto import FakeKyoto diff --git a/qiskit_ibm_runtime/fake_provider/backends/kyoto/conf_kyoto.json b/qiskit_ibm_runtime/fake_provider/backends/kyoto/conf_kyoto.json new file mode 100644 index 000000000..41cc56a9e --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kyoto/conf_kyoto.json @@ -0,0 +1 @@ +{"backend_name": "ibm_kyoto", "backend_version": "1.2.29", "n_qubits": 127, "basis_gates": ["ecr", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], 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61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]], "acquisition_latency": [], "conditional_latency": [], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{126}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{62,72}(\\sigma_{62}^{+}\\sigma_{72}^{-}+\\sigma_{62}^{-}\\sigma_{72}^{+}) + J_{67,68}(\\sigma_{67}^{+}\\sigma_{68}^{-}+\\sigma_{67}^{-}\\sigma_{68}^{+}) + J_{44,45}(\\sigma_{44}^{+}\\sigma_{45}^{-}+\\sigma_{44}^{-}\\sigma_{45}^{+}) + J_{99,100}(\\sigma_{99}^{+}\\sigma_{100}^{-}+\\sigma_{99}^{-}\\sigma_{100}^{+}) \\\\ & + J_{108,112}(\\sigma_{108}^{+}\\sigma_{112}^{-}+\\sigma_{108}^{-}\\sigma_{112}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{40,41}(\\sigma_{40}^{+}\\sigma_{41}^{-}+\\sigma_{40}^{-}\\sigma_{41}^{+}) + J_{0,14}(\\sigma_{0}^{+}\\sigma_{14}^{-}+\\sigma_{0}^{-}\\sigma_{14}^{+}) \\\\ & + J_{17,30}(\\sigma_{17}^{+}\\sigma_{30}^{-}+\\sigma_{17}^{-}\\sigma_{30}^{+}) + J_{100,101}(\\sigma_{100}^{+}\\sigma_{101}^{-}+\\sigma_{100}^{-}\\sigma_{101}^{+}) + J_{91,98}(\\sigma_{91}^{+}\\sigma_{98}^{-}+\\sigma_{91}^{-}\\sigma_{98}^{+}) + J_{100,110}(\\sigma_{100}^{+}\\sigma_{110}^{-}+\\sigma_{100}^{-}\\sigma_{110}^{+}) \\\\ & + J_{75,90}(\\sigma_{75}^{+}\\sigma_{90}^{-}+\\sigma_{75}^{-}\\sigma_{90}^{+}) + J_{96,97}(\\sigma_{96}^{+}\\sigma_{97}^{-}+\\sigma_{96}^{-}\\sigma_{97}^{+}) + J_{41,42}(\\sigma_{41}^{+}\\sigma_{42}^{-}+\\sigma_{41}^{-}\\sigma_{42}^{+}) + J_{18,19}(\\sigma_{18}^{+}\\sigma_{19}^{-}+\\sigma_{18}^{-}\\sigma_{19}^{+}) \\\\ & + J_{55,68}(\\sigma_{55}^{+}\\sigma_{68}^{-}+\\sigma_{55}^{-}\\sigma_{68}^{+}) + J_{9,10}(\\sigma_{9}^{+}\\sigma_{10}^{-}+\\sigma_{9}^{-}\\sigma_{10}^{+}) + J_{49,55}(\\sigma_{49}^{+}\\sigma_{55}^{-}+\\sigma_{49}^{-}\\sigma_{55}^{+}) + J_{106,107}(\\sigma_{106}^{+}\\sigma_{107}^{-}+\\sigma_{106}^{-}\\sigma_{107}^{+}) \\\\ & + J_{47,48}(\\sigma_{47}^{+}\\sigma_{48}^{-}+\\sigma_{47}^{-}\\sigma_{48}^{+}) + J_{42,43}(\\sigma_{42}^{+}\\sigma_{43}^{-}+\\sigma_{42}^{-}\\sigma_{43}^{+}) + J_{107,108}(\\sigma_{107}^{+}\\sigma_{108}^{-}+\\sigma_{107}^{-}\\sigma_{108}^{+}) + J_{73,85}(\\sigma_{73}^{+}\\sigma_{85}^{-}+\\sigma_{73}^{-}\\sigma_{85}^{+}) \\\\ & + J_{38,39}(\\sigma_{38}^{+}\\sigma_{39}^{-}+\\sigma_{38}^{-}\\sigma_{39}^{+}) + J_{20,33}(\\sigma_{20}^{+}\\sigma_{33}^{-}+\\sigma_{20}^{-}\\sigma_{33}^{+}) + J_{48,49}(\\sigma_{48}^{+}\\sigma_{49}^{-}+\\sigma_{48}^{-}\\sigma_{49}^{+}) + J_{103,104}(\\sigma_{103}^{+}\\sigma_{104}^{-}+\\sigma_{103}^{-}\\sigma_{104}^{+}) \\\\ & + J_{80,81}(\\sigma_{80}^{+}\\sigma_{81}^{-}+\\sigma_{80}^{-}\\sigma_{81}^{+}) + J_{75,76}(\\sigma_{75}^{+}\\sigma_{76}^{-}+\\sigma_{75}^{-}\\sigma_{76}^{+}) + J_{66,73}(\\sigma_{66}^{+}\\sigma_{73}^{-}+\\sigma_{66}^{-}\\sigma_{73}^{+}) + J_{85,86}(\\sigma_{85}^{+}\\sigma_{86}^{-}+\\sigma_{85}^{-}\\sigma_{86}^{+}) \\\\ & + J_{81,82}(\\sigma_{81}^{+}\\sigma_{82}^{-}+\\sigma_{81}^{-}\\sigma_{82}^{+}) + J_{110,118}(\\sigma_{110}^{+}\\sigma_{118}^{-}+\\sigma_{110}^{-}\\sigma_{118}^{+}) + J_{16,26}(\\sigma_{16}^{+}\\sigma_{26}^{-}+\\sigma_{16}^{-}\\sigma_{26}^{+}) + J_{90,94}(\\sigma_{90}^{+}\\sigma_{94}^{-}+\\sigma_{90}^{-}\\sigma_{94}^{+}) \\\\ & + J_{118,119}(\\sigma_{118}^{+}\\sigma_{119}^{-}+\\sigma_{118}^{-}\\sigma_{119}^{+}) + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{22,23}(\\sigma_{22}^{+}\\sigma_{23}^{-}+\\sigma_{22}^{-}\\sigma_{23}^{+}) + J_{77,78}(\\sigma_{77}^{+}\\sigma_{78}^{-}+\\sigma_{77}^{-}\\sigma_{78}^{+}) \\\\ & + J_{49,50}(\\sigma_{49}^{+}\\sigma_{50}^{-}+\\sigma_{49}^{-}\\sigma_{50}^{+}) + J_{104,105}(\\sigma_{104}^{+}\\sigma_{105}^{-}+\\sigma_{104}^{-}\\sigma_{105}^{+}) + J_{114,115}(\\sigma_{114}^{+}\\sigma_{115}^{-}+\\sigma_{114}^{-}\\sigma_{115}^{+}) + J_{45,46}(\\sigma_{45}^{+}\\sigma_{46}^{-}+\\sigma_{45}^{-}\\sigma_{46}^{+}) \\\\ & + J_{50,51}(\\sigma_{50}^{+}\\sigma_{51}^{-}+\\sigma_{50}^{-}\\sigma_{51}^{+}) + J_{105,106}(\\sigma_{105}^{+}\\sigma_{106}^{-}+\\sigma_{105}^{-}\\sigma_{106}^{+}) + J_{72,81}(\\sigma_{72}^{+}\\sigma_{81}^{-}+\\sigma_{72}^{-}\\sigma_{81}^{+}) + J_{82,83}(\\sigma_{82}^{+}\\sigma_{83}^{-}+\\sigma_{82}^{-}\\sigma_{83}^{+}) \\\\ & + J_{46,47}(\\sigma_{46}^{+}\\sigma_{47}^{-}+\\sigma_{46}^{-}\\sigma_{47}^{+}) + J_{78,79}(\\sigma_{78}^{+}\\sigma_{79}^{-}+\\sigma_{78}^{-}\\sigma_{79}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) + J_{83,84}(\\sigma_{83}^{+}\\sigma_{84}^{-}+\\sigma_{83}^{-}\\sigma_{84}^{+}) \\\\ & + J_{115,116}(\\sigma_{115}^{+}\\sigma_{116}^{-}+\\sigma_{115}^{-}\\sigma_{116}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) + J_{79,80}(\\sigma_{79}^{+}\\sigma_{80}^{-}+\\sigma_{79}^{-}\\sigma_{80}^{+}) \\\\ & + J_{56,57}(\\sigma_{56}^{+}\\sigma_{57}^{-}+\\sigma_{56}^{-}\\sigma_{57}^{+}) + J_{93,106}(\\sigma_{93}^{+}\\sigma_{106}^{-}+\\sigma_{93}^{-}\\sigma_{106}^{+}) + J_{116,117}(\\sigma_{116}^{+}\\sigma_{117}^{-}+\\sigma_{116}^{-}\\sigma_{117}^{+}) + J_{20,21}(\\sigma_{20}^{+}\\sigma_{21}^{-}+\\sigma_{20}^{-}\\sigma_{21}^{+}) \\\\ & + J_{12,17}(\\sigma_{12}^{+}\\sigma_{17}^{-}+\\sigma_{12}^{-}\\sigma_{17}^{+}) + J_{41,53}(\\sigma_{41}^{+}\\sigma_{53}^{-}+\\sigma_{41}^{-}\\sigma_{53}^{+}) + J_{57,58}(\\sigma_{57}^{+}\\sigma_{58}^{-}+\\sigma_{57}^{-}\\sigma_{58}^{+}) + J_{87,93}(\\sigma_{87}^{+}\\sigma_{93}^{-}+\\sigma_{87}^{-}\\sigma_{93}^{+}) \\\\ & + J_{30,31}(\\sigma_{30}^{+}\\sigma_{31}^{-}+\\sigma_{30}^{-}\\sigma_{31}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) + J_{79,91}(\\sigma_{79}^{+}\\sigma_{91}^{-}+\\sigma_{79}^{-}\\sigma_{91}^{+}) + J_{26,27}(\\sigma_{26}^{+}\\sigma_{27}^{-}+\\sigma_{26}^{-}\\sigma_{27}^{+}) \\\\ & + J_{21,22}(\\sigma_{21}^{+}\\sigma_{22}^{-}+\\sigma_{21}^{-}\\sigma_{22}^{+}) + J_{58,71}(\\sigma_{58}^{+}\\sigma_{71}^{-}+\\sigma_{58}^{-}\\sigma_{71}^{+}) + J_{31,32}(\\sigma_{31}^{+}\\sigma_{32}^{-}+\\sigma_{31}^{-}\\sigma_{32}^{+}) + J_{4,15}(\\sigma_{4}^{+}\\sigma_{15}^{-}+\\sigma_{4}^{-}\\sigma_{15}^{+}) \\\\ & + J_{86,87}(\\sigma_{86}^{+}\\sigma_{87}^{-}+\\sigma_{86}^{-}\\sigma_{87}^{+}) + J_{113,114}(\\sigma_{113}^{+}\\sigma_{114}^{-}+\\sigma_{113}^{-}\\sigma_{114}^{+}) + J_{104,111}(\\sigma_{104}^{+}\\sigma_{111}^{-}+\\sigma_{104}^{-}\\sigma_{111}^{+}) + J_{123,124}(\\sigma_{123}^{+}\\sigma_{124}^{-}+\\sigma_{123}^{-}\\sigma_{124}^{+}) \\\\ & + J_{27,28}(\\sigma_{27}^{+}\\sigma_{28}^{-}+\\sigma_{27}^{-}\\sigma_{28}^{+}) + J_{34,43}(\\sigma_{34}^{+}\\sigma_{43}^{-}+\\sigma_{34}^{-}\\sigma_{43}^{+}) + J_{64,65}(\\sigma_{64}^{+}\\sigma_{65}^{-}+\\sigma_{64}^{-}\\sigma_{65}^{+}) + J_{119,120}(\\sigma_{119}^{+}\\sigma_{120}^{-}+\\sigma_{119}^{-}\\sigma_{120}^{+}) \\\\ & + J_{54,64}(\\sigma_{54}^{+}\\sigma_{64}^{-}+\\sigma_{54}^{-}\\sigma_{64}^{+}) + J_{32,36}(\\sigma_{32}^{+}\\sigma_{36}^{-}+\\sigma_{32}^{-}\\sigma_{36}^{+}) + J_{60,61}(\\sigma_{60}^{+}\\sigma_{61}^{-}+\\sigma_{60}^{-}\\sigma_{61}^{+}) + J_{5,6}(\\sigma_{5}^{+}\\sigma_{6}^{-}+\\sigma_{5}^{-}\\sigma_{6}^{+}) \\\\ & + J_{14,18}(\\sigma_{14}^{+}\\sigma_{18}^{-}+\\sigma_{14}^{-}\\sigma_{18}^{+}) + J_{87,88}(\\sigma_{87}^{+}\\sigma_{88}^{-}+\\sigma_{87}^{-}\\sigma_{88}^{+}) + J_{97,98}(\\sigma_{97}^{+}\\sigma_{98}^{-}+\\sigma_{97}^{-}\\sigma_{98}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) \\\\ & + J_{112,126}(\\sigma_{112}^{+}\\sigma_{126}^{-}+\\sigma_{112}^{-}\\sigma_{126}^{+}) + J_{28,29}(\\sigma_{28}^{+}\\sigma_{29}^{-}+\\sigma_{28}^{-}\\sigma_{29}^{+}) + J_{45,54}(\\sigma_{45}^{+}\\sigma_{54}^{-}+\\sigma_{45}^{-}\\sigma_{54}^{+}) + J_{36,51}(\\sigma_{36}^{+}\\sigma_{51}^{-}+\\sigma_{36}^{-}\\sigma_{51}^{+}) \\\\ & + J_{88,89}(\\sigma_{88}^{+}\\sigma_{89}^{-}+\\sigma_{88}^{-}\\sigma_{89}^{+}) + J_{120,121}(\\sigma_{120}^{+}\\sigma_{121}^{-}+\\sigma_{120}^{-}\\sigma_{121}^{+}) + J_{15,22}(\\sigma_{15}^{+}\\sigma_{22}^{-}+\\sigma_{15}^{-}\\sigma_{22}^{+}) + J_{24,34}(\\sigma_{24}^{+}\\sigma_{34}^{-}+\\sigma_{24}^{-}\\sigma_{34}^{+}) \\\\ & + J_{29,30}(\\sigma_{29}^{+}\\sigma_{30}^{-}+\\sigma_{29}^{-}\\sigma_{30}^{+}) + J_{84,85}(\\sigma_{84}^{+}\\sigma_{85}^{-}+\\sigma_{84}^{-}\\sigma_{85}^{+}) + J_{61,62}(\\sigma_{61}^{+}\\sigma_{62}^{-}+\\sigma_{61}^{-}\\sigma_{62}^{+}) + J_{70,74}(\\sigma_{70}^{+}\\sigma_{74}^{-}+\\sigma_{70}^{-}\\sigma_{74}^{+}) \\\\ & + J_{121,122}(\\sigma_{121}^{+}\\sigma_{122}^{-}+\\sigma_{121}^{-}\\sigma_{122}^{+}) + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{122,123}(\\sigma_{122}^{+}\\sigma_{123}^{-}+\\sigma_{122}^{-}\\sigma_{123}^{+}) + J_{117,118}(\\sigma_{117}^{+}\\sigma_{118}^{-}+\\sigma_{117}^{-}\\sigma_{118}^{+}) \\\\ & + J_{62,63}(\\sigma_{62}^{+}\\sigma_{63}^{-}+\\sigma_{62}^{-}\\sigma_{63}^{+}) + J_{94,95}(\\sigma_{94}^{+}\\sigma_{95}^{-}+\\sigma_{94}^{-}\\sigma_{95}^{+}) + J_{109,114}(\\sigma_{109}^{+}\\sigma_{114}^{-}+\\sigma_{109}^{-}\\sigma_{114}^{+}) + J_{37,52}(\\sigma_{37}^{+}\\sigma_{52}^{-}+\\sigma_{37}^{-}\\sigma_{52}^{+}) \\\\ & + J_{3,4}(\\sigma_{3}^{+}\\sigma_{4}^{-}+\\sigma_{3}^{-}\\sigma_{4}^{+}) + J_{58,59}(\\sigma_{58}^{+}\\sigma_{59}^{-}+\\sigma_{58}^{-}\\sigma_{59}^{+}) + J_{33,39}(\\sigma_{33}^{+}\\sigma_{39}^{-}+\\sigma_{33}^{-}\\sigma_{39}^{+}) + J_{95,96}(\\sigma_{95}^{+}\\sigma_{96}^{-}+\\sigma_{95}^{-}\\sigma_{96}^{+}) \\\\ & + J_{68,69}(\\sigma_{68}^{+}\\sigma_{69}^{-}+\\sigma_{68}^{-}\\sigma_{69}^{+}) + J_{63,64}(\\sigma_{63}^{+}\\sigma_{64}^{-}+\\sigma_{63}^{-}\\sigma_{64}^{+}) + J_{71,77}(\\sigma_{71}^{+}\\sigma_{77}^{-}+\\sigma_{71}^{-}\\sigma_{77}^{+}) + J_{111,122}(\\sigma_{111}^{+}\\sigma_{122}^{-}+\\sigma_{111}^{-}\\sigma_{122}^{+}) \\\\ & + J_{4,5}(\\sigma_{4}^{+}\\sigma_{5}^{-}+\\sigma_{4}^{-}\\sigma_{5}^{+}) + J_{59,60}(\\sigma_{59}^{+}\\sigma_{60}^{-}+\\sigma_{59}^{-}\\sigma_{60}^{+}) + J_{96,109}(\\sigma_{96}^{+}\\sigma_{109}^{-}+\\sigma_{96}^{-}\\sigma_{109}^{+}) + J_{124,125}(\\sigma_{124}^{+}\\sigma_{125}^{-}+\\sigma_{124}^{-}\\sigma_{125}^{+}) \\\\ & + J_{69,70}(\\sigma_{69}^{+}\\sigma_{70}^{-}+\\sigma_{69}^{-}\\sigma_{70}^{+}) + J_{35,47}(\\sigma_{35}^{+}\\sigma_{47}^{-}+\\sigma_{35}^{-}\\sigma_{47}^{+}) + J_{101,102}(\\sigma_{101}^{+}\\sigma_{102}^{-}+\\sigma_{101}^{-}\\sigma_{102}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) \\\\ & + J_{65,66}(\\sigma_{65}^{+}\\sigma_{66}^{-}+\\sigma_{65}^{-}\\sigma_{66}^{+}) + J_{10,11}(\\sigma_{10}^{+}\\sigma_{11}^{-}+\\sigma_{10}^{-}\\sigma_{11}^{+}) + J_{37,38}(\\sigma_{37}^{+}\\sigma_{38}^{-}+\\sigma_{37}^{-}\\sigma_{38}^{+}) + J_{28,35}(\\sigma_{28}^{+}\\sigma_{35}^{-}+\\sigma_{28}^{-}\\sigma_{35}^{+}) \\\\ & + J_{102,103}(\\sigma_{102}^{+}\\sigma_{103}^{-}+\\sigma_{102}^{-}\\sigma_{103}^{+}) + J_{92,102}(\\sigma_{92}^{+}\\sigma_{102}^{-}+\\sigma_{92}^{-}\\sigma_{102}^{+}) + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{98,99}(\\sigma_{98}^{+}\\sigma_{99}^{-}+\\sigma_{98}^{-}\\sigma_{99}^{+}) \\\\ & + J_{43,44}(\\sigma_{43}^{+}\\sigma_{44}^{-}+\\sigma_{43}^{-}\\sigma_{44}^{+}) + J_{52,56}(\\sigma_{52}^{+}\\sigma_{56}^{-}+\\sigma_{52}^{-}\\sigma_{56}^{+}) + J_{125,126}(\\sigma_{125}^{+}\\sigma_{126}^{-}+\\sigma_{125}^{-}\\sigma_{126}^{+}) + J_{39,40}(\\sigma_{39}^{+}\\sigma_{40}^{-}+\\sigma_{39}^{-}\\sigma_{40}^{+}) \\\\ & + J_{8,16}(\\sigma_{8}^{+}\\sigma_{16}^{-}+\\sigma_{8}^{-}\\sigma_{16}^{+}) + J_{66,67}(\\sigma_{66}^{+}\\sigma_{67}^{-}+\\sigma_{66}^{-}\\sigma_{67}^{+}) + J_{11,12}(\\sigma_{11}^{+}\\sigma_{12}^{-}+\\sigma_{11}^{-}\\sigma_{12}^{+}) + J_{76,77}(\\sigma_{76}^{+}\\sigma_{77}^{-}+\\sigma_{76}^{-}\\sigma_{77}^{+}) \\\\ & + J_{83,92}(\\sigma_{83}^{+}\\sigma_{92}^{-}+\\sigma_{83}^{-}\\sigma_{92}^{+}) + J_{74,89}(\\sigma_{74}^{+}\\sigma_{89}^{-}+\\sigma_{74}^{-}\\sigma_{89}^{+}) + J_{7,8}(\\sigma_{7}^{+}\\sigma_{8}^{-}+\\sigma_{7}^{-}\\sigma_{8}^{+}) + J_{53,60}(\\sigma_{53}^{+}\\sigma_{60}^{-}+\\sigma_{53}^{-}\\sigma_{60}^{+}) \\\\ & + \\Omega_{d,0}(U_{0}^{(0,14)}(t))\\sigma_{0}^{X} + \\Omega_{d,1}(U_{1}^{(1,0)}(t)+U_{2}^{(1,2)}(t))\\sigma_{1}^{X} \\\\ & + \\Omega_{d,3}(U_{3}^{(3,2)}(t))\\sigma_{3}^{X} + \\Omega_{d,4}(U_{5}^{(4,5)}(t)+U_{4}^{(4,3)}(t))\\sigma_{4}^{X} \\\\ & + \\Omega_{d,6}(U_{6}^{(6,5)}(t))\\sigma_{6}^{X} + \\Omega_{d,7}(U_{7}^{(7,6)}(t))\\sigma_{7}^{X} \\\\ & + \\Omega_{d,8}(U_{8}^{(8,7)}(t)+U_{10}^{(8,16)}(t)+U_{9}^{(8,9)}(t))\\sigma_{8}^{X} + \\Omega_{d,9}(U_{11}^{(9,10)}(t))\\sigma_{9}^{X} \\\\ & + \\Omega_{d,11}(U_{12}^{(11,10)}(t)+U_{13}^{(11,12)}(t))\\sigma_{11}^{X} + \\Omega_{d,12}(U_{14}^{(12,13)}(t))\\sigma_{12}^{X} \\\\ & + \\Omega_{d,15}(U_{15}^{(15,4)}(t))\\sigma_{15}^{X} + \\Omega_{d,16}(U_{16}^{(16,26)}(t))\\sigma_{16}^{X} \\\\ & + \\Omega_{d,17}(U_{17}^{(17,12)}(t)+U_{18}^{(17,30)}(t))\\sigma_{17}^{X} + \\Omega_{d,18}(U_{19}^{(18,14)}(t)+U_{20}^{(18,19)}(t))\\sigma_{18}^{X} \\\\ & + \\Omega_{d,19}(U_{21}^{(19,20)}(t))\\sigma_{19}^{X} + \\Omega_{d,21}(U_{22}^{(21,20)}(t))\\sigma_{21}^{X} \\\\ & + \\Omega_{d,22}(U_{25}^{(22,23)}(t)+U_{24}^{(22,21)}(t)+U_{23}^{(22,15)}(t))\\sigma_{22}^{X} + \\Omega_{d,23}(U_{26}^{(23,24)}(t))\\sigma_{23}^{X} \\\\ & + \\Omega_{d,25}(U_{28}^{(25,26)}(t)+U_{27}^{(25,24)}(t))\\sigma_{25}^{X} + \\Omega_{d,27}(U_{29}^{(27,26)}(t)+U_{30}^{(27,28)}(t))\\sigma_{27}^{X} \\\\ & + \\Omega_{d,28}(U_{31}^{(28,29)}(t)+U_{32}^{(28,35)}(t))\\sigma_{28}^{X} + \\Omega_{d,30}(U_{33}^{(30,29)}(t)+U_{34}^{(30,31)}(t))\\sigma_{30}^{X} \\\\ & + \\Omega_{d,31}(U_{35}^{(31,32)}(t))\\sigma_{31}^{X} + \\Omega_{d,32}(U_{36}^{(32,36)}(t))\\sigma_{32}^{X} \\\\ & + \\Omega_{d,33}(U_{37}^{(33,20)}(t)+U_{38}^{(33,39)}(t))\\sigma_{33}^{X} + \\Omega_{d,34}(U_{40}^{(34,43)}(t)+U_{39}^{(34,24)}(t))\\sigma_{34}^{X} \\\\ & + \\Omega_{d,37}(U_{41}^{(37,38)}(t))\\sigma_{37}^{X} + \\Omega_{d,38}(U_{42}^{(38,39)}(t))\\sigma_{38}^{X} \\\\ & + \\Omega_{d,39}(U_{43}^{(39,40)}(t))\\sigma_{39}^{X} + \\Omega_{d,40}(U_{44}^{(40,41)}(t))\\sigma_{40}^{X} \\\\ & + \\Omega_{d,42}(U_{45}^{(42,41)}(t))\\sigma_{42}^{X} + \\Omega_{d,43}(U_{46}^{(43,42)}(t))\\sigma_{43}^{X} \\\\ & + \\Omega_{d,44}(U_{48}^{(44,45)}(t)+U_{47}^{(44,43)}(t))\\sigma_{44}^{X} + \\Omega_{d,46}(U_{49}^{(46,45)}(t))\\sigma_{46}^{X} \\\\ & + \\Omega_{d,47}(U_{50}^{(47,35)}(t)+U_{51}^{(47,46)}(t))\\sigma_{47}^{X} + \\Omega_{d,48}(U_{52}^{(48,47)}(t))\\sigma_{48}^{X} \\\\ & + \\Omega_{d,49}(U_{54}^{(49,55)}(t)+U_{53}^{(49,48)}(t))\\sigma_{49}^{X} + \\Omega_{d,50}(U_{56}^{(50,51)}(t)+U_{55}^{(50,49)}(t))\\sigma_{50}^{X} \\\\ & + \\Omega_{d,51}(U_{57}^{(51,36)}(t))\\sigma_{51}^{X} + \\Omega_{d,52}(U_{58}^{(52,37)}(t))\\sigma_{52}^{X} \\\\ & + \\Omega_{d,53}(U_{60}^{(53,60)}(t)+U_{59}^{(53,41)}(t))\\sigma_{53}^{X} + \\Omega_{d,54}(U_{62}^{(54,64)}(t)+U_{61}^{(54,45)}(t))\\sigma_{54}^{X} \\\\ & + \\Omega_{d,55}(U_{63}^{(55,68)}(t))\\sigma_{55}^{X} + \\Omega_{d,56}(U_{64}^{(56,52)}(t))\\sigma_{56}^{X} \\\\ & + \\Omega_{d,57}(U_{66}^{(57,58)}(t)+U_{65}^{(57,56)}(t))\\sigma_{57}^{X} + \\Omega_{d,59}(U_{68}^{(59,60)}(t)+U_{67}^{(59,58)}(t))\\sigma_{59}^{X} \\\\ & + \\Omega_{d,61}(U_{69}^{(61,60)}(t))\\sigma_{61}^{X} + \\Omega_{d,62}(U_{71}^{(62,63)}(t)+U_{70}^{(62,61)}(t))\\sigma_{62}^{X} \\\\ & + \\Omega_{d,63}(U_{72}^{(63,64)}(t))\\sigma_{63}^{X} + \\Omega_{d,64}(U_{73}^{(64,65)}(t))\\sigma_{64}^{X} \\\\ & + \\Omega_{d,65}(U_{74}^{(65,66)}(t))\\sigma_{65}^{X} + \\Omega_{d,67}(U_{75}^{(67,66)}(t)+U_{76}^{(67,68)}(t))\\sigma_{67}^{X} \\\\ & + \\Omega_{d,68}(U_{77}^{(68,69)}(t))\\sigma_{68}^{X} + \\Omega_{d,70}(U_{78}^{(70,69)}(t))\\sigma_{70}^{X} \\\\ & + \\Omega_{d,71}(U_{79}^{(71,58)}(t))\\sigma_{71}^{X} + \\Omega_{d,72}(U_{80}^{(72,62)}(t))\\sigma_{72}^{X} \\\\ & + \\Omega_{d,73}(U_{82}^{(73,85)}(t)+U_{81}^{(73,66)}(t))\\sigma_{73}^{X} + \\Omega_{d,74}(U_{83}^{(74,70)}(t))\\sigma_{74}^{X} \\\\ & + \\Omega_{d,75}(U_{84}^{(75,90)}(t))\\sigma_{75}^{X} + \\Omega_{d,76}(U_{86}^{(76,77)}(t)+U_{85}^{(76,75)}(t))\\sigma_{76}^{X} \\\\ & + \\Omega_{d,77}(U_{88}^{(77,78)}(t)+U_{87}^{(77,71)}(t))\\sigma_{77}^{X} + \\Omega_{d,79}(U_{90}^{(79,91)}(t)+U_{89}^{(79,78)}(t))\\sigma_{79}^{X} \\\\ & + \\Omega_{d,80}(U_{91}^{(80,79)}(t))\\sigma_{80}^{X} + \\Omega_{d,81}(U_{93}^{(81,80)}(t)+U_{92}^{(81,72)}(t))\\sigma_{81}^{X} \\\\ & + \\Omega_{d,82}(U_{95}^{(82,83)}(t)+U_{94}^{(82,81)}(t))\\sigma_{82}^{X} + \\Omega_{d,83}(U_{96}^{(83,92)}(t))\\sigma_{83}^{X} \\\\ & + \\Omega_{d,84}(U_{97}^{(84,83)}(t)+U_{98}^{(84,85)}(t))\\sigma_{84}^{X} + \\Omega_{d,86}(U_{99}^{(86,85)}(t))\\sigma_{86}^{X} \\\\ & + \\Omega_{d,87}(U_{100}^{(87,86)}(t)+U_{101}^{(87,93)}(t))\\sigma_{87}^{X} + \\Omega_{d,88}(U_{102}^{(88,87)}(t))\\sigma_{88}^{X} \\\\ & + \\Omega_{d,89}(U_{104}^{(89,88)}(t)+U_{103}^{(89,74)}(t))\\sigma_{89}^{X} + \\Omega_{d,93}(U_{105}^{(93,106)}(t))\\sigma_{93}^{X} \\\\ & + \\Omega_{d,94}(U_{107}^{(94,95)}(t)+U_{106}^{(94,90)}(t))\\sigma_{94}^{X} + \\Omega_{d,96}(U_{110}^{(96,109)}(t)+U_{109}^{(96,97)}(t)+U_{108}^{(96,95)}(t))\\sigma_{96}^{X} \\\\ & + \\Omega_{d,97}(U_{111}^{(97,98)}(t))\\sigma_{97}^{X} + \\Omega_{d,98}(U_{113}^{(98,99)}(t)+U_{112}^{(98,91)}(t))\\sigma_{98}^{X} \\\\ & + \\Omega_{d,99}(U_{114}^{(99,100)}(t))\\sigma_{99}^{X} + \\Omega_{d,101}(U_{116}^{(101,102)}(t)+U_{115}^{(101,100)}(t))\\sigma_{101}^{X} \\\\ & + \\Omega_{d,102}(U_{117}^{(102,92)}(t)+U_{118}^{(102,103)}(t))\\sigma_{102}^{X} + \\Omega_{d,104}(U_{120}^{(104,111)}(t)+U_{119}^{(104,103)}(t))\\sigma_{104}^{X} \\\\ & + \\Omega_{d,105}(U_{122}^{(105,106)}(t)+U_{121}^{(105,104)}(t))\\sigma_{105}^{X} + \\Omega_{d,106}(U_{123}^{(106,107)}(t))\\sigma_{106}^{X} \\\\ & + \\Omega_{d,107}(U_{124}^{(107,108)}(t))\\sigma_{107}^{X} + \\Omega_{d,109}(U_{125}^{(109,114)}(t))\\sigma_{109}^{X} \\\\ & + \\Omega_{d,110}(U_{126}^{(110,100)}(t))\\sigma_{110}^{X} + \\Omega_{d,112}(U_{127}^{(112,108)}(t))\\sigma_{112}^{X} \\\\ & + \\Omega_{d,113}(U_{128}^{(113,114)}(t))\\sigma_{113}^{X} + \\Omega_{d,115}(U_{129}^{(115,114)}(t))\\sigma_{115}^{X} \\\\ & + \\Omega_{d,116}(U_{130}^{(116,115)}(t))\\sigma_{116}^{X} + \\Omega_{d,117}(U_{131}^{(117,116)}(t))\\sigma_{117}^{X} \\\\ & + \\Omega_{d,118}(U_{132}^{(118,110)}(t)+U_{133}^{(118,117)}(t))\\sigma_{118}^{X} + \\Omega_{d,119}(U_{134}^{(119,118)}(t))\\sigma_{119}^{X} \\\\ & + \\Omega_{d,120}(U_{135}^{(120,119)}(t))\\sigma_{120}^{X} + \\Omega_{d,121}(U_{136}^{(121,120)}(t))\\sigma_{121}^{X} \\\\ & + \\Omega_{d,122}(U_{137}^{(122,111)}(t)+U_{138}^{(122,121)}(t)+U_{139}^{(122,123)}(t))\\sigma_{122}^{X} + \\Omega_{d,124}(U_{140}^{(124,123)}(t))\\sigma_{124}^{X} \\\\ & + \\Omega_{d,125}(U_{142}^{(125,126)}(t)+U_{141}^{(125,124)}(t))\\sigma_{125}^{X} + \\Omega_{d,126}(U_{143}^{(126,112)}(t))\\sigma_{126}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,126,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,126,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,126,-delta{i}/2*O{i}]", "_SUM[i,0,126,omegad{i}*X{i}||D{i}]", "jq62q72*Sp62*Sm72", "jq62q72*Sm62*Sp72", "jq67q68*Sp67*Sm68", "jq67q68*Sm67*Sp68", "jq44q45*Sp44*Sm45", "jq44q45*Sm44*Sp45", "jq99q100*Sp99*Sm100", "jq99q100*Sm99*Sp100", "jq108q112*Sp108*Sm112", "jq108q112*Sm108*Sp112", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq40q41*Sp40*Sm41", "jq40q41*Sm40*Sp41", "jq0q14*Sp0*Sm14", "jq0q14*Sm0*Sp14", "jq17q30*Sp17*Sm30", "jq17q30*Sm17*Sp30", "jq100q101*Sp100*Sm101", "jq100q101*Sm100*Sp101", "jq91q98*Sp91*Sm98", "jq91q98*Sm91*Sp98", "jq100q110*Sp100*Sm110", "jq100q110*Sm100*Sp110", "jq75q90*Sp75*Sm90", "jq75q90*Sm75*Sp90", "jq96q97*Sp96*Sm97", "jq96q97*Sm96*Sp97", "jq41q42*Sp41*Sm42", "jq41q42*Sm41*Sp42", "jq18q19*Sp18*Sm19", "jq18q19*Sm18*Sp19", "jq55q68*Sp55*Sm68", "jq55q68*Sm55*Sp68", "jq9q10*Sp9*Sm10", "jq9q10*Sm9*Sp10", "jq49q55*Sp49*Sm55", "jq49q55*Sm49*Sp55", "jq106q107*Sp106*Sm107", "jq106q107*Sm106*Sp107", "jq47q48*Sp47*Sm48", "jq47q48*Sm47*Sp48", "jq42q43*Sp42*Sm43", "jq42q43*Sm42*Sp43", "jq107q108*Sp107*Sm108", "jq107q108*Sm107*Sp108", "jq73q85*Sp73*Sm85", "jq73q85*Sm73*Sp85", "jq38q39*Sp38*Sm39", "jq38q39*Sm38*Sp39", "jq20q33*Sp20*Sm33", "jq20q33*Sm20*Sp33", "jq48q49*Sp48*Sm49", "jq48q49*Sm48*Sp49", "jq103q104*Sp103*Sm104", "jq103q104*Sm103*Sp104", "jq80q81*Sp80*Sm81", "jq80q81*Sm80*Sp81", "jq75q76*Sp75*Sm76", "jq75q76*Sm75*Sp76", "jq66q73*Sp66*Sm73", "jq66q73*Sm66*Sp73", "jq85q86*Sp85*Sm86", "jq85q86*Sm85*Sp86", "jq81q82*Sp81*Sm82", "jq81q82*Sm81*Sp82", "jq110q118*Sp110*Sm118", "jq110q118*Sm110*Sp118", "jq16q26*Sp16*Sm26", "jq16q26*Sm16*Sp26", "jq90q94*Sp90*Sm94", "jq90q94*Sm90*Sp94", "jq118q119*Sp118*Sm119", "jq118q119*Sm118*Sp119", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq22q23*Sp22*Sm23", "jq22q23*Sm22*Sp23", "jq77q78*Sp77*Sm78", "jq77q78*Sm77*Sp78", "jq49q50*Sp49*Sm50", "jq49q50*Sm49*Sp50", "jq104q105*Sp104*Sm105", "jq104q105*Sm104*Sp105", "jq114q115*Sp114*Sm115", "jq114q115*Sm114*Sp115", "jq45q46*Sp45*Sm46", "jq45q46*Sm45*Sp46", "jq50q51*Sp50*Sm51", "jq50q51*Sm50*Sp51", "jq105q106*Sp105*Sm106", "jq105q106*Sm105*Sp106", "jq72q81*Sp72*Sm81", "jq72q81*Sm72*Sp81", "jq82q83*Sp82*Sm83", "jq82q83*Sm82*Sp83", "jq46q47*Sp46*Sm47", "jq46q47*Sm46*Sp47", "jq78q79*Sp78*Sm79", "jq78q79*Sm78*Sp79", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq83q84*Sp83*Sm84", "jq83q84*Sm83*Sp84", "jq115q116*Sp115*Sm116", "jq115q116*Sm115*Sp116", "jq19q20*Sp19*Sm20", "jq19q20*Sm19*Sp20", "jq24q25*Sp24*Sm25", "jq24q25*Sm24*Sp25", "jq79q80*Sp79*Sm80", "jq79q80*Sm79*Sp80", "jq56q57*Sp56*Sm57", "jq56q57*Sm56*Sp57", "jq93q106*Sp93*Sm106", "jq93q106*Sm93*Sp106", "jq116q117*Sp116*Sm117", "jq116q117*Sm116*Sp117", "jq20q21*Sp20*Sm21", "jq20q21*Sm20*Sp21", "jq12q17*Sp12*Sm17", "jq12q17*Sm12*Sp17", "jq41q53*Sp41*Sm53", "jq41q53*Sm41*Sp53", "jq57q58*Sp57*Sm58", "jq57q58*Sm57*Sp58", "jq87q93*Sp87*Sm93", "jq87q93*Sm87*Sp93", "jq30q31*Sp30*Sm31", "jq30q31*Sm30*Sp31", "jq25q26*Sp25*Sm26", "jq25q26*Sm25*Sp26", "jq79q91*Sp79*Sm91", "jq79q91*Sm79*Sp91", "jq26q27*Sp26*Sm27", "jq26q27*Sm26*Sp27", "jq21q22*Sp21*Sm22", "jq21q22*Sm21*Sp22", "jq58q71*Sp58*Sm71", "jq58q71*Sm58*Sp71", "jq31q32*Sp31*Sm32", "jq31q32*Sm31*Sp32", "jq4q15*Sp4*Sm15", "jq4q15*Sm4*Sp15", "jq86q87*Sp86*Sm87", "jq86q87*Sm86*Sp87", "jq113q114*Sp113*Sm114", "jq113q114*Sm113*Sp114", "jq104q111*Sp104*Sm111", "jq104q111*Sm104*Sp111", "jq123q124*Sp123*Sm124", "jq123q124*Sm123*Sp124", "jq27q28*Sp27*Sm28", "jq27q28*Sm27*Sp28", "jq34q43*Sp34*Sm43", "jq34q43*Sm34*Sp43", "jq64q65*Sp64*Sm65", "jq64q65*Sm64*Sp65", "jq119q120*Sp119*Sm120", "jq119q120*Sm119*Sp120", "jq54q64*Sp54*Sm64", "jq54q64*Sm54*Sp64", "jq32q36*Sp32*Sm36", "jq32q36*Sm32*Sp36", "jq60q61*Sp60*Sm61", "jq60q61*Sm60*Sp61", "jq5q6*Sp5*Sm6", "jq5q6*Sm5*Sp6", "jq14q18*Sp14*Sm18", "jq14q18*Sm14*Sp18", "jq87q88*Sp87*Sm88", "jq87q88*Sm87*Sp88", "jq97q98*Sp97*Sm98", "jq97q98*Sm97*Sp98", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq112q126*Sp112*Sm126", "jq112q126*Sm112*Sp126", "jq28q29*Sp28*Sm29", "jq28q29*Sm28*Sp29", "jq45q54*Sp45*Sm54", "jq45q54*Sm45*Sp54", "jq36q51*Sp36*Sm51", "jq36q51*Sm36*Sp51", "jq88q89*Sp88*Sm89", "jq88q89*Sm88*Sp89", "jq120q121*Sp120*Sm121", "jq120q121*Sm120*Sp121", "jq15q22*Sp15*Sm22", "jq15q22*Sm15*Sp22", "jq24q34*Sp24*Sm34", "jq24q34*Sm24*Sp34", "jq29q30*Sp29*Sm30", "jq29q30*Sm29*Sp30", "jq84q85*Sp84*Sm85", "jq84q85*Sm84*Sp85", "jq61q62*Sp61*Sm62", "jq61q62*Sm61*Sp62", "jq70q74*Sp70*Sm74", "jq70q74*Sm70*Sp74", "jq121q122*Sp121*Sm122", "jq121q122*Sm121*Sp122", "jq2q3*Sp2*Sm3", "jq2q3*Sm2*Sp3", "jq122q123*Sp122*Sm123", "jq122q123*Sm122*Sp123", "jq117q118*Sp117*Sm118", "jq117q118*Sm117*Sp118", "jq62q63*Sp62*Sm63", "jq62q63*Sm62*Sp63", "jq94q95*Sp94*Sm95", "jq94q95*Sm94*Sp95", "jq109q114*Sp109*Sm114", "jq109q114*Sm109*Sp114", "jq37q52*Sp37*Sm52", "jq37q52*Sm37*Sp52", "jq3q4*Sp3*Sm4", "jq3q4*Sm3*Sp4", "jq58q59*Sp58*Sm59", "jq58q59*Sm58*Sp59", "jq33q39*Sp33*Sm39", "jq33q39*Sm33*Sp39", "jq95q96*Sp95*Sm96", "jq95q96*Sm95*Sp96", "jq68q69*Sp68*Sm69", "jq68q69*Sm68*Sp69", "jq63q64*Sp63*Sm64", "jq63q64*Sm63*Sp64", "jq71q77*Sp71*Sm77", "jq71q77*Sm71*Sp77", "jq111q122*Sp111*Sm122", "jq111q122*Sm111*Sp122", "jq4q5*Sp4*Sm5", "jq4q5*Sm4*Sp5", "jq59q60*Sp59*Sm60", "jq59q60*Sm59*Sp60", "jq96q109*Sp96*Sm109", "jq96q109*Sm96*Sp109", "jq124q125*Sp124*Sm125", "jq124q125*Sm124*Sp125", "jq69q70*Sp69*Sm70", "jq69q70*Sm69*Sp70", "jq35q47*Sp35*Sm47", "jq35q47*Sm35*Sp47", "jq101q102*Sp101*Sm102", "jq101q102*Sm101*Sp102", "jq0q1*Sp0*Sm1", "jq0q1*Sm0*Sp1", "jq65q66*Sp65*Sm66", "jq65q66*Sm65*Sp66", "jq10q11*Sp10*Sm11", "jq10q11*Sm10*Sp11", "jq37q38*Sp37*Sm38", "jq37q38*Sm37*Sp38", "jq28q35*Sp28*Sm35", "jq28q35*Sm28*Sp35", "jq102q103*Sp102*Sm103", "jq102q103*Sm102*Sp103", "jq92q102*Sp92*Sm102", "jq92q102*Sm92*Sp102", "jq6q7*Sp6*Sm7", "jq6q7*Sm6*Sp7", "jq98q99*Sp98*Sm99", "jq98q99*Sm98*Sp99", "jq43q44*Sp43*Sm44", "jq43q44*Sm43*Sp44", "jq52q56*Sp52*Sm56", "jq52q56*Sm52*Sp56", "jq125q126*Sp125*Sm126", "jq125q126*Sm125*Sp126", "jq39q40*Sp39*Sm40", "jq39q40*Sm39*Sp40", "jq8q16*Sp8*Sm16", "jq8q16*Sm8*Sp16", "jq66q67*Sp66*Sm67", "jq66q67*Sm66*Sp67", "jq11q12*Sp11*Sm12", "jq11q12*Sm11*Sp12", "jq76q77*Sp76*Sm77", "jq76q77*Sm76*Sp77", "jq83q92*Sp83*Sm92", "jq83q92*Sm83*Sp92", "jq74q89*Sp74*Sm89", "jq74q89*Sm74*Sp89", "jq7q8*Sp7*Sm8", "jq7q8*Sm7*Sp8", "jq53q60*Sp53*Sm60", "jq53q60*Sm53*Sp60", "omegad14*X0||U0", "omegad0*X1||U1", "omegad2*X1||U2", "omegad2*X3||U3", "omegad5*X4||U5", "omegad3*X4||U4", "omegad5*X6||U6", "omegad6*X7||U7", "omegad7*X8||U8", "omegad16*X8||U10", "omegad9*X8||U9", "omegad10*X9||U11", "omegad10*X11||U12", "omegad12*X11||U13", "omegad13*X12||U14", "omegad4*X15||U15", "omegad26*X16||U16", "omegad12*X17||U17", "omegad30*X17||U18", "omegad14*X18||U19", "omegad19*X18||U20", "omegad20*X19||U21", "omegad20*X21||U22", "omegad23*X22||U25", "omegad21*X22||U24", "omegad15*X22||U23", "omegad24*X23||U26", "omegad26*X25||U28", "omegad24*X25||U27", "omegad26*X27||U29", "omegad28*X27||U30", "omegad29*X28||U31", "omegad35*X28||U32", "omegad29*X30||U33", "omegad31*X30||U34", "omegad32*X31||U35", "omegad36*X32||U36", "omegad20*X33||U37", "omegad39*X33||U38", "omegad43*X34||U40", "omegad24*X34||U39", "omegad38*X37||U41", "omegad39*X38||U42", "omegad40*X39||U43", "omegad41*X40||U44", "omegad41*X42||U45", "omegad42*X43||U46", "omegad45*X44||U48", "omegad43*X44||U47", "omegad45*X46||U49", "omegad35*X47||U50", "omegad46*X47||U51", "omegad47*X48||U52", "omegad55*X49||U54", "omegad48*X49||U53", "omegad51*X50||U56", "omegad49*X50||U55", "omegad36*X51||U57", "omegad37*X52||U58", "omegad60*X53||U60", "omegad41*X53||U59", "omegad64*X54||U62", "omegad45*X54||U61", "omegad68*X55||U63", "omegad52*X56||U64", "omegad58*X57||U66", "omegad56*X57||U65", "omegad60*X59||U68", "omegad58*X59||U67", "omegad60*X61||U69", "omegad63*X62||U71", "omegad61*X62||U70", "omegad64*X63||U72", "omegad65*X64||U73", "omegad66*X65||U74", "omegad66*X67||U75", "omegad68*X67||U76", "omegad69*X68||U77", "omegad69*X70||U78", "omegad58*X71||U79", "omegad62*X72||U80", "omegad85*X73||U82", "omegad66*X73||U81", "omegad70*X74||U83", "omegad90*X75||U84", "omegad77*X76||U86", "omegad75*X76||U85", "omegad78*X77||U88", "omegad71*X77||U87", "omegad91*X79||U90", "omegad78*X79||U89", "omegad79*X80||U91", "omegad80*X81||U93", "omegad72*X81||U92", "omegad83*X82||U95", "omegad81*X82||U94", "omegad92*X83||U96", "omegad83*X84||U97", "omegad85*X84||U98", "omegad85*X86||U99", 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a/qiskit_ibm_runtime/fake_provider/backends/kyoto/defs_kyoto.json b/qiskit_ibm_runtime/fake_provider/backends/kyoto/defs_kyoto.json new file mode 100644 index 000000000..e5dcd61b9 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kyoto/defs_kyoto.json @@ -0,0 +1 @@ +{"qubit_freq_est": [4.908674148226789, 4.85572824315697, 4.733158874245776, 4.820261994494087, 4.854406917156434, 4.728166249638585, 4.782684691120985, 4.943905052046705, 5.169275414363777, 4.9357064613528605, 4.83862942031162, 5.085447972428554, 4.952377258022041, 4.859079285831473, 4.941688204193792, 4.965355300967371, 4.9894491981828235, 5.049580851790653, 4.840965065553309, 4.798677072129157, 4.731394913319142, 4.832575638820544, 4.907107031566938, 4.811721667817013, 4.8725190942237635, 4.910013684731585, 4.806398486081192, 4.8954021144497935, 4.962318530055217, 5.080049181461419, 5.16472017327588, 5.0855454636046185, 5.022224766386669, 4.9596329337017595, 4.931395076298819, 4.843699620467231, 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119, 120, 121, 122, 123, 124, 125, 126]}]}, {"name": "measure", "qubits": [112], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m112", "label": "M_m112", "pulse_shape": "gaussian_square", "parameters": {"amp": [-0.10318621231620882, -0.37974033982161326], "duration": 1440, "sigma": 32, "width": 1312}}, {"name": "delay", "t0": 1440, "ch": "m112", "duration": 1360}, {"name": "acquire", "t0": 0, "duration": 1440, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 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"_data": {}} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/kyoto/fake_kyoto.py b/qiskit_ibm_runtime/fake_provider/backends/kyoto/fake_kyoto.py new file mode 100644 index 000000000..184bf13f3 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kyoto/fake_kyoto.py @@ -0,0 +1,28 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Kyoto device (127 qubit). +""" + +import os +from qiskit_ibm_runtime.fake_provider import fake_backend + + +class FakeKyoto(fake_backend.FakeBackendV2): + """A fake 127 qubit backend.""" + + dirname = os.path.dirname(__file__) # type: ignore + conf_filename = "conf_kyoto.json" # type: ignore + props_filename = "props_kyoto.json" # type: ignore + defs_filename = "defs_kyoto.json" # type: ignore + backend_name = "fake_kyoto" # type: ignore diff --git a/qiskit_ibm_runtime/fake_provider/backends/kyoto/props_kyoto.json b/qiskit_ibm_runtime/fake_provider/backends/kyoto/props_kyoto.json new file mode 100644 index 000000000..730de3626 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/kyoto/props_kyoto.json @@ -0,0 +1 @@ +{"backend_name": "ibm_kyoto", "backend_version": "1.2.29", "last_update_date": "2024-02-28T06:38:20-05:00", "qubits": [[{"date": "2024-02-28T04:35:31-05:00", "name": "T1", "unit": "us", "value": 122.88385453004375}, {"date": "2024-02-28T04:50:46-05:00", "name": "T2", "unit": "us", "value": 24.42187737169765}, {"date": "2024-02-28T06:38:20-05:00", "name": "frequency", "unit": "GHz", "value": 4.908674148226789}, {"date": "2024-02-28T06:38:20-05:00", "name": "anharmonicity", "unit": "GHz", "value": -0.30802879619250306}, {"date": "2024-02-28T04:22:04-05:00", "name": "readout_error", "unit": "", "value": 0.1612}, {"date": "2024-02-28T04:22:04-05:00", "name": "prob_meas0_prep1", "unit": "", "value": 0.1628}, {"date": "2024-02-28T04:22:04-05:00", "name": "prob_meas1_prep0", "unit": "", "value": 0.15959999999999996}, {"date": "2024-02-28T04:22:04-05:00", "name": 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"2023-11-20T00:00:00-05:00", "name": "lf_100", "unit": "", "value": 0.02701590644233078}], "general_qlists": [{"name": "lf_100", "qubits": [67, 68, 69, 70, 74, 89, 88, 87, 86, 85, 84, 83, 92, 102, 103, 104, 105, 106, 107, 108, 112, 126, 125, 124, 123, 122, 121, 120, 119, 118, 110, 100, 99, 98, 97, 96, 95, 94, 90, 75, 76, 77, 78, 79, 80, 81, 72, 62, 63, 64, 54, 45, 44, 43, 42, 41, 53, 60, 59, 58, 57, 56, 52, 37, 38, 39, 33, 20, 19, 18, 14, 0, 1, 2, 3, 4, 15, 22, 23, 24, 25, 26, 27, 28, 35, 47, 48, 49, 50, 51, 36, 32, 31, 30, 17, 12, 11, 10, 9, 8]}]} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/osaka/__init__.py b/qiskit_ibm_runtime/fake_provider/backends/osaka/__init__.py new file mode 100644 index 000000000..0b3a8ac07 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/osaka/__init__.py @@ -0,0 +1,17 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Osaka backend (127 qubit). +""" + +from .fake_osaka import FakeOsaka diff --git a/qiskit_ibm_runtime/fake_provider/backends/osaka/conf_osaka.json b/qiskit_ibm_runtime/fake_provider/backends/osaka/conf_osaka.json new file mode 100644 index 000000000..6addb8654 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/osaka/conf_osaka.json @@ -0,0 +1 @@ +{"backend_name": "ibm_osaka", "backend_version": "1.0.16", "n_qubits": 127, "basis_gates": ["ecr", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], 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[4.346348605454618, 5.346348605454618], [4.542881983065722, 5.542881983065722], [4.4933325837800115, 5.4933325837800115]], "meas_lo_range": [[6.675636988000001, 7.675636988000001], [6.616707744, 7.616707744], [6.744164864, 7.744164864000001], [6.678859578000001, 7.678859578000001], [6.6154420510000005, 7.6154420510000005], [6.740112632000001, 7.740112632000001], [6.2890596720000005, 7.2890596720000005], [6.678586321, 7.678586321], [6.798122677, 7.798122677], [6.860605155, 7.860605155000001], [6.73109058, 7.73109058], [6.279966663000001, 7.279966663000001], [6.785782, 7.785782], [6.667445527000001, 7.667445527000001], [6.611654812, 7.611654812], [6.79510836, 7.79510836], [6.411510653000001, 7.411510653000001], [6.396178743, 7.396178743], [6.794922215000001, 7.794922215000001], [6.862561053, 7.862561053], [6.2823368120000005, 7.2823368120000005], [6.348478121, 7.348478121], [6.411055200000001, 7.411055200000001], [6.865279115000001, 7.865279115000001], [6.35072041, 7.35072041], [6.738685599, 7.738685599], [6.675001946, 7.675001946], [6.463534312, 7.463534312], [6.730239709, 7.730239709], [6.339244642000001, 7.339244642000001], [6.662248514000001, 7.662248514000001], [6.786480194, 7.786480194], [6.277657444000001, 7.277657444000001], [6.467394863, 7.467394863000001], [6.467306733, 7.467306733], [6.607479583000001, 7.607479583000001], [6.346598053, 7.346598053], [6.402179427, 7.402179427], [6.737950111000001, 7.737950111000001], [6.459825497000001, 7.459825497000001], [6.613683782000001, 7.613683782000001], [6.740537487, 7.740537487], [6.674760152, 7.674760152], [6.612863459000001, 7.612863459000001], [6.861300295, 7.861300295], [6.284612650000001, 7.284612650000001], [6.7996864210000005, 7.7996864210000005], [6.859356932000001, 7.859356932000001], [6.461223827, 7.461223827], [6.734272649, 7.734272649], [6.664494294000001, 7.664494294000001], [6.402849649, 7.402849649], [6.340275063, 7.340275063000001], [6.28102186, 7.28102186], [6.347016581, 7.347016581], [6.792597634000001, 7.792597634000001], [6.611494293000001, 7.611494293000001], [6.286441435, 7.286441435], [6.851248891, 7.851248891000001], [6.464584483, 7.464584483], [6.341918328, 7.341918328], [6.790412701, 7.790412701], [6.456572802, 7.456572802], [6.607362747000001, 7.607362747000001], [6.729912322000001, 7.729912322000001], [6.409744633000001, 7.409744633000001], [6.607049917, 7.607049917], [6.8579695460000005, 7.8579695460000005], [6.282426844000001, 7.282426844000001], [6.347634458000001, 7.347634458000001], [6.401653876, 7.401653876], [6.668311592, 7.668311592], [6.406997720000001, 7.406997720000001], [6.672777692, 7.672777692], [6.662717639, 7.662717639], [6.396845015, 7.396845015], [6.735737192, 7.735737192], [6.790593907000001, 7.790593907000001], [6.457292269000001, 7.457292269000001], [6.603415753, 7.603415753], [6.732408606000001, 7.732408606000001], [6.66517696, 7.66517696], [6.790532433, 7.790532433], [6.859504145000001, 7.859504145000001], [6.282473855, 7.282473855], [6.796619206000001, 7.796619206000001], [6.407685292, 7.407685292], [6.461718402000001, 7.461718402000001], [6.736777255000001, 7.736777255000001], [6.7883126240000005, 7.7883126240000005], [6.281912037000001, 7.281912037000001], [6.853857417, 7.853857417], [6.463692789, 7.463692789], [6.607696629, 7.607696629], [6.664990765000001, 7.664990765000001], [6.791534926000001, 7.791534926000001], [6.455866835, 7.455866835], [6.603411566, 7.603411566], [6.459296456000001, 7.459296456000001], [6.276057336, 7.276057336], [6.406521397000001, 7.406521397000001], [6.661612715, 7.661612715], [6.606980868000001, 7.606980868000001], [6.3443702250000005, 7.3443702250000005], [6.674913812000001, 7.674913812000001], [6.790376346, 7.790376346], [6.856621584, 7.856621584000001], [6.280133761, 7.280133761], [6.406136152, 7.406136152], [6.342740367, 7.342740367], [6.341478311, 7.341478311], [6.731002188000001, 7.731002188000001], [6.347084774000001, 7.347084774000001], [6.85189701, 7.85189701], [6.278127492, 7.278127492], [6.459106716, 7.459106716000001], [6.336550450000001, 7.336550450000001], [6.276211172, 7.276211172000001], [6.727112347, 7.727112347], [6.793339574, 7.793339574000001], [6.401047504, 7.401047504], [6.853518286000001, 7.853518286000001], [6.279831157, 7.279831157], [6.459415493000001, 7.459415493000001], [6.338218262000001, 7.338218262000001], [6.407122395, 7.407122395], [6.457577265, 7.457577265]], "meas_kernels": ["hw_qmfk"], "discriminators": ["hw_qmfk", "linear_discriminator", "quadratic_discriminator"], "rep_times": [1000.0], "meas_map": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]], "acquisition_latency": [], "conditional_latency": [], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{126}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{62,72}(\\sigma_{62}^{+}\\sigma_{72}^{-}+\\sigma_{62}^{-}\\sigma_{72}^{+}) + J_{67,68}(\\sigma_{67}^{+}\\sigma_{68}^{-}+\\sigma_{67}^{-}\\sigma_{68}^{+}) + J_{44,45}(\\sigma_{44}^{+}\\sigma_{45}^{-}+\\sigma_{44}^{-}\\sigma_{45}^{+}) + J_{99,100}(\\sigma_{99}^{+}\\sigma_{100}^{-}+\\sigma_{99}^{-}\\sigma_{100}^{+}) \\\\ & + J_{108,112}(\\sigma_{108}^{+}\\sigma_{112}^{-}+\\sigma_{108}^{-}\\sigma_{112}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{40,41}(\\sigma_{40}^{+}\\sigma_{41}^{-}+\\sigma_{40}^{-}\\sigma_{41}^{+}) + J_{0,14}(\\sigma_{0}^{+}\\sigma_{14}^{-}+\\sigma_{0}^{-}\\sigma_{14}^{+}) \\\\ & + J_{17,30}(\\sigma_{17}^{+}\\sigma_{30}^{-}+\\sigma_{17}^{-}\\sigma_{30}^{+}) + J_{100,101}(\\sigma_{100}^{+}\\sigma_{101}^{-}+\\sigma_{100}^{-}\\sigma_{101}^{+}) + J_{91,98}(\\sigma_{91}^{+}\\sigma_{98}^{-}+\\sigma_{91}^{-}\\sigma_{98}^{+}) + J_{100,110}(\\sigma_{100}^{+}\\sigma_{110}^{-}+\\sigma_{100}^{-}\\sigma_{110}^{+}) \\\\ & + J_{75,90}(\\sigma_{75}^{+}\\sigma_{90}^{-}+\\sigma_{75}^{-}\\sigma_{90}^{+}) + J_{96,97}(\\sigma_{96}^{+}\\sigma_{97}^{-}+\\sigma_{96}^{-}\\sigma_{97}^{+}) + J_{41,42}(\\sigma_{41}^{+}\\sigma_{42}^{-}+\\sigma_{41}^{-}\\sigma_{42}^{+}) + J_{18,19}(\\sigma_{18}^{+}\\sigma_{19}^{-}+\\sigma_{18}^{-}\\sigma_{19}^{+}) \\\\ & + J_{55,68}(\\sigma_{55}^{+}\\sigma_{68}^{-}+\\sigma_{55}^{-}\\sigma_{68}^{+}) + J_{9,10}(\\sigma_{9}^{+}\\sigma_{10}^{-}+\\sigma_{9}^{-}\\sigma_{10}^{+}) + J_{49,55}(\\sigma_{49}^{+}\\sigma_{55}^{-}+\\sigma_{49}^{-}\\sigma_{55}^{+}) + J_{106,107}(\\sigma_{106}^{+}\\sigma_{107}^{-}+\\sigma_{106}^{-}\\sigma_{107}^{+}) \\\\ & + J_{47,48}(\\sigma_{47}^{+}\\sigma_{48}^{-}+\\sigma_{47}^{-}\\sigma_{48}^{+}) + J_{42,43}(\\sigma_{42}^{+}\\sigma_{43}^{-}+\\sigma_{42}^{-}\\sigma_{43}^{+}) + J_{107,108}(\\sigma_{107}^{+}\\sigma_{108}^{-}+\\sigma_{107}^{-}\\sigma_{108}^{+}) + J_{73,85}(\\sigma_{73}^{+}\\sigma_{85}^{-}+\\sigma_{73}^{-}\\sigma_{85}^{+}) \\\\ & + J_{38,39}(\\sigma_{38}^{+}\\sigma_{39}^{-}+\\sigma_{38}^{-}\\sigma_{39}^{+}) + J_{20,33}(\\sigma_{20}^{+}\\sigma_{33}^{-}+\\sigma_{20}^{-}\\sigma_{33}^{+}) + J_{48,49}(\\sigma_{48}^{+}\\sigma_{49}^{-}+\\sigma_{48}^{-}\\sigma_{49}^{+}) + J_{103,104}(\\sigma_{103}^{+}\\sigma_{104}^{-}+\\sigma_{103}^{-}\\sigma_{104}^{+}) \\\\ & + J_{80,81}(\\sigma_{80}^{+}\\sigma_{81}^{-}+\\sigma_{80}^{-}\\sigma_{81}^{+}) + J_{75,76}(\\sigma_{75}^{+}\\sigma_{76}^{-}+\\sigma_{75}^{-}\\sigma_{76}^{+}) + J_{66,73}(\\sigma_{66}^{+}\\sigma_{73}^{-}+\\sigma_{66}^{-}\\sigma_{73}^{+}) + J_{85,86}(\\sigma_{85}^{+}\\sigma_{86}^{-}+\\sigma_{85}^{-}\\sigma_{86}^{+}) \\\\ & + J_{81,82}(\\sigma_{81}^{+}\\sigma_{82}^{-}+\\sigma_{81}^{-}\\sigma_{82}^{+}) + J_{110,118}(\\sigma_{110}^{+}\\sigma_{118}^{-}+\\sigma_{110}^{-}\\sigma_{118}^{+}) + J_{16,26}(\\sigma_{16}^{+}\\sigma_{26}^{-}+\\sigma_{16}^{-}\\sigma_{26}^{+}) + J_{90,94}(\\sigma_{90}^{+}\\sigma_{94}^{-}+\\sigma_{90}^{-}\\sigma_{94}^{+}) \\\\ & + J_{118,119}(\\sigma_{118}^{+}\\sigma_{119}^{-}+\\sigma_{118}^{-}\\sigma_{119}^{+}) + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{77,78}(\\sigma_{77}^{+}\\sigma_{78}^{-}+\\sigma_{77}^{-}\\sigma_{78}^{+}) + J_{22,23}(\\sigma_{22}^{+}\\sigma_{23}^{-}+\\sigma_{22}^{-}\\sigma_{23}^{+}) \\\\ & + J_{49,50}(\\sigma_{49}^{+}\\sigma_{50}^{-}+\\sigma_{49}^{-}\\sigma_{50}^{+}) + J_{104,105}(\\sigma_{104}^{+}\\sigma_{105}^{-}+\\sigma_{104}^{-}\\sigma_{105}^{+}) + J_{114,115}(\\sigma_{114}^{+}\\sigma_{115}^{-}+\\sigma_{114}^{-}\\sigma_{115}^{+}) + J_{45,46}(\\sigma_{45}^{+}\\sigma_{46}^{-}+\\sigma_{45}^{-}\\sigma_{46}^{+}) \\\\ & + J_{50,51}(\\sigma_{50}^{+}\\sigma_{51}^{-}+\\sigma_{50}^{-}\\sigma_{51}^{+}) + J_{105,106}(\\sigma_{105}^{+}\\sigma_{106}^{-}+\\sigma_{105}^{-}\\sigma_{106}^{+}) + J_{72,81}(\\sigma_{72}^{+}\\sigma_{81}^{-}+\\sigma_{72}^{-}\\sigma_{81}^{+}) + J_{82,83}(\\sigma_{82}^{+}\\sigma_{83}^{-}+\\sigma_{82}^{-}\\sigma_{83}^{+}) \\\\ & + J_{46,47}(\\sigma_{46}^{+}\\sigma_{47}^{-}+\\sigma_{46}^{-}\\sigma_{47}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) + J_{78,79}(\\sigma_{78}^{+}\\sigma_{79}^{-}+\\sigma_{78}^{-}\\sigma_{79}^{+}) + J_{83,84}(\\sigma_{83}^{+}\\sigma_{84}^{-}+\\sigma_{83}^{-}\\sigma_{84}^{+}) \\\\ & + J_{115,116}(\\sigma_{115}^{+}\\sigma_{116}^{-}+\\sigma_{115}^{-}\\sigma_{116}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) + J_{79,80}(\\sigma_{79}^{+}\\sigma_{80}^{-}+\\sigma_{79}^{-}\\sigma_{80}^{+}) \\\\ & + J_{56,57}(\\sigma_{56}^{+}\\sigma_{57}^{-}+\\sigma_{56}^{-}\\sigma_{57}^{+}) + J_{93,106}(\\sigma_{93}^{+}\\sigma_{106}^{-}+\\sigma_{93}^{-}\\sigma_{106}^{+}) + J_{116,117}(\\sigma_{116}^{+}\\sigma_{117}^{-}+\\sigma_{116}^{-}\\sigma_{117}^{+}) + J_{20,21}(\\sigma_{20}^{+}\\sigma_{21}^{-}+\\sigma_{20}^{-}\\sigma_{21}^{+}) \\\\ & + J_{12,17}(\\sigma_{12}^{+}\\sigma_{17}^{-}+\\sigma_{12}^{-}\\sigma_{17}^{+}) + J_{41,53}(\\sigma_{41}^{+}\\sigma_{53}^{-}+\\sigma_{41}^{-}\\sigma_{53}^{+}) + J_{57,58}(\\sigma_{57}^{+}\\sigma_{58}^{-}+\\sigma_{57}^{-}\\sigma_{58}^{+}) + J_{87,93}(\\sigma_{87}^{+}\\sigma_{93}^{-}+\\sigma_{87}^{-}\\sigma_{93}^{+}) \\\\ & + J_{30,31}(\\sigma_{30}^{+}\\sigma_{31}^{-}+\\sigma_{30}^{-}\\sigma_{31}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) + J_{79,91}(\\sigma_{79}^{+}\\sigma_{91}^{-}+\\sigma_{79}^{-}\\sigma_{91}^{+}) + J_{26,27}(\\sigma_{26}^{+}\\sigma_{27}^{-}+\\sigma_{26}^{-}\\sigma_{27}^{+}) \\\\ & + J_{21,22}(\\sigma_{21}^{+}\\sigma_{22}^{-}+\\sigma_{21}^{-}\\sigma_{22}^{+}) + J_{58,71}(\\sigma_{58}^{+}\\sigma_{71}^{-}+\\sigma_{58}^{-}\\sigma_{71}^{+}) + J_{31,32}(\\sigma_{31}^{+}\\sigma_{32}^{-}+\\sigma_{31}^{-}\\sigma_{32}^{+}) + J_{4,15}(\\sigma_{4}^{+}\\sigma_{15}^{-}+\\sigma_{4}^{-}\\sigma_{15}^{+}) \\\\ & + J_{86,87}(\\sigma_{86}^{+}\\sigma_{87}^{-}+\\sigma_{86}^{-}\\sigma_{87}^{+}) + J_{113,114}(\\sigma_{113}^{+}\\sigma_{114}^{-}+\\sigma_{113}^{-}\\sigma_{114}^{+}) + J_{104,111}(\\sigma_{104}^{+}\\sigma_{111}^{-}+\\sigma_{104}^{-}\\sigma_{111}^{+}) + J_{123,124}(\\sigma_{123}^{+}\\sigma_{124}^{-}+\\sigma_{123}^{-}\\sigma_{124}^{+}) \\\\ & + J_{27,28}(\\sigma_{27}^{+}\\sigma_{28}^{-}+\\sigma_{27}^{-}\\sigma_{28}^{+}) + J_{34,43}(\\sigma_{34}^{+}\\sigma_{43}^{-}+\\sigma_{34}^{-}\\sigma_{43}^{+}) + J_{119,120}(\\sigma_{119}^{+}\\sigma_{120}^{-}+\\sigma_{119}^{-}\\sigma_{120}^{+}) + J_{64,65}(\\sigma_{64}^{+}\\sigma_{65}^{-}+\\sigma_{64}^{-}\\sigma_{65}^{+}) \\\\ & + J_{54,64}(\\sigma_{54}^{+}\\sigma_{64}^{-}+\\sigma_{54}^{-}\\sigma_{64}^{+}) + J_{32,36}(\\sigma_{32}^{+}\\sigma_{36}^{-}+\\sigma_{32}^{-}\\sigma_{36}^{+}) + J_{60,61}(\\sigma_{60}^{+}\\sigma_{61}^{-}+\\sigma_{60}^{-}\\sigma_{61}^{+}) + J_{5,6}(\\sigma_{5}^{+}\\sigma_{6}^{-}+\\sigma_{5}^{-}\\sigma_{6}^{+}) \\\\ & + J_{14,18}(\\sigma_{14}^{+}\\sigma_{18}^{-}+\\sigma_{14}^{-}\\sigma_{18}^{+}) + J_{87,88}(\\sigma_{87}^{+}\\sigma_{88}^{-}+\\sigma_{87}^{-}\\sigma_{88}^{+}) + J_{97,98}(\\sigma_{97}^{+}\\sigma_{98}^{-}+\\sigma_{97}^{-}\\sigma_{98}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) \\\\ & + J_{112,126}(\\sigma_{112}^{+}\\sigma_{126}^{-}+\\sigma_{112}^{-}\\sigma_{126}^{+}) + J_{28,29}(\\sigma_{28}^{+}\\sigma_{29}^{-}+\\sigma_{28}^{-}\\sigma_{29}^{+}) + J_{45,54}(\\sigma_{45}^{+}\\sigma_{54}^{-}+\\sigma_{45}^{-}\\sigma_{54}^{+}) + J_{36,51}(\\sigma_{36}^{+}\\sigma_{51}^{-}+\\sigma_{36}^{-}\\sigma_{51}^{+}) \\\\ & + J_{88,89}(\\sigma_{88}^{+}\\sigma_{89}^{-}+\\sigma_{88}^{-}\\sigma_{89}^{+}) + J_{120,121}(\\sigma_{120}^{+}\\sigma_{121}^{-}+\\sigma_{120}^{-}\\sigma_{121}^{+}) + J_{15,22}(\\sigma_{15}^{+}\\sigma_{22}^{-}+\\sigma_{15}^{-}\\sigma_{22}^{+}) + J_{24,34}(\\sigma_{24}^{+}\\sigma_{34}^{-}+\\sigma_{24}^{-}\\sigma_{34}^{+}) \\\\ & + J_{84,85}(\\sigma_{84}^{+}\\sigma_{85}^{-}+\\sigma_{84}^{-}\\sigma_{85}^{+}) + J_{29,30}(\\sigma_{29}^{+}\\sigma_{30}^{-}+\\sigma_{29}^{-}\\sigma_{30}^{+}) + J_{61,62}(\\sigma_{61}^{+}\\sigma_{62}^{-}+\\sigma_{61}^{-}\\sigma_{62}^{+}) + J_{70,74}(\\sigma_{70}^{+}\\sigma_{74}^{-}+\\sigma_{70}^{-}\\sigma_{74}^{+}) \\\\ & + J_{121,122}(\\sigma_{121}^{+}\\sigma_{122}^{-}+\\sigma_{121}^{-}\\sigma_{122}^{+}) + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{122,123}(\\sigma_{122}^{+}\\sigma_{123}^{-}+\\sigma_{122}^{-}\\sigma_{123}^{+}) + J_{117,118}(\\sigma_{117}^{+}\\sigma_{118}^{-}+\\sigma_{117}^{-}\\sigma_{118}^{+}) \\\\ & + J_{62,63}(\\sigma_{62}^{+}\\sigma_{63}^{-}+\\sigma_{62}^{-}\\sigma_{63}^{+}) + J_{94,95}(\\sigma_{94}^{+}\\sigma_{95}^{-}+\\sigma_{94}^{-}\\sigma_{95}^{+}) + J_{109,114}(\\sigma_{109}^{+}\\sigma_{114}^{-}+\\sigma_{109}^{-}\\sigma_{114}^{+}) + J_{37,52}(\\sigma_{37}^{+}\\sigma_{52}^{-}+\\sigma_{37}^{-}\\sigma_{52}^{+}) \\\\ & + J_{3,4}(\\sigma_{3}^{+}\\sigma_{4}^{-}+\\sigma_{3}^{-}\\sigma_{4}^{+}) + J_{58,59}(\\sigma_{58}^{+}\\sigma_{59}^{-}+\\sigma_{58}^{-}\\sigma_{59}^{+}) + J_{33,39}(\\sigma_{33}^{+}\\sigma_{39}^{-}+\\sigma_{33}^{-}\\sigma_{39}^{+}) + J_{95,96}(\\sigma_{95}^{+}\\sigma_{96}^{-}+\\sigma_{95}^{-}\\sigma_{96}^{+}) \\\\ & + J_{68,69}(\\sigma_{68}^{+}\\sigma_{69}^{-}+\\sigma_{68}^{-}\\sigma_{69}^{+}) + J_{63,64}(\\sigma_{63}^{+}\\sigma_{64}^{-}+\\sigma_{63}^{-}\\sigma_{64}^{+}) + J_{71,77}(\\sigma_{71}^{+}\\sigma_{77}^{-}+\\sigma_{71}^{-}\\sigma_{77}^{+}) + J_{111,122}(\\sigma_{111}^{+}\\sigma_{122}^{-}+\\sigma_{111}^{-}\\sigma_{122}^{+}) \\\\ & + J_{4,5}(\\sigma_{4}^{+}\\sigma_{5}^{-}+\\sigma_{4}^{-}\\sigma_{5}^{+}) + J_{59,60}(\\sigma_{59}^{+}\\sigma_{60}^{-}+\\sigma_{59}^{-}\\sigma_{60}^{+}) + J_{96,109}(\\sigma_{96}^{+}\\sigma_{109}^{-}+\\sigma_{96}^{-}\\sigma_{109}^{+}) + J_{124,125}(\\sigma_{124}^{+}\\sigma_{125}^{-}+\\sigma_{124}^{-}\\sigma_{125}^{+}) \\\\ & + J_{69,70}(\\sigma_{69}^{+}\\sigma_{70}^{-}+\\sigma_{69}^{-}\\sigma_{70}^{+}) + J_{35,47}(\\sigma_{35}^{+}\\sigma_{47}^{-}+\\sigma_{35}^{-}\\sigma_{47}^{+}) + J_{101,102}(\\sigma_{101}^{+}\\sigma_{102}^{-}+\\sigma_{101}^{-}\\sigma_{102}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) \\\\ & + J_{10,11}(\\sigma_{10}^{+}\\sigma_{11}^{-}+\\sigma_{10}^{-}\\sigma_{11}^{+}) + J_{65,66}(\\sigma_{65}^{+}\\sigma_{66}^{-}+\\sigma_{65}^{-}\\sigma_{66}^{+}) + J_{37,38}(\\sigma_{37}^{+}\\sigma_{38}^{-}+\\sigma_{37}^{-}\\sigma_{38}^{+}) + J_{28,35}(\\sigma_{28}^{+}\\sigma_{35}^{-}+\\sigma_{28}^{-}\\sigma_{35}^{+}) \\\\ & + J_{102,103}(\\sigma_{102}^{+}\\sigma_{103}^{-}+\\sigma_{102}^{-}\\sigma_{103}^{+}) + J_{92,102}(\\sigma_{92}^{+}\\sigma_{102}^{-}+\\sigma_{92}^{-}\\sigma_{102}^{+}) + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{98,99}(\\sigma_{98}^{+}\\sigma_{99}^{-}+\\sigma_{98}^{-}\\sigma_{99}^{+}) \\\\ & + J_{43,44}(\\sigma_{43}^{+}\\sigma_{44}^{-}+\\sigma_{43}^{-}\\sigma_{44}^{+}) + J_{52,56}(\\sigma_{52}^{+}\\sigma_{56}^{-}+\\sigma_{52}^{-}\\sigma_{56}^{+}) + J_{125,126}(\\sigma_{125}^{+}\\sigma_{126}^{-}+\\sigma_{125}^{-}\\sigma_{126}^{+}) + J_{39,40}(\\sigma_{39}^{+}\\sigma_{40}^{-}+\\sigma_{39}^{-}\\sigma_{40}^{+}) \\\\ & + J_{8,16}(\\sigma_{8}^{+}\\sigma_{16}^{-}+\\sigma_{8}^{-}\\sigma_{16}^{+}) + J_{11,12}(\\sigma_{11}^{+}\\sigma_{12}^{-}+\\sigma_{11}^{-}\\sigma_{12}^{+}) + J_{66,67}(\\sigma_{66}^{+}\\sigma_{67}^{-}+\\sigma_{66}^{-}\\sigma_{67}^{+}) + J_{76,77}(\\sigma_{76}^{+}\\sigma_{77}^{-}+\\sigma_{76}^{-}\\sigma_{77}^{+}) \\\\ & + J_{83,92}(\\sigma_{83}^{+}\\sigma_{92}^{-}+\\sigma_{83}^{-}\\sigma_{92}^{+}) + J_{74,89}(\\sigma_{74}^{+}\\sigma_{89}^{-}+\\sigma_{74}^{-}\\sigma_{89}^{+}) + J_{7,8}(\\sigma_{7}^{+}\\sigma_{8}^{-}+\\sigma_{7}^{-}\\sigma_{8}^{+}) + J_{53,60}(\\sigma_{53}^{+}\\sigma_{60}^{-}+\\sigma_{53}^{-}\\sigma_{60}^{+}) \\\\ & + \\Omega_{d,1}(U_{0}^{(1,0)}(t))\\sigma_{1}^{X} + \\Omega_{d,2}(U_{2}^{(2,3)}(t)+U_{1}^{(2,1)}(t))\\sigma_{2}^{X} \\\\ & + \\Omega_{d,3}(U_{3}^{(3,4)}(t))\\sigma_{3}^{X} + \\Omega_{d,5}(U_{4}^{(5,4)}(t))\\sigma_{5}^{X} \\\\ & + \\Omega_{d,6}(U_{6}^{(6,7)}(t)+U_{5}^{(6,5)}(t))\\sigma_{6}^{X} + \\Omega_{d,7}(U_{7}^{(7,8)}(t))\\sigma_{7}^{X} \\\\ & + \\Omega_{d,8}(U_{8}^{(8,16)}(t))\\sigma_{8}^{X} + \\Omega_{d,9}(U_{10}^{(9,10)}(t)+U_{9}^{(9,8)}(t))\\sigma_{9}^{X} \\\\ & + \\Omega_{d,11}(U_{11}^{(11,10)}(t))\\sigma_{11}^{X} + \\Omega_{d,12}(U_{12}^{(12,11)}(t))\\sigma_{12}^{X} \\\\ & + \\Omega_{d,13}(U_{13}^{(13,12)}(t))\\sigma_{13}^{X} + \\Omega_{d,14}(U_{15}^{(14,18)}(t)+U_{14}^{(14,0)}(t))\\sigma_{14}^{X} \\\\ & + \\Omega_{d,15}(U_{16}^{(15,4)}(t))\\sigma_{15}^{X} + \\Omega_{d,16}(U_{17}^{(16,26)}(t))\\sigma_{16}^{X} \\\\ & + \\Omega_{d,17}(U_{19}^{(17,30)}(t)+U_{18}^{(17,12)}(t))\\sigma_{17}^{X} + \\Omega_{d,18}(U_{20}^{(18,19)}(t))\\sigma_{18}^{X} \\\\ & + \\Omega_{d,20}(U_{21}^{(20,19)}(t))\\sigma_{20}^{X} + \\Omega_{d,21}(U_{23}^{(21,22)}(t)+U_{22}^{(21,20)}(t))\\sigma_{21}^{X} \\\\ & + \\Omega_{d,22}(U_{24}^{(22,15)}(t))\\sigma_{22}^{X} + \\Omega_{d,23}(U_{25}^{(23,22)}(t))\\sigma_{23}^{X} \\\\ & + \\Omega_{d,24}(U_{27}^{(24,25)}(t)+U_{26}^{(24,23)}(t)+U_{28}^{(24,34)}(t))\\sigma_{24}^{X} + \\Omega_{d,25}(U_{29}^{(25,26)}(t))\\sigma_{25}^{X} \\\\ & + \\Omega_{d,27}(U_{31}^{(27,28)}(t)+U_{30}^{(27,26)}(t))\\sigma_{27}^{X} + \\Omega_{d,28}(U_{33}^{(28,35)}(t)+U_{32}^{(28,29)}(t))\\sigma_{28}^{X} \\\\ & + \\Omega_{d,30}(U_{34}^{(30,29)}(t))\\sigma_{30}^{X} + \\Omega_{d,31}(U_{35}^{(31,30)}(t)+U_{36}^{(31,32)}(t))\\sigma_{31}^{X} \\\\ & + \\Omega_{d,33}(U_{37}^{(33,20)}(t))\\sigma_{33}^{X} + \\Omega_{d,35}(U_{38}^{(35,47)}(t))\\sigma_{35}^{X} \\\\ & + \\Omega_{d,36}(U_{39}^{(36,32)}(t))\\sigma_{36}^{X} + \\Omega_{d,37}(U_{41}^{(37,52)}(t)+U_{40}^{(37,38)}(t))\\sigma_{37}^{X} \\\\ & + \\Omega_{d,39}(U_{42}^{(39,33)}(t)+U_{43}^{(39,38)}(t))\\sigma_{39}^{X} + \\Omega_{d,40}(U_{45}^{(40,41)}(t)+U_{44}^{(40,39)}(t))\\sigma_{40}^{X} \\\\ & + \\Omega_{d,42}(U_{46}^{(42,41)}(t)+U_{47}^{(42,43)}(t))\\sigma_{42}^{X} + \\Omega_{d,43}(U_{48}^{(43,34)}(t)+U_{49}^{(43,44)}(t))\\sigma_{43}^{X} \\\\ & + \\Omega_{d,45}(U_{50}^{(45,44)}(t)+U_{52}^{(45,54)}(t)+U_{51}^{(45,46)}(t))\\sigma_{45}^{X} + \\Omega_{d,46}(U_{53}^{(46,47)}(t))\\sigma_{46}^{X} \\\\ & + \\Omega_{d,48}(U_{54}^{(48,47)}(t)+U_{55}^{(48,49)}(t))\\sigma_{48}^{X} + \\Omega_{d,49}(U_{56}^{(49,50)}(t))\\sigma_{49}^{X} \\\\ & + \\Omega_{d,50}(U_{57}^{(50,51)}(t))\\sigma_{50}^{X} + \\Omega_{d,51}(U_{58}^{(51,36)}(t))\\sigma_{51}^{X} \\\\ & + \\Omega_{d,52}(U_{59}^{(52,56)}(t))\\sigma_{52}^{X} + \\Omega_{d,53}(U_{60}^{(53,41)}(t))\\sigma_{53}^{X} \\\\ & + \\Omega_{d,55}(U_{61}^{(55,49)}(t))\\sigma_{55}^{X} + \\Omega_{d,57}(U_{63}^{(57,58)}(t)+U_{62}^{(57,56)}(t))\\sigma_{57}^{X} \\\\ & + \\Omega_{d,58}(U_{64}^{(58,71)}(t))\\sigma_{58}^{X} + \\Omega_{d,59}(U_{65}^{(59,58)}(t)+U_{66}^{(59,60)}(t))\\sigma_{59}^{X} \\\\ & + \\Omega_{d,60}(U_{67}^{(60,53)}(t))\\sigma_{60}^{X} + \\Omega_{d,61}(U_{69}^{(61,62)}(t)+U_{68}^{(61,60)}(t))\\sigma_{61}^{X} \\\\ & + \\Omega_{d,62}(U_{70}^{(62,72)}(t))\\sigma_{62}^{X} + \\Omega_{d,63}(U_{71}^{(63,62)}(t))\\sigma_{63}^{X} \\\\ & + \\Omega_{d,64}(U_{72}^{(64,54)}(t)+U_{73}^{(64,63)}(t))\\sigma_{64}^{X} + \\Omega_{d,65}(U_{74}^{(65,64)}(t))\\sigma_{65}^{X} \\\\ & + \\Omega_{d,66}(U_{75}^{(66,65)}(t)+U_{76}^{(66,73)}(t))\\sigma_{66}^{X} + \\Omega_{d,67}(U_{77}^{(67,66)}(t))\\sigma_{67}^{X} \\\\ & + \\Omega_{d,68}(U_{78}^{(68,55)}(t)+U_{80}^{(68,69)}(t)+U_{79}^{(68,67)}(t))\\sigma_{68}^{X} + \\Omega_{d,69}(U_{81}^{(69,70)}(t))\\sigma_{69}^{X} \\\\ & + \\Omega_{d,71}(U_{82}^{(71,77)}(t))\\sigma_{71}^{X} + \\Omega_{d,74}(U_{83}^{(74,70)}(t))\\sigma_{74}^{X} \\\\ & + \\Omega_{d,75}(U_{84}^{(75,76)}(t))\\sigma_{75}^{X} + \\Omega_{d,76}(U_{85}^{(76,77)}(t))\\sigma_{76}^{X} \\\\ & + \\Omega_{d,78}(U_{86}^{(78,77)}(t)+U_{87}^{(78,79)}(t))\\sigma_{78}^{X} + \\Omega_{d,79}(U_{88}^{(79,80)}(t))\\sigma_{79}^{X} \\\\ & + \\Omega_{d,81}(U_{90}^{(81,80)}(t)+U_{89}^{(81,72)}(t)+U_{91}^{(81,82)}(t))\\sigma_{81}^{X} + \\Omega_{d,83}(U_{92}^{(83,82)}(t))\\sigma_{83}^{X} \\\\ & + \\Omega_{d,84}(U_{93}^{(84,83)}(t))\\sigma_{84}^{X} + \\Omega_{d,85}(U_{94}^{(85,73)}(t)+U_{95}^{(85,84)}(t))\\sigma_{85}^{X} \\\\ & + \\Omega_{d,86}(U_{96}^{(86,85)}(t))\\sigma_{86}^{X} + \\Omega_{d,87}(U_{99}^{(87,93)}(t)+U_{98}^{(87,88)}(t)+U_{97}^{(87,86)}(t))\\sigma_{87}^{X} \\\\ & + \\Omega_{d,88}(U_{100}^{(88,89)}(t))\\sigma_{88}^{X} + \\Omega_{d,89}(U_{101}^{(89,74)}(t))\\sigma_{89}^{X} \\\\ & + \\Omega_{d,90}(U_{103}^{(90,94)}(t)+U_{102}^{(90,75)}(t))\\sigma_{90}^{X} + \\Omega_{d,91}(U_{104}^{(91,79)}(t))\\sigma_{91}^{X} \\\\ & + \\Omega_{d,92}(U_{105}^{(92,83)}(t)+U_{106}^{(92,102)}(t))\\sigma_{92}^{X} + \\Omega_{d,93}(U_{107}^{(93,106)}(t))\\sigma_{93}^{X} \\\\ & + \\Omega_{d,94}(U_{108}^{(94,95)}(t))\\sigma_{94}^{X} + \\Omega_{d,96}(U_{111}^{(96,109)}(t)+U_{110}^{(96,97)}(t)+U_{109}^{(96,95)}(t))\\sigma_{96}^{X} \\\\ & + \\Omega_{d,97}(U_{112}^{(97,98)}(t))\\sigma_{97}^{X} + \\Omega_{d,98}(U_{113}^{(98,91)}(t))\\sigma_{98}^{X} \\\\ & + \\Omega_{d,99}(U_{114}^{(99,98)}(t))\\sigma_{99}^{X} + \\Omega_{d,100}(U_{116}^{(100,110)}(t)+U_{115}^{(100,99)}(t))\\sigma_{100}^{X} \\\\ & + \\Omega_{d,101}(U_{118}^{(101,102)}(t)+U_{117}^{(101,100)}(t))\\sigma_{101}^{X} + \\Omega_{d,103}(U_{120}^{(103,104)}(t)+U_{119}^{(103,102)}(t))\\sigma_{103}^{X} \\\\ & + \\Omega_{d,104}(U_{121}^{(104,105)}(t)+U_{122}^{(104,111)}(t))\\sigma_{104}^{X} + \\Omega_{d,105}(U_{123}^{(105,106)}(t))\\sigma_{105}^{X} \\\\ & + \\Omega_{d,106}(U_{124}^{(106,107)}(t))\\sigma_{106}^{X} + \\Omega_{d,108}(U_{126}^{(108,112)}(t)+U_{125}^{(108,107)}(t))\\sigma_{108}^{X} \\\\ & + \\Omega_{d,109}(U_{127}^{(109,114)}(t))\\sigma_{109}^{X} + \\Omega_{d,110}(U_{128}^{(110,118)}(t))\\sigma_{110}^{X} \\\\ & + \\Omega_{d,114}(U_{130}^{(114,115)}(t)+U_{129}^{(114,113)}(t))\\sigma_{114}^{X} + \\Omega_{d,115}(U_{131}^{(115,116)}(t))\\sigma_{115}^{X} \\\\ & + \\Omega_{d,116}(U_{132}^{(116,117)}(t))\\sigma_{116}^{X} + \\Omega_{d,117}(U_{133}^{(117,118)}(t))\\sigma_{117}^{X} \\\\ & + \\Omega_{d,119}(U_{134}^{(119,118)}(t))\\sigma_{119}^{X} + \\Omega_{d,120}(U_{136}^{(120,121)}(t)+U_{135}^{(120,119)}(t))\\sigma_{120}^{X} \\\\ & + \\Omega_{d,121}(U_{137}^{(121,122)}(t))\\sigma_{121}^{X} + \\Omega_{d,122}(U_{138}^{(122,111)}(t))\\sigma_{122}^{X} \\\\ & + \\Omega_{d,123}(U_{140}^{(123,124)}(t)+U_{139}^{(123,122)}(t))\\sigma_{123}^{X} + \\Omega_{d,125}(U_{142}^{(125,126)}(t)+U_{141}^{(125,124)}(t))\\sigma_{125}^{X} \\\\ & + \\Omega_{d,126}(U_{143}^{(126,112)}(t))\\sigma_{126}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,126,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,126,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,126,-delta{i}/2*O{i}]", "_SUM[i,0,126,omegad{i}*X{i}||D{i}]", "jq62q72*Sp62*Sm72", "jq62q72*Sm62*Sp72", "jq67q68*Sp67*Sm68", "jq67q68*Sm67*Sp68", "jq44q45*Sp44*Sm45", "jq44q45*Sm44*Sp45", "jq99q100*Sp99*Sm100", "jq99q100*Sm99*Sp100", "jq108q112*Sp108*Sm112", "jq108q112*Sm108*Sp112", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq40q41*Sp40*Sm41", "jq40q41*Sm40*Sp41", "jq0q14*Sp0*Sm14", "jq0q14*Sm0*Sp14", "jq17q30*Sp17*Sm30", "jq17q30*Sm17*Sp30", "jq100q101*Sp100*Sm101", "jq100q101*Sm100*Sp101", "jq91q98*Sp91*Sm98", "jq91q98*Sm91*Sp98", "jq100q110*Sp100*Sm110", "jq100q110*Sm100*Sp110", "jq75q90*Sp75*Sm90", "jq75q90*Sm75*Sp90", "jq96q97*Sp96*Sm97", "jq96q97*Sm96*Sp97", "jq41q42*Sp41*Sm42", "jq41q42*Sm41*Sp42", "jq18q19*Sp18*Sm19", "jq18q19*Sm18*Sp19", "jq55q68*Sp55*Sm68", "jq55q68*Sm55*Sp68", "jq9q10*Sp9*Sm10", "jq9q10*Sm9*Sp10", "jq49q55*Sp49*Sm55", "jq49q55*Sm49*Sp55", "jq106q107*Sp106*Sm107", "jq106q107*Sm106*Sp107", "jq47q48*Sp47*Sm48", "jq47q48*Sm47*Sp48", "jq42q43*Sp42*Sm43", "jq42q43*Sm42*Sp43", "jq107q108*Sp107*Sm108", "jq107q108*Sm107*Sp108", "jq73q85*Sp73*Sm85", "jq73q85*Sm73*Sp85", "jq38q39*Sp38*Sm39", "jq38q39*Sm38*Sp39", "jq20q33*Sp20*Sm33", "jq20q33*Sm20*Sp33", "jq48q49*Sp48*Sm49", "jq48q49*Sm48*Sp49", "jq103q104*Sp103*Sm104", "jq103q104*Sm103*Sp104", "jq80q81*Sp80*Sm81", "jq80q81*Sm80*Sp81", "jq75q76*Sp75*Sm76", "jq75q76*Sm75*Sp76", "jq66q73*Sp66*Sm73", "jq66q73*Sm66*Sp73", "jq85q86*Sp85*Sm86", "jq85q86*Sm85*Sp86", "jq81q82*Sp81*Sm82", "jq81q82*Sm81*Sp82", "jq110q118*Sp110*Sm118", "jq110q118*Sm110*Sp118", "jq16q26*Sp16*Sm26", "jq16q26*Sm16*Sp26", "jq90q94*Sp90*Sm94", "jq90q94*Sm90*Sp94", "jq118q119*Sp118*Sm119", "jq118q119*Sm118*Sp119", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq77q78*Sp77*Sm78", "jq77q78*Sm77*Sp78", "jq22q23*Sp22*Sm23", "jq22q23*Sm22*Sp23", "jq49q50*Sp49*Sm50", "jq49q50*Sm49*Sp50", "jq104q105*Sp104*Sm105", "jq104q105*Sm104*Sp105", "jq114q115*Sp114*Sm115", "jq114q115*Sm114*Sp115", "jq45q46*Sp45*Sm46", "jq45q46*Sm45*Sp46", "jq50q51*Sp50*Sm51", "jq50q51*Sm50*Sp51", "jq105q106*Sp105*Sm106", "jq105q106*Sm105*Sp106", "jq72q81*Sp72*Sm81", "jq72q81*Sm72*Sp81", "jq82q83*Sp82*Sm83", "jq82q83*Sm82*Sp83", "jq46q47*Sp46*Sm47", "jq46q47*Sm46*Sp47", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq78q79*Sp78*Sm79", "jq78q79*Sm78*Sp79", "jq83q84*Sp83*Sm84", "jq83q84*Sm83*Sp84", "jq115q116*Sp115*Sm116", "jq115q116*Sm115*Sp116", "jq19q20*Sp19*Sm20", "jq19q20*Sm19*Sp20", "jq24q25*Sp24*Sm25", "jq24q25*Sm24*Sp25", "jq79q80*Sp79*Sm80", "jq79q80*Sm79*Sp80", "jq56q57*Sp56*Sm57", "jq56q57*Sm56*Sp57", "jq93q106*Sp93*Sm106", "jq93q106*Sm93*Sp106", "jq116q117*Sp116*Sm117", "jq116q117*Sm116*Sp117", "jq20q21*Sp20*Sm21", "jq20q21*Sm20*Sp21", "jq12q17*Sp12*Sm17", "jq12q17*Sm12*Sp17", "jq41q53*Sp41*Sm53", "jq41q53*Sm41*Sp53", "jq57q58*Sp57*Sm58", "jq57q58*Sm57*Sp58", "jq87q93*Sp87*Sm93", "jq87q93*Sm87*Sp93", "jq30q31*Sp30*Sm31", "jq30q31*Sm30*Sp31", "jq25q26*Sp25*Sm26", "jq25q26*Sm25*Sp26", "jq79q91*Sp79*Sm91", "jq79q91*Sm79*Sp91", "jq26q27*Sp26*Sm27", "jq26q27*Sm26*Sp27", "jq21q22*Sp21*Sm22", "jq21q22*Sm21*Sp22", "jq58q71*Sp58*Sm71", "jq58q71*Sm58*Sp71", "jq31q32*Sp31*Sm32", "jq31q32*Sm31*Sp32", "jq4q15*Sp4*Sm15", "jq4q15*Sm4*Sp15", "jq86q87*Sp86*Sm87", "jq86q87*Sm86*Sp87", "jq113q114*Sp113*Sm114", "jq113q114*Sm113*Sp114", "jq104q111*Sp104*Sm111", "jq104q111*Sm104*Sp111", "jq123q124*Sp123*Sm124", "jq123q124*Sm123*Sp124", "jq27q28*Sp27*Sm28", "jq27q28*Sm27*Sp28", "jq34q43*Sp34*Sm43", "jq34q43*Sm34*Sp43", "jq119q120*Sp119*Sm120", "jq119q120*Sm119*Sp120", "jq64q65*Sp64*Sm65", "jq64q65*Sm64*Sp65", "jq54q64*Sp54*Sm64", "jq54q64*Sm54*Sp64", "jq32q36*Sp32*Sm36", "jq32q36*Sm32*Sp36", "jq60q61*Sp60*Sm61", "jq60q61*Sm60*Sp61", "jq5q6*Sp5*Sm6", "jq5q6*Sm5*Sp6", "jq14q18*Sp14*Sm18", "jq14q18*Sm14*Sp18", "jq87q88*Sp87*Sm88", "jq87q88*Sm87*Sp88", "jq97q98*Sp97*Sm98", "jq97q98*Sm97*Sp98", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq112q126*Sp112*Sm126", "jq112q126*Sm112*Sp126", "jq28q29*Sp28*Sm29", "jq28q29*Sm28*Sp29", "jq45q54*Sp45*Sm54", "jq45q54*Sm45*Sp54", "jq36q51*Sp36*Sm51", "jq36q51*Sm36*Sp51", "jq88q89*Sp88*Sm89", "jq88q89*Sm88*Sp89", "jq120q121*Sp120*Sm121", "jq120q121*Sm120*Sp121", "jq15q22*Sp15*Sm22", "jq15q22*Sm15*Sp22", "jq24q34*Sp24*Sm34", "jq24q34*Sm24*Sp34", "jq84q85*Sp84*Sm85", "jq84q85*Sm84*Sp85", "jq29q30*Sp29*Sm30", "jq29q30*Sm29*Sp30", "jq61q62*Sp61*Sm62", "jq61q62*Sm61*Sp62", 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"qubits": [112], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m112", "label": "M_m112", "pulse_shape": "gaussian_square", "parameters": {"amp": [-0.19617149755387364, -0.0390479698252105], "duration": 1440, "sigma": 32, "width": 1312}}, {"name": "delay", "t0": 1440, "ch": "m112", "duration": 1360}, {"name": "acquire", "t0": 0, "duration": 1440, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 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"m114", "label": "M_m114", "pulse_shape": "gaussian_square", "parameters": {"amp": [-0.1265506634335098, -0.2498145936180241], "duration": 1440, "sigma": 32, "width": 1312}}, {"name": "delay", "t0": 1440, "ch": "m114", "duration": 1360}, {"name": "acquire", "t0": 0, "duration": 1440, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 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2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Osaka device (127 qubit). +""" + +import os +from qiskit_ibm_runtime.fake_provider import fake_backend + + +class FakeOsaka(fake_backend.FakeBackendV2): + """A fake 127 qubit backend.""" + + dirname = os.path.dirname(__file__) # type: ignore + conf_filename = "conf_osaka.json" # type: ignore + props_filename = "props_osaka.json" # type: ignore + defs_filename = "defs_osaka.json" # type: ignore + backend_name = "fake_osaka" # type: ignore diff --git a/qiskit_ibm_runtime/fake_provider/backends/osaka/props_osaka.json b/qiskit_ibm_runtime/fake_provider/backends/osaka/props_osaka.json new file mode 100644 index 000000000..35f83802c --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/osaka/props_osaka.json @@ -0,0 +1 @@ +{"backend_name": "ibm_osaka", "backend_version": "1.0.16", "last_update_date": "2024-02-28T04:34:29-05:00", "qubits": [[{"date": "2024-02-22T00:57:12-05:00", "name": "T1", "unit": "us", "value": 412.7753747617601}, {"date": "2024-02-26T01:02:29-05:00", "name": "T2", "unit": "us", "value": 223.83903857126694}, {"date": "2024-02-28T04:34:29-05:00", "name": "frequency", "unit": "GHz", "value": 4.822505531556077}, {"date": "2024-02-28T04:34:29-05:00", "name": "anharmonicity", "unit": "GHz", "value": -0.30896613792557315}, {"date": "2024-02-28T03:06:15-05:00", "name": "readout_error", "unit": "", "value": 0.025600000000000067}, {"date": "2024-02-28T03:06:15-05:00", "name": "prob_meas0_prep1", "unit": "", "value": 0.026}, {"date": "2024-02-28T03:06:15-05:00", "name": "prob_meas1_prep0", "unit": "", "value": 0.0252}, {"date": "2024-02-28T03:06:15-05:00", "name": 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a/qiskit_ibm_runtime/fake_provider/backends/peekskill/__init__.py b/qiskit_ibm_runtime/fake_provider/backends/peekskill/__init__.py new file mode 100644 index 000000000..0bb24c3f8 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/peekskill/__init__.py @@ -0,0 +1,15 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2021, 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +"""Mock peekskill backend""" + +from .fake_peekskill import FakePeekskill diff --git a/qiskit_ibm_runtime/fake_provider/backends/peekskill/conf_peekskill.json b/qiskit_ibm_runtime/fake_provider/backends/peekskill/conf_peekskill.json new file mode 100644 index 000000000..076d14916 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/peekskill/conf_peekskill.json @@ -0,0 +1 @@ +{"backend_name": "ibm_peekskill", "backend_version": "2.10.1", "n_qubits": 27, "basis_gates": ["ecr", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "rz", "parameters": ["theta"], "qasm_def": "gate rz(theta) q { U(0, 0, theta) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "sx", "parameters": [], "qasm_def": "gate sx q { U(pi/2, 3*pi/2, pi/2) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "x", "parameters": [], "qasm_def": "gate x q { U(pi, 0, pi) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]]}, {"name": "ecr", "parameters": [], "qasm_def": "gate ecr q0, q1 { U(pi, pi/2, 7*pi/2) q0; U(pi, 7*pi/2, pi/2) q1; CX q0, q1; U(0, 0, 7*pi/2) q0; U(pi/2, 7*pi/2, pi/2) q1; }", "coupling_map": [[0, 1], [2, 1], [2, 3], [3, 5], [4, 1], [5, 8], [6, 7], [7, 4], [7, 10], [9, 8], [11, 8], [11, 14], [12, 10], [13, 12], [14, 13], [15, 12], [15, 18], [16, 14], [16, 19], [18, 17], [18, 21], [20, 19], [21, 23], [22, 19], [22, 25], [23, 24], [25, 24], [26, 25]]}, {"name": "reset", "parameters": null, "qasm_def": null}], "local": false, "simulator": false, "conditional": false, "open_pulse": true, "memory": true, "max_shots": 500000, "coupling_map": [[0, 1], [2, 1], [2, 3], [3, 5], [4, 1], [5, 8], [6, 7], [7, 4], [7, 10], [9, 8], [11, 8], [11, 14], [12, 10], [13, 12], [14, 13], [15, 12], [15, 18], [16, 14], [16, 19], [18, 17], [18, 21], [20, 19], [21, 23], [22, 19], [22, 25], [23, 24], [25, 24], [26, 25]], "dynamic_reprate_enabled": true, "supported_instructions": ["ecr", "id", "delay", "measure", "reset", "rz", "sx", "x", "if_else", "for_loop", "switch_case"], "rep_delay_range": [0.0, 1000.0], "default_rep_delay": 199.99999999999997, "max_experiments": 3000, "sample_name": "FalconR8", "n_registers": 1, "credits_required": true, "online_date": "2021-09-23T04:00:00+00:00", "description": "27 qubit device", "dt": 0.2222222222222222, "dtm": 0.2222222222222222, "processor_type": {"family": "Falcon", "revision": 8}, "parametric_pulses": ["gaussian", "gaussian_square", "gaussian_square_drag", "drag", "constant"], "allow_q_object": true, "clops": null, "clops_h": null, "clops_v": null, "coords": [[1, 2], [2, 2], [2, 3], [2, 4], [3, 2], [3, 4], [4, 1], [4, 2], [4, 4], [4, 5], [5, 2], [5, 4], [6, 2], [6, 3], [6, 4], [7, 2], [7, 4], [8, 1], [8, 2], [8, 4], [8, 5], [9, 2], [9, 4], [10, 2], [10, 3], [10, 4], [11, 4]], "measure_esp_enabled": false, "multi_meas_enabled": true, "parallel_compilation": true, "quantum_volume": null, "qubit_channel_mapping": [["u0", "d0", "m0"], ["u4", "u0", "m1", "u1", "d1"], ["d2", "m2", "u1", "u2"], ["u3", "d3", "u2", "m3"], ["u4", "d4", "u7", "m4"], ["u3", "d5", "m5", "u5"], ["m6", "u6", "d6"], ["u7", "u8", "m7", "u6", "d7"], ["u9", "d8", "u5", "m8", "u10"], ["u9", "d9", "m9"], ["u8", "d10", "m10", "u12"], ["m11", "u10", "u11", "d11"], ["m12", "u12", "d12", "u15", "u13"], ["d13", "u13", "u14", "m13"], ["u14", "d14", "m14", "u17", "u11"], ["d15", "m15", "u15", "u16"], ["u17", "m16", "d16", "u18"], ["u19", "m17", "d17"], ["u20", "m18", "u16", "u19", "d18"], ["d19", "m19", "u18", "u23", "u21"], ["m20", "u21", "d20"], ["u20", "u22", "m21", "d21"], ["m22", "u23", "d22", "u24"], ["m23", "u22", "d23", "u25"], ["u26", "m24", "u25", "d24"], ["u26", "u24", "m25", "d25", "u27"], ["u27", "m26", "d26"]], "supported_features": ["qobj", "qasm3", "parameters"], "timing_constraints": {"acquire_alignment": 16, "granularity": 16, "min_length": 64, "pulse_alignment": 16}, "uchannels_enabled": true, "url": "None", "n_uchannels": 28, "u_channel_lo": [[{"q": 1, "scale": [1.0, 0.0]}], [{"q": 1, "scale": [1.0, 0.0]}], [{"q": 3, "scale": [1.0, 0.0]}], [{"q": 5, "scale": [1.0, 0.0]}], [{"q": 1, "scale": [1.0, 0.0]}], [{"q": 8, "scale": [1.0, 0.0]}], [{"q": 7, "scale": [1.0, 0.0]}], [{"q": 4, "scale": [1.0, 0.0]}], [{"q": 10, "scale": [1.0, 0.0]}], [{"q": 8, "scale": [1.0, 0.0]}], [{"q": 8, "scale": [1.0, 0.0]}], [{"q": 14, "scale": [1.0, 0.0]}], [{"q": 10, "scale": [1.0, 0.0]}], [{"q": 12, "scale": [1.0, 0.0]}], [{"q": 13, "scale": [1.0, 0.0]}], [{"q": 12, "scale": [1.0, 0.0]}], [{"q": 18, "scale": [1.0, 0.0]}], [{"q": 14, "scale": [1.0, 0.0]}], [{"q": 19, "scale": [1.0, 0.0]}], [{"q": 17, "scale": [1.0, 0.0]}], [{"q": 21, "scale": [1.0, 0.0]}], [{"q": 19, "scale": [1.0, 0.0]}], [{"q": 23, "scale": [1.0, 0.0]}], [{"q": 19, "scale": [1.0, 0.0]}], [{"q": 25, "scale": [1.0, 0.0]}], [{"q": 24, "scale": [1.0, 0.0]}], [{"q": 24, "scale": [1.0, 0.0]}], [{"q": 25, "scale": [1.0, 0.0]}]], "meas_levels": [1, 2], "qubit_lo_range": [[4.3833540929588395, 5.3833540929588395], [4.127746028357075, 5.127746028357075], [4.256546095866816, 5.256546095866816], [4.339444715435514, 5.339444715435514], [4.4137781617399945, 5.4137781617399945], [4.47330891159201, 5.47330891159201], [4.493149756605063, 5.493149756605063], [4.228374015326138, 5.228374015326138], [4.410675288207697, 5.410675288207697], [4.67502270166348, 5.67502270166348], [4.3375137330491755, 5.3375137330491755], [4.6046656872694385, 5.6046656872694385], [4.399892865072125, 5.399892865072125], [4.472038389757867, 5.472038389757867], [4.317846690390836, 5.317846690390836], [4.457605023869311, 5.457605023869311], [4.577464515096522, 5.577464515096522], [4.651147601336018, 5.651147601336018], [4.583034710323727, 5.5830347103237274], [4.303581251988357, 5.303581251988357], [4.5998596121486734, 5.5998596121486734], [4.358215040679912, 5.358215040679912], [4.421254209746218, 5.421254209746218], [4.521137791227942, 5.521137791227942], [4.632990003793948, 5.632990003793948], [4.487110706967762, 5.487110706967762], [4.6088203289777185, 5.6088203289777185]], "meas_lo_range": [[6.667933286, 7.667933286], [6.786716377, 7.786716377], [6.664784423, 7.664784423], [6.789407126, 7.789407126], [6.7277919530000005, 7.7277919530000005], [6.738470961, 7.738470961000001], [6.845099843000001, 7.845099843000001], [6.604428468, 7.604428468], [6.603484532, 7.603484532], [6.838377702000001, 7.838377702000001], [6.662523161, 7.662523161], [6.726224107, 7.726224107], [6.841229060000001, 7.841229060000001], [6.727401346000001, 7.727401346000001], [6.780579499000001, 7.780579499000001], [6.7806119, 7.7806119], [6.657793862, 7.657793862], [6.844414457, 7.844414457], [6.6051959060000005, 7.6051959060000005], [6.598768996, 7.598768996], [6.835699237, 7.835699237000001], [6.7294343130000005, 7.7294343130000005], [6.72155199, 7.721551990000001], [6.790183408000001, 7.790183408000001], [6.6535428130000005, 7.6535428130000005], [6.771028607000001, 7.771028607000001], [6.649538551, 7.649538551000001]], "meas_kernels": ["hw_qmfk"], "discriminators": ["linear_discriminator", "quadratic_discriminator", "hw_qmfk"], "rep_times": [1000.0], "meas_map": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]], "acquisition_latency": [], "conditional_latency": [], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{26}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{14,16}(\\sigma_{14}^{+}\\sigma_{16}^{-}+\\sigma_{14}^{-}\\sigma_{16}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{17,18}(\\sigma_{17}^{+}\\sigma_{18}^{-}+\\sigma_{17}^{-}\\sigma_{18}^{+}) \\\\ & + J_{11,14}(\\sigma_{11}^{+}\\sigma_{14}^{-}+\\sigma_{11}^{-}\\sigma_{14}^{+}) + J_{10,12}(\\sigma_{10}^{+}\\sigma_{12}^{-}+\\sigma_{10}^{-}\\sigma_{12}^{+}) + J_{13,14}(\\sigma_{13}^{+}\\sigma_{14}^{-}+\\sigma_{13}^{-}\\sigma_{14}^{+}) + J_{7,10}(\\sigma_{7}^{+}\\sigma_{10}^{-}+\\sigma_{7}^{-}\\sigma_{10}^{+}) \\\\ & + J_{16,19}(\\sigma_{16}^{+}\\sigma_{19}^{-}+\\sigma_{16}^{-}\\sigma_{19}^{+}) + J_{12,15}(\\sigma_{12}^{+}\\sigma_{15}^{-}+\\sigma_{12}^{-}\\sigma_{15}^{+}) + J_{22,25}(\\sigma_{22}^{+}\\sigma_{25}^{-}+\\sigma_{22}^{-}\\sigma_{25}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) \\\\ & + J_{8,11}(\\sigma_{8}^{+}\\sigma_{11}^{-}+\\sigma_{8}^{-}\\sigma_{11}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) \\\\ & + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) + J_{18,21}(\\sigma_{18}^{+}\\sigma_{21}^{-}+\\sigma_{18}^{-}\\sigma_{21}^{+}) + J_{4,7}(\\sigma_{4}^{+}\\sigma_{7}^{-}+\\sigma_{4}^{-}\\sigma_{7}^{+}) \\\\ & + J_{21,23}(\\sigma_{21}^{+}\\sigma_{23}^{-}+\\sigma_{21}^{-}\\sigma_{23}^{+}) + J_{3,5}(\\sigma_{3}^{+}\\sigma_{5}^{-}+\\sigma_{3}^{-}\\sigma_{5}^{+}) + J_{5,8}(\\sigma_{5}^{+}\\sigma_{8}^{-}+\\sigma_{5}^{-}\\sigma_{8}^{+}) + J_{1,4}(\\sigma_{1}^{+}\\sigma_{4}^{-}+\\sigma_{1}^{-}\\sigma_{4}^{+}) \\\\ & + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{19,22}(\\sigma_{19}^{+}\\sigma_{22}^{-}+\\sigma_{19}^{-}\\sigma_{22}^{+}) + J_{15,18}(\\sigma_{15}^{+}\\sigma_{18}^{-}+\\sigma_{15}^{-}\\sigma_{18}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) \\\\ & + \\Omega_{d,0}(U_{0}^{(0,1)}(t))\\sigma_{0}^{X} + \\Omega_{d,2}(U_{2}^{(2,3)}(t)+U_{1}^{(2,1)}(t))\\sigma_{2}^{X} \\\\ & + \\Omega_{d,3}(U_{3}^{(3,5)}(t))\\sigma_{3}^{X} + \\Omega_{d,4}(U_{4}^{(4,1)}(t))\\sigma_{4}^{X} \\\\ & + \\Omega_{d,5}(U_{5}^{(5,8)}(t))\\sigma_{5}^{X} + \\Omega_{d,6}(U_{6}^{(6,7)}(t))\\sigma_{6}^{X} \\\\ & + \\Omega_{d,7}(U_{7}^{(7,4)}(t)+U_{8}^{(7,10)}(t))\\sigma_{7}^{X} + \\Omega_{d,9}(U_{9}^{(9,8)}(t))\\sigma_{9}^{X} \\\\ & + \\Omega_{d,11}(U_{11}^{(11,14)}(t)+U_{10}^{(11,8)}(t))\\sigma_{11}^{X} + \\Omega_{d,12}(U_{12}^{(12,10)}(t))\\sigma_{12}^{X} \\\\ & + \\Omega_{d,13}(U_{13}^{(13,12)}(t))\\sigma_{13}^{X} + \\Omega_{d,14}(U_{14}^{(14,13)}(t))\\sigma_{14}^{X} \\\\ & + \\Omega_{d,15}(U_{15}^{(15,12)}(t)+U_{16}^{(15,18)}(t))\\sigma_{15}^{X} + \\Omega_{d,16}(U_{17}^{(16,14)}(t)+U_{18}^{(16,19)}(t))\\sigma_{16}^{X} \\\\ & + \\Omega_{d,18}(U_{19}^{(18,17)}(t)+U_{20}^{(18,21)}(t))\\sigma_{18}^{X} + \\Omega_{d,20}(U_{21}^{(20,19)}(t))\\sigma_{20}^{X} \\\\ & + \\Omega_{d,21}(U_{22}^{(21,23)}(t))\\sigma_{21}^{X} + \\Omega_{d,22}(U_{24}^{(22,25)}(t)+U_{23}^{(22,19)}(t))\\sigma_{22}^{X} \\\\ & + \\Omega_{d,23}(U_{25}^{(23,24)}(t))\\sigma_{23}^{X} + \\Omega_{d,25}(U_{26}^{(25,24)}(t))\\sigma_{25}^{X} \\\\ & + \\Omega_{d,26}(U_{27}^{(26,25)}(t))\\sigma_{26}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,26,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,26,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,26,-delta{i}/2*O{i}]", "_SUM[i,0,26,omegad{i}*X{i}||D{i}]", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq14q16*Sp14*Sm16", "jq14q16*Sm14*Sp16", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq17q18*Sp17*Sm18", "jq17q18*Sm17*Sp18", "jq11q14*Sp11*Sm14", "jq11q14*Sm11*Sp14", "jq10q12*Sp10*Sm12", "jq10q12*Sm10*Sp12", "jq13q14*Sp13*Sm14", "jq13q14*Sm13*Sp14", "jq7q10*Sp7*Sm10", "jq7q10*Sm7*Sp10", "jq16q19*Sp16*Sm19", "jq16q19*Sm16*Sp19", "jq12q15*Sp12*Sm15", "jq12q15*Sm12*Sp15", "jq22q25*Sp22*Sm25", "jq22q25*Sm22*Sp25", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq8q11*Sp8*Sm11", "jq8q11*Sm8*Sp11", "jq0q1*Sp0*Sm1", "jq0q1*Sm0*Sp1", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq19q20*Sp19*Sm20", "jq19q20*Sm19*Sp20", "jq6q7*Sp6*Sm7", "jq6q7*Sm6*Sp7", "jq24q25*Sp24*Sm25", "jq24q25*Sm24*Sp25", "jq18q21*Sp18*Sm21", "jq18q21*Sm18*Sp21", "jq4q7*Sp4*Sm7", "jq4q7*Sm4*Sp7", "jq21q23*Sp21*Sm23", "jq21q23*Sm21*Sp23", "jq3q5*Sp3*Sm5", "jq3q5*Sm3*Sp5", "jq5q8*Sp5*Sm8", "jq5q8*Sm5*Sp8", "jq1q4*Sp1*Sm4", "jq1q4*Sm1*Sp4", "jq2q3*Sp2*Sm3", "jq2q3*Sm2*Sp3", "jq19q22*Sp19*Sm22", "jq19q22*Sm19*Sp22", "jq15q18*Sp15*Sm18", "jq15q18*Sm15*Sp18", "jq25q26*Sp25*Sm26", "jq25q26*Sm25*Sp26", "omegad1*X0||U0", "omegad3*X2||U2", "omegad1*X2||U1", "omegad5*X3||U3", "omegad1*X4||U4", "omegad8*X5||U5", "omegad7*X6||U6", "omegad4*X7||U7", "omegad10*X7||U8", "omegad8*X9||U9", "omegad14*X11||U11", "omegad8*X11||U10", "omegad10*X12||U12", "omegad12*X13||U13", "omegad13*X14||U14", "omegad12*X15||U15", "omegad18*X15||U16", "omegad14*X16||U17", "omegad19*X16||U18", "omegad17*X18||U19", "omegad21*X18||U20", "omegad19*X20||U21", "omegad23*X21||U22", 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"beta": -0.5086454403874947, "duration": 160, "sigma": 40}}]}, {"name": "xprs", "qubits": [26], "sequence": [{"name": "RSdelay_d26", "t0": 0, "ch": "d26"}, {"name": "parametric_pulse", "t0": 368, "ch": "d26", "label": "XpRS_d26", "pulse_shape": "drag", "parameters": {"amp": [0.24347873428719782, 0.0], "beta": -1.7530808518399932, "duration": 160, "sigma": 40}}]}], "meas_kernel": {"name": "hw_qmfk", "params": {}}, "discriminator": {"name": "hw_qmfk", "params": {}}, "_data": {}} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/peekskill/fake_peekskill.py b/qiskit_ibm_runtime/fake_provider/backends/peekskill/fake_peekskill.py new file mode 100644 index 000000000..467e30f65 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/peekskill/fake_peekskill.py @@ -0,0 +1,28 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2021, 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Peekskill device (27 qubit). +""" + +import os +from qiskit_ibm_runtime.fake_provider import fake_backend + + +class FakePeekskill(fake_backend.FakeBackendV2): + """A fake 27 qubit backend.""" + + dirname = os.path.dirname(__file__) # type: ignore + conf_filename = "conf_peekskill.json" # type: ignore + props_filename = "props_peekskill.json" # type: ignore + defs_filename = "defs_peekskill.json" # type: ignore + backend_name = "fake_peekskill" # type: ignore diff --git a/qiskit_ibm_runtime/fake_provider/backends/peekskill/props_peekskill.json b/qiskit_ibm_runtime/fake_provider/backends/peekskill/props_peekskill.json new file mode 100644 index 000000000..003836474 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/peekskill/props_peekskill.json @@ -0,0 +1 @@ +{"backend_name": "ibm_peekskill", "backend_version": "2.10.1", "last_update_date": "2024-02-28T09:02:02-05:00", "qubits": [[{"date": "2024-02-28T00:19:43-05:00", "name": "T1", "unit": "us", "value": 346.64835383424025}, {"date": "2024-02-28T00:22:45-05:00", "name": "T2", "unit": "us", "value": 478.084996571691}, {"date": "2024-02-28T09:02:02-05:00", "name": "frequency", "unit": "GHz", "value": 4.8833540929588395}, {"date": "2024-02-28T09:02:02-05:00", "name": "anharmonicity", "unit": "GHz", "value": -0.3448280631378064}, {"date": "2024-02-28T00:16:48-05:00", "name": "readout_error", "unit": "", "value": 0.09570000000000001}, {"date": "2024-02-28T00:16:48-05:00", "name": "prob_meas0_prep1", "unit": "", "value": 0.09399999999999997}, {"date": "2024-02-28T00:16:48-05:00", "name": "prob_meas1_prep0", "unit": "", "value": 0.0974}, {"date": 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000000000..0eac0ae4e --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/quebec/__init__.py @@ -0,0 +1,17 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Quebec backend (127 qubit). +""" + +from .fake_quebec import FakeQuebec diff --git a/qiskit_ibm_runtime/fake_provider/backends/quebec/conf_quebec.json b/qiskit_ibm_runtime/fake_provider/backends/quebec/conf_quebec.json new file mode 100644 index 000000000..2026d5a71 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/quebec/conf_quebec.json @@ -0,0 +1 @@ +{"backend_name": "ibm_quebec", "backend_version": "1.2.4", "n_qubits": 127, "basis_gates": ["ecr", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], 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5.542690613120907], [4.438641756202589, 5.438641756202589], [4.355477286027597, 5.355477286027597], [4.495511865139029, 5.49551186513903], [4.452439221806371, 5.452439221806371], [4.376449549968204, 5.376449549968205], [4.513933256736149, 5.513933256736149], [4.449859454081683, 5.449859454081683], [4.313222992115686, 5.313222992115686], [4.450006025256749, 5.450006025256749], [4.369022472717591, 5.369022472717591], [4.421185177133235, 5.421185177133235], [4.654385610591269, 5.654385610591269], [4.5269622133326015, 5.5269622133326015], [4.4992331058158195, 5.4992331058158195], [4.445429701819692, 5.445429701819692], [4.492223438589489, 5.492223438589489], [4.5683251080431875, 5.5683251080431875], [4.645353552192069, 5.645353552192069], [4.506697773711086, 5.506697773711086], [4.373288633834303, 5.373288633834303], [4.452688457025637, 5.452688457025637], [4.281490034596688, 5.281490034596689], [4.417003986117116, 5.417003986117116], [4.466359652969616, 5.466359652969616], [4.591740932118076, 5.591740932118076], [4.659257010534543, 5.659257010534543], [4.426441382606766, 5.426441382606766], [4.6987559915797705, 5.6987559915797705], [4.568019152150738, 5.568019152150738]], "meas_lo_range": [[6.680676895, 7.680676895], [6.615939020000001, 7.615939020000001], [6.735055620000001, 7.735055620000001], [6.675563519000001, 7.675563519000001], [6.606465780000001, 7.606465780000001], [6.735789149, 7.735789149], [6.277998944, 7.277998944], [6.6722297610000005, 7.6722297610000005], [6.789689119, 7.789689119], [6.860519765, 7.860519765], [6.735755336, 7.735755336], [6.2822344260000005, 7.2822344260000005], [6.80087389, 7.80087389], [6.680999943000001, 7.680999943000001], [6.6167026280000005, 7.6167026280000005], [6.783358032000001, 7.783358032000001], [6.413742713, 7.413742713], [6.414147428000001, 7.414147428000001], [6.800878205, 7.800878205], [6.864305278000001, 7.864305278000001], [6.280905276, 7.280905276], [6.344639077, 7.344639077], [6.404229235000001, 7.404229235000001], [6.856914646000001, 7.856914646000001], [6.34989934, 7.34989934], [6.735262481, 7.735262481], [6.675748908, 7.675748908], [6.466401123000001, 7.466401123000001], [6.737411457, 7.737411457], [6.348840936, 7.348840936], [6.677162362000001, 7.677162362000001], [6.798594545, 7.798594545], [6.283020672, 7.283020672], [6.469117276, 7.469117276], [6.4668551050000005, 7.4668551050000005], [6.610114565000001, 7.610114565000001], [6.349625559000001, 7.349625559000001], [6.395806426, 7.395806426], [6.7384616170000005, 7.7384616170000005], [6.462382407000001, 7.462382407000001], [6.6120342690000005, 7.6120342690000005], [6.73289661, 7.73289661], [6.667948233000001, 7.667948233000001], [6.6112702500000005, 7.6112702500000005], [6.864172255000001, 7.864172255000001], [6.282674511000001, 7.282674511000001], [6.801008984, 7.801008984], [6.859067149, 7.859067149], [6.465269979, 7.465269979], [6.7361049920000005, 7.7361049920000005], [6.67783217, 7.67783217], [6.412573168000001, 7.412573168000001], [6.341239745, 7.341239745], [6.281320418, 7.281320418000001], [6.349049596, 7.349049596], [6.800622564, 7.800622564], [6.611809792000001, 7.611809792000001], [6.287678387000001, 7.287678387000001], [6.862640682, 7.862640682], [6.465465709, 7.465465709], [6.344697398, 7.344697398], [6.793386304, 7.793386304], [6.4617575590000005, 7.4617575590000005], [6.607543144, 7.607543144], [6.7359669900000005, 7.7359669900000005], [6.411712598, 7.411712598], [6.613862377, 7.613862377], [6.862035392, 7.862035392], [6.279319736000001, 7.279319736000001], [6.344008769, 7.344008769], [6.413745961, 7.413745961], [6.674388380000001, 7.674388380000001], [6.402236105, 7.402236105], [6.678092161, 7.678092161], [6.674416036, 7.674416036], [6.402937679000001, 7.402937679000001], [6.73942548, 7.73942548], [6.800285152000001, 7.800285152000001], [6.463662531000001, 7.463662531000001], [6.614438938, 7.614438938], [6.7383810660000005, 7.7383810660000005], [6.670166834000001, 7.670166834000001], [6.793759388000001, 7.793759388000001], [6.861136836, 7.861136836000001], [6.277508294, 7.277508294], [6.798903017000001, 7.798903017000001], [6.409597981, 7.409597981], [6.464053776, 7.464053776], [6.735942006, 7.735942006], [6.8003394010000004, 7.8003394010000004], [6.287156240000001, 7.287156240000001], [6.862635201000001, 7.862635201000001], [6.459833859000001, 7.459833859000001], [6.613161948, 7.613161948], [6.6781446980000005, 7.6781446980000005], [6.798828763, 7.798828763], [6.461823034, 7.461823034], [6.607170245000001, 7.607170245000001], [6.461529105, 7.461529105], [6.281338874, 7.281338874], [6.4041221120000005, 7.4041221120000005], [6.6650627810000005, 7.6650627810000005], [6.607526975000001, 7.607526975000001], [6.344935583000001, 7.344935583000001], [6.674316171, 7.674316171], [6.799285466000001, 7.799285466000001], [6.855901468000001, 7.855901468000001], [6.280517209, 7.280517209], [6.408244548000001, 7.408244548000001], [6.34329397, 7.34329397], [6.3413553700000005, 7.3413553700000005], [6.738096405, 7.738096405], [6.345083111, 7.345083111], [6.863937529, 7.863937529], [6.284397037000001, 7.284397037000001], [6.4629141080000005, 7.4629141080000005], [6.342118157000001, 7.342118157000001], [6.2729470460000005, 7.2729470460000005], [6.7334105300000004, 7.7334105300000004], [6.78490544, 7.78490544], [6.401915231, 7.401915231], [6.8612364260000005, 7.8612364260000005], [6.284719408, 7.284719408000001], [6.468010979000001, 7.468010979000001], [6.342887082000001, 7.342887082000001], [6.4109466280000005, 7.4109466280000005], [6.4663977820000005, 7.4663977820000005]], "meas_kernels": ["hw_qmfk"], "discriminators": ["quadratic_discriminator", "hw_qmfk", "linear_discriminator"], "rep_times": [1000.0], "meas_map": [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126]], "acquisition_latency": [], "conditional_latency": [], "hamiltonian": {"description": "Qubits are modeled as Duffing oscillators. In this case, the system includes higher energy states, i.e. not just |0> and |1>. The Pauli operators are generalized via the following set of transformations:\n\n$(\\mathbb{I}-\\sigma_{i}^z)/2 \\rightarrow O_i \\equiv b^\\dagger_{i} b_{i}$,\n\n$\\sigma_{+} \\rightarrow b^\\dagger$,\n\n$\\sigma_{-} \\rightarrow b$,\n\n$\\sigma_{i}^X \\rightarrow b^\\dagger_{i} + b_{i}$.\n\nQubits are coupled through resonator buses. The provided Hamiltonian has been projected into the zero excitation subspace of the resonator buses leading to an effective qubit-qubit flip-flop interaction. The qubit resonance frequencies in the Hamiltonian are the cavity dressed frequencies and not exactly what is returned by the backend defaults, which also includes the dressing due to the qubit-qubit interactions.\n\nQuantities are returned in angular frequencies, with units 2*pi*GHz.\n\nWARNING: Currently not all system Hamiltonian information is available to the public, missing values have been replaced with 0.\n", "h_latex": "\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{126}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{62,72}(\\sigma_{62}^{+}\\sigma_{72}^{-}+\\sigma_{62}^{-}\\sigma_{72}^{+}) + J_{67,68}(\\sigma_{67}^{+}\\sigma_{68}^{-}+\\sigma_{67}^{-}\\sigma_{68}^{+}) + J_{44,45}(\\sigma_{44}^{+}\\sigma_{45}^{-}+\\sigma_{44}^{-}\\sigma_{45}^{+}) + J_{99,100}(\\sigma_{99}^{+}\\sigma_{100}^{-}+\\sigma_{99}^{-}\\sigma_{100}^{+}) \\\\ & + J_{108,112}(\\sigma_{108}^{+}\\sigma_{112}^{-}+\\sigma_{108}^{-}\\sigma_{112}^{+}) + J_{8,9}(\\sigma_{8}^{+}\\sigma_{9}^{-}+\\sigma_{8}^{-}\\sigma_{9}^{+}) + J_{40,41}(\\sigma_{40}^{+}\\sigma_{41}^{-}+\\sigma_{40}^{-}\\sigma_{41}^{+}) + J_{0,14}(\\sigma_{0}^{+}\\sigma_{14}^{-}+\\sigma_{0}^{-}\\sigma_{14}^{+}) \\\\ & + J_{17,30}(\\sigma_{17}^{+}\\sigma_{30}^{-}+\\sigma_{17}^{-}\\sigma_{30}^{+}) + J_{100,101}(\\sigma_{100}^{+}\\sigma_{101}^{-}+\\sigma_{100}^{-}\\sigma_{101}^{+}) + J_{91,98}(\\sigma_{91}^{+}\\sigma_{98}^{-}+\\sigma_{91}^{-}\\sigma_{98}^{+}) + J_{100,110}(\\sigma_{100}^{+}\\sigma_{110}^{-}+\\sigma_{100}^{-}\\sigma_{110}^{+}) \\\\ & + J_{75,90}(\\sigma_{75}^{+}\\sigma_{90}^{-}+\\sigma_{75}^{-}\\sigma_{90}^{+}) + J_{41,42}(\\sigma_{41}^{+}\\sigma_{42}^{-}+\\sigma_{41}^{-}\\sigma_{42}^{+}) + J_{96,97}(\\sigma_{96}^{+}\\sigma_{97}^{-}+\\sigma_{96}^{-}\\sigma_{97}^{+}) + J_{18,19}(\\sigma_{18}^{+}\\sigma_{19}^{-}+\\sigma_{18}^{-}\\sigma_{19}^{+}) \\\\ & + J_{55,68}(\\sigma_{55}^{+}\\sigma_{68}^{-}+\\sigma_{55}^{-}\\sigma_{68}^{+}) + J_{9,10}(\\sigma_{9}^{+}\\sigma_{10}^{-}+\\sigma_{9}^{-}\\sigma_{10}^{+}) + J_{49,55}(\\sigma_{49}^{+}\\sigma_{55}^{-}+\\sigma_{49}^{-}\\sigma_{55}^{+}) + J_{106,107}(\\sigma_{106}^{+}\\sigma_{107}^{-}+\\sigma_{106}^{-}\\sigma_{107}^{+}) \\\\ & + J_{47,48}(\\sigma_{47}^{+}\\sigma_{48}^{-}+\\sigma_{47}^{-}\\sigma_{48}^{+}) + J_{42,43}(\\sigma_{42}^{+}\\sigma_{43}^{-}+\\sigma_{42}^{-}\\sigma_{43}^{+}) + J_{107,108}(\\sigma_{107}^{+}\\sigma_{108}^{-}+\\sigma_{107}^{-}\\sigma_{108}^{+}) + J_{73,85}(\\sigma_{73}^{+}\\sigma_{85}^{-}+\\sigma_{73}^{-}\\sigma_{85}^{+}) \\\\ & + J_{38,39}(\\sigma_{38}^{+}\\sigma_{39}^{-}+\\sigma_{38}^{-}\\sigma_{39}^{+}) + J_{20,33}(\\sigma_{20}^{+}\\sigma_{33}^{-}+\\sigma_{20}^{-}\\sigma_{33}^{+}) + J_{48,49}(\\sigma_{48}^{+}\\sigma_{49}^{-}+\\sigma_{48}^{-}\\sigma_{49}^{+}) + J_{103,104}(\\sigma_{103}^{+}\\sigma_{104}^{-}+\\sigma_{103}^{-}\\sigma_{104}^{+}) \\\\ & + J_{80,81}(\\sigma_{80}^{+}\\sigma_{81}^{-}+\\sigma_{80}^{-}\\sigma_{81}^{+}) + J_{75,76}(\\sigma_{75}^{+}\\sigma_{76}^{-}+\\sigma_{75}^{-}\\sigma_{76}^{+}) + J_{66,73}(\\sigma_{66}^{+}\\sigma_{73}^{-}+\\sigma_{66}^{-}\\sigma_{73}^{+}) + J_{85,86}(\\sigma_{85}^{+}\\sigma_{86}^{-}+\\sigma_{85}^{-}\\sigma_{86}^{+}) \\\\ & + J_{110,118}(\\sigma_{110}^{+}\\sigma_{118}^{-}+\\sigma_{110}^{-}\\sigma_{118}^{+}) + J_{81,82}(\\sigma_{81}^{+}\\sigma_{82}^{-}+\\sigma_{81}^{-}\\sigma_{82}^{+}) + J_{16,26}(\\sigma_{16}^{+}\\sigma_{26}^{-}+\\sigma_{16}^{-}\\sigma_{26}^{+}) + J_{90,94}(\\sigma_{90}^{+}\\sigma_{94}^{-}+\\sigma_{90}^{-}\\sigma_{94}^{+}) \\\\ & + J_{118,119}(\\sigma_{118}^{+}\\sigma_{119}^{-}+\\sigma_{118}^{-}\\sigma_{119}^{+}) + J_{12,13}(\\sigma_{12}^{+}\\sigma_{13}^{-}+\\sigma_{12}^{-}\\sigma_{13}^{+}) + J_{77,78}(\\sigma_{77}^{+}\\sigma_{78}^{-}+\\sigma_{77}^{-}\\sigma_{78}^{+}) + J_{22,23}(\\sigma_{22}^{+}\\sigma_{23}^{-}+\\sigma_{22}^{-}\\sigma_{23}^{+}) \\\\ & + J_{49,50}(\\sigma_{49}^{+}\\sigma_{50}^{-}+\\sigma_{49}^{-}\\sigma_{50}^{+}) + J_{104,105}(\\sigma_{104}^{+}\\sigma_{105}^{-}+\\sigma_{104}^{-}\\sigma_{105}^{+}) + J_{114,115}(\\sigma_{114}^{+}\\sigma_{115}^{-}+\\sigma_{114}^{-}\\sigma_{115}^{+}) + J_{45,46}(\\sigma_{45}^{+}\\sigma_{46}^{-}+\\sigma_{45}^{-}\\sigma_{46}^{+}) \\\\ & + J_{50,51}(\\sigma_{50}^{+}\\sigma_{51}^{-}+\\sigma_{50}^{-}\\sigma_{51}^{+}) + J_{105,106}(\\sigma_{105}^{+}\\sigma_{106}^{-}+\\sigma_{105}^{-}\\sigma_{106}^{+}) + J_{72,81}(\\sigma_{72}^{+}\\sigma_{81}^{-}+\\sigma_{72}^{-}\\sigma_{81}^{+}) + J_{82,83}(\\sigma_{82}^{+}\\sigma_{83}^{-}+\\sigma_{82}^{-}\\sigma_{83}^{+}) \\\\ & + J_{46,47}(\\sigma_{46}^{+}\\sigma_{47}^{-}+\\sigma_{46}^{-}\\sigma_{47}^{+}) + J_{23,24}(\\sigma_{23}^{+}\\sigma_{24}^{-}+\\sigma_{23}^{-}\\sigma_{24}^{+}) + J_{78,79}(\\sigma_{78}^{+}\\sigma_{79}^{-}+\\sigma_{78}^{-}\\sigma_{79}^{+}) + J_{83,84}(\\sigma_{83}^{+}\\sigma_{84}^{-}+\\sigma_{83}^{-}\\sigma_{84}^{+}) \\\\ & + J_{115,116}(\\sigma_{115}^{+}\\sigma_{116}^{-}+\\sigma_{115}^{-}\\sigma_{116}^{+}) + J_{19,20}(\\sigma_{19}^{+}\\sigma_{20}^{-}+\\sigma_{19}^{-}\\sigma_{20}^{+}) + J_{24,25}(\\sigma_{24}^{+}\\sigma_{25}^{-}+\\sigma_{24}^{-}\\sigma_{25}^{+}) + J_{79,80}(\\sigma_{79}^{+}\\sigma_{80}^{-}+\\sigma_{79}^{-}\\sigma_{80}^{+}) \\\\ & + J_{56,57}(\\sigma_{56}^{+}\\sigma_{57}^{-}+\\sigma_{56}^{-}\\sigma_{57}^{+}) + J_{93,106}(\\sigma_{93}^{+}\\sigma_{106}^{-}+\\sigma_{93}^{-}\\sigma_{106}^{+}) + J_{116,117}(\\sigma_{116}^{+}\\sigma_{117}^{-}+\\sigma_{116}^{-}\\sigma_{117}^{+}) + J_{20,21}(\\sigma_{20}^{+}\\sigma_{21}^{-}+\\sigma_{20}^{-}\\sigma_{21}^{+}) \\\\ & + J_{12,17}(\\sigma_{12}^{+}\\sigma_{17}^{-}+\\sigma_{12}^{-}\\sigma_{17}^{+}) + J_{41,53}(\\sigma_{41}^{+}\\sigma_{53}^{-}+\\sigma_{41}^{-}\\sigma_{53}^{+}) + J_{57,58}(\\sigma_{57}^{+}\\sigma_{58}^{-}+\\sigma_{57}^{-}\\sigma_{58}^{+}) + J_{87,93}(\\sigma_{87}^{+}\\sigma_{93}^{-}+\\sigma_{87}^{-}\\sigma_{93}^{+}) \\\\ & + J_{30,31}(\\sigma_{30}^{+}\\sigma_{31}^{-}+\\sigma_{30}^{-}\\sigma_{31}^{+}) + J_{25,26}(\\sigma_{25}^{+}\\sigma_{26}^{-}+\\sigma_{25}^{-}\\sigma_{26}^{+}) + J_{79,91}(\\sigma_{79}^{+}\\sigma_{91}^{-}+\\sigma_{79}^{-}\\sigma_{91}^{+}) + J_{26,27}(\\sigma_{26}^{+}\\sigma_{27}^{-}+\\sigma_{26}^{-}\\sigma_{27}^{+}) \\\\ & + J_{21,22}(\\sigma_{21}^{+}\\sigma_{22}^{-}+\\sigma_{21}^{-}\\sigma_{22}^{+}) + J_{58,71}(\\sigma_{58}^{+}\\sigma_{71}^{-}+\\sigma_{58}^{-}\\sigma_{71}^{+}) + J_{86,87}(\\sigma_{86}^{+}\\sigma_{87}^{-}+\\sigma_{86}^{-}\\sigma_{87}^{+}) + J_{31,32}(\\sigma_{31}^{+}\\sigma_{32}^{-}+\\sigma_{31}^{-}\\sigma_{32}^{+}) \\\\ & + J_{4,15}(\\sigma_{4}^{+}\\sigma_{15}^{-}+\\sigma_{4}^{-}\\sigma_{15}^{+}) + J_{113,114}(\\sigma_{113}^{+}\\sigma_{114}^{-}+\\sigma_{113}^{-}\\sigma_{114}^{+}) + J_{104,111}(\\sigma_{104}^{+}\\sigma_{111}^{-}+\\sigma_{104}^{-}\\sigma_{111}^{+}) + J_{123,124}(\\sigma_{123}^{+}\\sigma_{124}^{-}+\\sigma_{123}^{-}\\sigma_{124}^{+}) \\\\ & + J_{27,28}(\\sigma_{27}^{+}\\sigma_{28}^{-}+\\sigma_{27}^{-}\\sigma_{28}^{+}) + J_{34,43}(\\sigma_{34}^{+}\\sigma_{43}^{-}+\\sigma_{34}^{-}\\sigma_{43}^{+}) + J_{119,120}(\\sigma_{119}^{+}\\sigma_{120}^{-}+\\sigma_{119}^{-}\\sigma_{120}^{+}) + J_{64,65}(\\sigma_{64}^{+}\\sigma_{65}^{-}+\\sigma_{64}^{-}\\sigma_{65}^{+}) \\\\ & + J_{54,64}(\\sigma_{54}^{+}\\sigma_{64}^{-}+\\sigma_{54}^{-}\\sigma_{64}^{+}) + J_{32,36}(\\sigma_{32}^{+}\\sigma_{36}^{-}+\\sigma_{32}^{-}\\sigma_{36}^{+}) + J_{5,6}(\\sigma_{5}^{+}\\sigma_{6}^{-}+\\sigma_{5}^{-}\\sigma_{6}^{+}) + J_{60,61}(\\sigma_{60}^{+}\\sigma_{61}^{-}+\\sigma_{60}^{-}\\sigma_{61}^{+}) \\\\ & + J_{14,18}(\\sigma_{14}^{+}\\sigma_{18}^{-}+\\sigma_{14}^{-}\\sigma_{18}^{+}) + J_{87,88}(\\sigma_{87}^{+}\\sigma_{88}^{-}+\\sigma_{87}^{-}\\sigma_{88}^{+}) + J_{97,98}(\\sigma_{97}^{+}\\sigma_{98}^{-}+\\sigma_{97}^{-}\\sigma_{98}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) \\\\ & + J_{112,126}(\\sigma_{112}^{+}\\sigma_{126}^{-}+\\sigma_{112}^{-}\\sigma_{126}^{+}) + J_{28,29}(\\sigma_{28}^{+}\\sigma_{29}^{-}+\\sigma_{28}^{-}\\sigma_{29}^{+}) + J_{45,54}(\\sigma_{45}^{+}\\sigma_{54}^{-}+\\sigma_{45}^{-}\\sigma_{54}^{+}) + J_{36,51}(\\sigma_{36}^{+}\\sigma_{51}^{-}+\\sigma_{36}^{-}\\sigma_{51}^{+}) \\\\ & + J_{88,89}(\\sigma_{88}^{+}\\sigma_{89}^{-}+\\sigma_{88}^{-}\\sigma_{89}^{+}) + J_{120,121}(\\sigma_{120}^{+}\\sigma_{121}^{-}+\\sigma_{120}^{-}\\sigma_{121}^{+}) + J_{15,22}(\\sigma_{15}^{+}\\sigma_{22}^{-}+\\sigma_{15}^{-}\\sigma_{22}^{+}) + J_{24,34}(\\sigma_{24}^{+}\\sigma_{34}^{-}+\\sigma_{24}^{-}\\sigma_{34}^{+}) \\\\ & + J_{84,85}(\\sigma_{84}^{+}\\sigma_{85}^{-}+\\sigma_{84}^{-}\\sigma_{85}^{+}) + J_{29,30}(\\sigma_{29}^{+}\\sigma_{30}^{-}+\\sigma_{29}^{-}\\sigma_{30}^{+}) + J_{61,62}(\\sigma_{61}^{+}\\sigma_{62}^{-}+\\sigma_{61}^{-}\\sigma_{62}^{+}) + J_{70,74}(\\sigma_{70}^{+}\\sigma_{74}^{-}+\\sigma_{70}^{-}\\sigma_{74}^{+}) \\\\ & + J_{121,122}(\\sigma_{121}^{+}\\sigma_{122}^{-}+\\sigma_{121}^{-}\\sigma_{122}^{+}) + J_{2,3}(\\sigma_{2}^{+}\\sigma_{3}^{-}+\\sigma_{2}^{-}\\sigma_{3}^{+}) + J_{122,123}(\\sigma_{122}^{+}\\sigma_{123}^{-}+\\sigma_{122}^{-}\\sigma_{123}^{+}) + J_{117,118}(\\sigma_{117}^{+}\\sigma_{118}^{-}+\\sigma_{117}^{-}\\sigma_{118}^{+}) \\\\ & + J_{62,63}(\\sigma_{62}^{+}\\sigma_{63}^{-}+\\sigma_{62}^{-}\\sigma_{63}^{+}) + J_{94,95}(\\sigma_{94}^{+}\\sigma_{95}^{-}+\\sigma_{94}^{-}\\sigma_{95}^{+}) + J_{109,114}(\\sigma_{109}^{+}\\sigma_{114}^{-}+\\sigma_{109}^{-}\\sigma_{114}^{+}) + J_{37,52}(\\sigma_{37}^{+}\\sigma_{52}^{-}+\\sigma_{37}^{-}\\sigma_{52}^{+}) \\\\ & + J_{3,4}(\\sigma_{3}^{+}\\sigma_{4}^{-}+\\sigma_{3}^{-}\\sigma_{4}^{+}) + J_{58,59}(\\sigma_{58}^{+}\\sigma_{59}^{-}+\\sigma_{58}^{-}\\sigma_{59}^{+}) + J_{33,39}(\\sigma_{33}^{+}\\sigma_{39}^{-}+\\sigma_{33}^{-}\\sigma_{39}^{+}) + J_{95,96}(\\sigma_{95}^{+}\\sigma_{96}^{-}+\\sigma_{95}^{-}\\sigma_{96}^{+}) \\\\ & + J_{68,69}(\\sigma_{68}^{+}\\sigma_{69}^{-}+\\sigma_{68}^{-}\\sigma_{69}^{+}) + J_{63,64}(\\sigma_{63}^{+}\\sigma_{64}^{-}+\\sigma_{63}^{-}\\sigma_{64}^{+}) + J_{71,77}(\\sigma_{71}^{+}\\sigma_{77}^{-}+\\sigma_{71}^{-}\\sigma_{77}^{+}) + J_{111,122}(\\sigma_{111}^{+}\\sigma_{122}^{-}+\\sigma_{111}^{-}\\sigma_{122}^{+}) \\\\ & + J_{4,5}(\\sigma_{4}^{+}\\sigma_{5}^{-}+\\sigma_{4}^{-}\\sigma_{5}^{+}) + J_{59,60}(\\sigma_{59}^{+}\\sigma_{60}^{-}+\\sigma_{59}^{-}\\sigma_{60}^{+}) + J_{96,109}(\\sigma_{96}^{+}\\sigma_{109}^{-}+\\sigma_{96}^{-}\\sigma_{109}^{+}) + J_{124,125}(\\sigma_{124}^{+}\\sigma_{125}^{-}+\\sigma_{124}^{-}\\sigma_{125}^{+}) \\\\ & + J_{69,70}(\\sigma_{69}^{+}\\sigma_{70}^{-}+\\sigma_{69}^{-}\\sigma_{70}^{+}) + J_{35,47}(\\sigma_{35}^{+}\\sigma_{47}^{-}+\\sigma_{35}^{-}\\sigma_{47}^{+}) + J_{101,102}(\\sigma_{101}^{+}\\sigma_{102}^{-}+\\sigma_{101}^{-}\\sigma_{102}^{+}) + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) \\\\ & + J_{65,66}(\\sigma_{65}^{+}\\sigma_{66}^{-}+\\sigma_{65}^{-}\\sigma_{66}^{+}) + J_{10,11}(\\sigma_{10}^{+}\\sigma_{11}^{-}+\\sigma_{10}^{-}\\sigma_{11}^{+}) + J_{37,38}(\\sigma_{37}^{+}\\sigma_{38}^{-}+\\sigma_{37}^{-}\\sigma_{38}^{+}) + J_{28,35}(\\sigma_{28}^{+}\\sigma_{35}^{-}+\\sigma_{28}^{-}\\sigma_{35}^{+}) \\\\ & + J_{102,103}(\\sigma_{102}^{+}\\sigma_{103}^{-}+\\sigma_{102}^{-}\\sigma_{103}^{+}) + J_{92,102}(\\sigma_{92}^{+}\\sigma_{102}^{-}+\\sigma_{92}^{-}\\sigma_{102}^{+}) + J_{6,7}(\\sigma_{6}^{+}\\sigma_{7}^{-}+\\sigma_{6}^{-}\\sigma_{7}^{+}) + J_{43,44}(\\sigma_{43}^{+}\\sigma_{44}^{-}+\\sigma_{43}^{-}\\sigma_{44}^{+}) \\\\ & + J_{98,99}(\\sigma_{98}^{+}\\sigma_{99}^{-}+\\sigma_{98}^{-}\\sigma_{99}^{+}) + J_{52,56}(\\sigma_{52}^{+}\\sigma_{56}^{-}+\\sigma_{52}^{-}\\sigma_{56}^{+}) + J_{125,126}(\\sigma_{125}^{+}\\sigma_{126}^{-}+\\sigma_{125}^{-}\\sigma_{126}^{+}) + J_{39,40}(\\sigma_{39}^{+}\\sigma_{40}^{-}+\\sigma_{39}^{-}\\sigma_{40}^{+}) \\\\ & + J_{8,16}(\\sigma_{8}^{+}\\sigma_{16}^{-}+\\sigma_{8}^{-}\\sigma_{16}^{+}) + J_{11,12}(\\sigma_{11}^{+}\\sigma_{12}^{-}+\\sigma_{11}^{-}\\sigma_{12}^{+}) + J_{66,67}(\\sigma_{66}^{+}\\sigma_{67}^{-}+\\sigma_{66}^{-}\\sigma_{67}^{+}) + J_{76,77}(\\sigma_{76}^{+}\\sigma_{77}^{-}+\\sigma_{76}^{-}\\sigma_{77}^{+}) \\\\ & + J_{83,92}(\\sigma_{83}^{+}\\sigma_{92}^{-}+\\sigma_{83}^{-}\\sigma_{92}^{+}) + J_{74,89}(\\sigma_{74}^{+}\\sigma_{89}^{-}+\\sigma_{74}^{-}\\sigma_{89}^{+}) + J_{7,8}(\\sigma_{7}^{+}\\sigma_{8}^{-}+\\sigma_{7}^{-}\\sigma_{8}^{+}) + J_{53,60}(\\sigma_{53}^{+}\\sigma_{60}^{-}+\\sigma_{53}^{-}\\sigma_{60}^{+}) \\\\ & + \\Omega_{d,1}(U_{0}^{(1,0)}(t))\\sigma_{1}^{X} + \\Omega_{d,2}(U_{1}^{(2,1)}(t))\\sigma_{2}^{X} \\\\ & + \\Omega_{d,3}(U_{3}^{(3,4)}(t)+U_{2}^{(3,2)}(t))\\sigma_{3}^{X} + \\Omega_{d,4}(U_{4}^{(4,15)}(t))\\sigma_{4}^{X} \\\\ & + \\Omega_{d,5}(U_{6}^{(5,6)}(t)+U_{5}^{(5,4)}(t))\\sigma_{5}^{X} + \\Omega_{d,6}(U_{7}^{(6,7)}(t))\\sigma_{6}^{X} \\\\ & + \\Omega_{d,7}(U_{8}^{(7,8)}(t))\\sigma_{7}^{X} + \\Omega_{d,8}(U_{9}^{(8,16)}(t))\\sigma_{8}^{X} \\\\ & + \\Omega_{d,9}(U_{11}^{(9,10)}(t)+U_{10}^{(9,8)}(t))\\sigma_{9}^{X} + \\Omega_{d,11}(U_{12}^{(11,10)}(t)+U_{13}^{(11,12)}(t))\\sigma_{11}^{X} \\\\ & + \\Omega_{d,13}(U_{14}^{(13,12)}(t))\\sigma_{13}^{X} + \\Omega_{d,14}(U_{15}^{(14,0)}(t)+U_{16}^{(14,18)}(t))\\sigma_{14}^{X} \\\\ & + \\Omega_{d,16}(U_{17}^{(16,26)}(t))\\sigma_{16}^{X} + \\Omega_{d,17}(U_{18}^{(17,12)}(t))\\sigma_{17}^{X} \\\\ & + \\Omega_{d,19}(U_{19}^{(19,18)}(t)+U_{20}^{(19,20)}(t))\\sigma_{19}^{X} + \\Omega_{d,20}(U_{21}^{(20,33)}(t))\\sigma_{20}^{X} \\\\ & + \\Omega_{d,21}(U_{23}^{(21,22)}(t)+U_{22}^{(21,20)}(t))\\sigma_{21}^{X} + \\Omega_{d,22}(U_{24}^{(22,15)}(t))\\sigma_{22}^{X} \\\\ & + \\Omega_{d,23}(U_{25}^{(23,22)}(t))\\sigma_{23}^{X} + \\Omega_{d,24}(U_{26}^{(24,23)}(t))\\sigma_{24}^{X} \\\\ & + \\Omega_{d,25}(U_{27}^{(25,24)}(t))\\sigma_{25}^{X} + \\Omega_{d,26}(U_{29}^{(26,27)}(t)+U_{28}^{(26,25)}(t))\\sigma_{26}^{X} \\\\ & + \\Omega_{d,28}(U_{31}^{(28,35)}(t)+U_{30}^{(28,27)}(t))\\sigma_{28}^{X} + \\Omega_{d,29}(U_{32}^{(29,28)}(t))\\sigma_{29}^{X} \\\\ & + \\Omega_{d,30}(U_{33}^{(30,17)}(t)+U_{34}^{(30,29)}(t))\\sigma_{30}^{X} + \\Omega_{d,31}(U_{35}^{(31,30)}(t)+U_{36}^{(31,32)}(t))\\sigma_{31}^{X} \\\\ & + \\Omega_{d,34}(U_{38}^{(34,43)}(t)+U_{37}^{(34,24)}(t))\\sigma_{34}^{X} + \\Omega_{d,35}(U_{39}^{(35,47)}(t))\\sigma_{35}^{X} \\\\ & + \\Omega_{d,36}(U_{40}^{(36,32)}(t))\\sigma_{36}^{X} + \\Omega_{d,38}(U_{42}^{(38,39)}(t)+U_{41}^{(38,37)}(t))\\sigma_{38}^{X} \\\\ & + \\Omega_{d,39}(U_{44}^{(39,40)}(t)+U_{43}^{(39,33)}(t))\\sigma_{39}^{X} + \\Omega_{d,40}(U_{45}^{(40,41)}(t))\\sigma_{40}^{X} \\\\ & + \\Omega_{d,41}(U_{46}^{(41,42)}(t))\\sigma_{41}^{X} + \\Omega_{d,43}(U_{48}^{(43,44)}(t)+U_{47}^{(43,42)}(t))\\sigma_{43}^{X} \\\\ & + \\Omega_{d,44}(U_{49}^{(44,45)}(t))\\sigma_{44}^{X} + \\Omega_{d,46}(U_{50}^{(46,45)}(t))\\sigma_{46}^{X} \\\\ & + \\Omega_{d,47}(U_{51}^{(47,46)}(t))\\sigma_{47}^{X} + \\Omega_{d,48}(U_{53}^{(48,49)}(t)+U_{52}^{(48,47)}(t))\\sigma_{48}^{X} \\\\ & + \\Omega_{d,50}(U_{54}^{(50,49)}(t))\\sigma_{50}^{X} + \\Omega_{d,51}(U_{56}^{(51,50)}(t)+U_{55}^{(51,36)}(t))\\sigma_{51}^{X} \\\\ & + \\Omega_{d,52}(U_{58}^{(52,56)}(t)+U_{57}^{(52,37)}(t))\\sigma_{52}^{X} + \\Omega_{d,53}(U_{60}^{(53,60)}(t)+U_{59}^{(53,41)}(t))\\sigma_{53}^{X} \\\\ & + \\Omega_{d,54}(U_{62}^{(54,64)}(t)+U_{61}^{(54,45)}(t))\\sigma_{54}^{X} + \\Omega_{d,55}(U_{64}^{(55,68)}(t)+U_{63}^{(55,49)}(t))\\sigma_{55}^{X} \\\\ & + \\Omega_{d,57}(U_{65}^{(57,56)}(t))\\sigma_{57}^{X} + \\Omega_{d,58}(U_{67}^{(58,59)}(t)+U_{66}^{(58,57)}(t))\\sigma_{58}^{X} \\\\ & + \\Omega_{d,59}(U_{68}^{(59,60)}(t))\\sigma_{59}^{X} + \\Omega_{d,60}(U_{69}^{(60,61)}(t))\\sigma_{60}^{X} \\\\ & + \\Omega_{d,62}(U_{72}^{(62,72)}(t)+U_{71}^{(62,63)}(t)+U_{70}^{(62,61)}(t))\\sigma_{62}^{X} + \\Omega_{d,64}(U_{73}^{(64,63)}(t))\\sigma_{64}^{X} \\\\ & + \\Omega_{d,65}(U_{75}^{(65,66)}(t)+U_{74}^{(65,64)}(t))\\sigma_{65}^{X} + \\Omega_{d,66}(U_{77}^{(66,73)}(t)+U_{76}^{(66,67)}(t))\\sigma_{66}^{X} \\\\ & + \\Omega_{d,68}(U_{78}^{(68,67)}(t))\\sigma_{68}^{X} + \\Omega_{d,69}(U_{79}^{(69,68)}(t))\\sigma_{69}^{X} \\\\ & + \\Omega_{d,70}(U_{80}^{(70,69)}(t)+U_{81}^{(70,74)}(t))\\sigma_{70}^{X} + \\Omega_{d,71}(U_{83}^{(71,77)}(t)+U_{82}^{(71,58)}(t))\\sigma_{71}^{X} \\\\ & + \\Omega_{d,74}(U_{84}^{(74,89)}(t))\\sigma_{74}^{X} + \\Omega_{d,75}(U_{85}^{(75,76)}(t))\\sigma_{75}^{X} \\\\ & + \\Omega_{d,76}(U_{86}^{(76,77)}(t))\\sigma_{76}^{X} + \\Omega_{d,77}(U_{87}^{(77,78)}(t))\\sigma_{77}^{X} \\\\ & + \\Omega_{d,79}(U_{88}^{(79,78)}(t))\\sigma_{79}^{X} + \\Omega_{d,80}(U_{90}^{(80,81)}(t)+U_{89}^{(80,79)}(t))\\sigma_{80}^{X} \\\\ & + \\Omega_{d,81}(U_{91}^{(81,72)}(t))\\sigma_{81}^{X} + \\Omega_{d,82}(U_{92}^{(82,81)}(t)+U_{93}^{(82,83)}(t))\\sigma_{82}^{X} \\\\ & + \\Omega_{d,83}(U_{94}^{(83,84)}(t))\\sigma_{83}^{X} + \\Omega_{d,85}(U_{96}^{(85,84)}(t)+U_{97}^{(85,86)}(t)+U_{95}^{(85,73)}(t))\\sigma_{85}^{X} \\\\ & + \\Omega_{d,86}(U_{98}^{(86,87)}(t))\\sigma_{86}^{X} + \\Omega_{d,87}(U_{100}^{(87,93)}(t)+U_{99}^{(87,88)}(t))\\sigma_{87}^{X} \\\\ & + \\Omega_{d,89}(U_{101}^{(89,88)}(t))\\sigma_{89}^{X} + \\Omega_{d,90}(U_{102}^{(90,75)}(t))\\sigma_{90}^{X} \\\\ & + \\Omega_{d,91}(U_{104}^{(91,98)}(t)+U_{103}^{(91,79)}(t))\\sigma_{91}^{X} + \\Omega_{d,92}(U_{105}^{(92,83)}(t))\\sigma_{92}^{X} \\\\ & + \\Omega_{d,94}(U_{107}^{(94,95)}(t)+U_{106}^{(94,90)}(t))\\sigma_{94}^{X} + \\Omega_{d,96}(U_{109}^{(96,109)}(t)+U_{108}^{(96,95)}(t))\\sigma_{96}^{X} \\\\ & + \\Omega_{d,97}(U_{111}^{(97,98)}(t)+U_{110}^{(97,96)}(t))\\sigma_{97}^{X} + \\Omega_{d,98}(U_{112}^{(98,99)}(t))\\sigma_{98}^{X} \\\\ & + \\Omega_{d,100}(U_{113}^{(100,99)}(t)+U_{114}^{(100,110)}(t))\\sigma_{100}^{X} + \\Omega_{d,101}(U_{116}^{(101,102)}(t)+U_{115}^{(101,100)}(t))\\sigma_{101}^{X} \\\\ & + \\Omega_{d,102}(U_{117}^{(102,92)}(t))\\sigma_{102}^{X} + \\Omega_{d,103}(U_{119}^{(103,104)}(t)+U_{118}^{(103,102)}(t))\\sigma_{103}^{X} \\\\ & + \\Omega_{d,104}(U_{120}^{(104,105)}(t))\\sigma_{104}^{X} + \\Omega_{d,106}(U_{121}^{(106,93)}(t)+U_{123}^{(106,107)}(t)+U_{122}^{(106,105)}(t))\\sigma_{106}^{X} \\\\ & + \\Omega_{d,108}(U_{124}^{(108,107)}(t)+U_{125}^{(108,112)}(t))\\sigma_{108}^{X} + \\Omega_{d,109}(U_{126}^{(109,114)}(t))\\sigma_{109}^{X} \\\\ & + \\Omega_{d,110}(U_{127}^{(110,118)}(t))\\sigma_{110}^{X} + \\Omega_{d,111}(U_{128}^{(111,104)}(t))\\sigma_{111}^{X} \\\\ & + \\Omega_{d,114}(U_{129}^{(114,113)}(t))\\sigma_{114}^{X} + \\Omega_{d,115}(U_{130}^{(115,114)}(t)+U_{131}^{(115,116)}(t))\\sigma_{115}^{X} \\\\ & + \\Omega_{d,116}(U_{132}^{(116,117)}(t))\\sigma_{116}^{X} + \\Omega_{d,118}(U_{134}^{(118,119)}(t)+U_{133}^{(118,117)}(t))\\sigma_{118}^{X} \\\\ & + \\Omega_{d,120}(U_{135}^{(120,119)}(t))\\sigma_{120}^{X} + \\Omega_{d,121}(U_{136}^{(121,120)}(t))\\sigma_{121}^{X} \\\\ & + \\Omega_{d,122}(U_{137}^{(122,111)}(t)+U_{138}^{(122,121)}(t))\\sigma_{122}^{X} + \\Omega_{d,123}(U_{140}^{(123,124)}(t)+U_{139}^{(123,122)}(t))\\sigma_{123}^{X} \\\\ & + \\Omega_{d,124}(U_{141}^{(124,125)}(t))\\sigma_{124}^{X} + \\Omega_{d,126}(U_{142}^{(126,112)}(t)+U_{143}^{(126,125)}(t))\\sigma_{126}^{X} \\\\ \\end{align}", "h_str": ["_SUM[i,0,126,wq{i}/2*(I{i}-Z{i})]", "_SUM[i,0,126,delta{i}/2*O{i}*O{i}]", "_SUM[i,0,126,-delta{i}/2*O{i}]", "_SUM[i,0,126,omegad{i}*X{i}||D{i}]", "jq62q72*Sp62*Sm72", "jq62q72*Sm62*Sp72", "jq67q68*Sp67*Sm68", "jq67q68*Sm67*Sp68", "jq44q45*Sp44*Sm45", "jq44q45*Sm44*Sp45", "jq99q100*Sp99*Sm100", "jq99q100*Sm99*Sp100", "jq108q112*Sp108*Sm112", "jq108q112*Sm108*Sp112", "jq8q9*Sp8*Sm9", "jq8q9*Sm8*Sp9", "jq40q41*Sp40*Sm41", "jq40q41*Sm40*Sp41", "jq0q14*Sp0*Sm14", "jq0q14*Sm0*Sp14", "jq17q30*Sp17*Sm30", "jq17q30*Sm17*Sp30", "jq100q101*Sp100*Sm101", "jq100q101*Sm100*Sp101", "jq91q98*Sp91*Sm98", "jq91q98*Sm91*Sp98", "jq100q110*Sp100*Sm110", "jq100q110*Sm100*Sp110", "jq75q90*Sp75*Sm90", "jq75q90*Sm75*Sp90", "jq41q42*Sp41*Sm42", "jq41q42*Sm41*Sp42", "jq96q97*Sp96*Sm97", "jq96q97*Sm96*Sp97", "jq18q19*Sp18*Sm19", "jq18q19*Sm18*Sp19", "jq55q68*Sp55*Sm68", "jq55q68*Sm55*Sp68", "jq9q10*Sp9*Sm10", "jq9q10*Sm9*Sp10", "jq49q55*Sp49*Sm55", "jq49q55*Sm49*Sp55", "jq106q107*Sp106*Sm107", "jq106q107*Sm106*Sp107", "jq47q48*Sp47*Sm48", "jq47q48*Sm47*Sp48", "jq42q43*Sp42*Sm43", "jq42q43*Sm42*Sp43", "jq107q108*Sp107*Sm108", "jq107q108*Sm107*Sp108", "jq73q85*Sp73*Sm85", "jq73q85*Sm73*Sp85", "jq38q39*Sp38*Sm39", "jq38q39*Sm38*Sp39", "jq20q33*Sp20*Sm33", "jq20q33*Sm20*Sp33", "jq48q49*Sp48*Sm49", "jq48q49*Sm48*Sp49", "jq103q104*Sp103*Sm104", "jq103q104*Sm103*Sp104", "jq80q81*Sp80*Sm81", "jq80q81*Sm80*Sp81", "jq75q76*Sp75*Sm76", "jq75q76*Sm75*Sp76", "jq66q73*Sp66*Sm73", "jq66q73*Sm66*Sp73", "jq85q86*Sp85*Sm86", "jq85q86*Sm85*Sp86", "jq110q118*Sp110*Sm118", "jq110q118*Sm110*Sp118", "jq81q82*Sp81*Sm82", "jq81q82*Sm81*Sp82", "jq16q26*Sp16*Sm26", "jq16q26*Sm16*Sp26", "jq90q94*Sp90*Sm94", "jq90q94*Sm90*Sp94", "jq118q119*Sp118*Sm119", "jq118q119*Sm118*Sp119", "jq12q13*Sp12*Sm13", "jq12q13*Sm12*Sp13", "jq77q78*Sp77*Sm78", "jq77q78*Sm77*Sp78", "jq22q23*Sp22*Sm23", "jq22q23*Sm22*Sp23", "jq49q50*Sp49*Sm50", "jq49q50*Sm49*Sp50", "jq104q105*Sp104*Sm105", "jq104q105*Sm104*Sp105", "jq114q115*Sp114*Sm115", "jq114q115*Sm114*Sp115", "jq45q46*Sp45*Sm46", "jq45q46*Sm45*Sp46", "jq50q51*Sp50*Sm51", "jq50q51*Sm50*Sp51", "jq105q106*Sp105*Sm106", "jq105q106*Sm105*Sp106", "jq72q81*Sp72*Sm81", "jq72q81*Sm72*Sp81", "jq82q83*Sp82*Sm83", "jq82q83*Sm82*Sp83", "jq46q47*Sp46*Sm47", "jq46q47*Sm46*Sp47", "jq23q24*Sp23*Sm24", "jq23q24*Sm23*Sp24", "jq78q79*Sp78*Sm79", "jq78q79*Sm78*Sp79", "jq83q84*Sp83*Sm84", "jq83q84*Sm83*Sp84", "jq115q116*Sp115*Sm116", "jq115q116*Sm115*Sp116", "jq19q20*Sp19*Sm20", "jq19q20*Sm19*Sp20", "jq24q25*Sp24*Sm25", "jq24q25*Sm24*Sp25", "jq79q80*Sp79*Sm80", "jq79q80*Sm79*Sp80", "jq56q57*Sp56*Sm57", "jq56q57*Sm56*Sp57", "jq93q106*Sp93*Sm106", "jq93q106*Sm93*Sp106", "jq116q117*Sp116*Sm117", "jq116q117*Sm116*Sp117", "jq20q21*Sp20*Sm21", "jq20q21*Sm20*Sp21", "jq12q17*Sp12*Sm17", "jq12q17*Sm12*Sp17", "jq41q53*Sp41*Sm53", "jq41q53*Sm41*Sp53", "jq57q58*Sp57*Sm58", "jq57q58*Sm57*Sp58", "jq87q93*Sp87*Sm93", "jq87q93*Sm87*Sp93", "jq30q31*Sp30*Sm31", "jq30q31*Sm30*Sp31", "jq25q26*Sp25*Sm26", "jq25q26*Sm25*Sp26", "jq79q91*Sp79*Sm91", "jq79q91*Sm79*Sp91", "jq26q27*Sp26*Sm27", "jq26q27*Sm26*Sp27", "jq21q22*Sp21*Sm22", "jq21q22*Sm21*Sp22", "jq58q71*Sp58*Sm71", "jq58q71*Sm58*Sp71", "jq86q87*Sp86*Sm87", "jq86q87*Sm86*Sp87", "jq31q32*Sp31*Sm32", "jq31q32*Sm31*Sp32", "jq4q15*Sp4*Sm15", "jq4q15*Sm4*Sp15", "jq113q114*Sp113*Sm114", "jq113q114*Sm113*Sp114", "jq104q111*Sp104*Sm111", "jq104q111*Sm104*Sp111", "jq123q124*Sp123*Sm124", "jq123q124*Sm123*Sp124", "jq27q28*Sp27*Sm28", "jq27q28*Sm27*Sp28", "jq34q43*Sp34*Sm43", "jq34q43*Sm34*Sp43", "jq119q120*Sp119*Sm120", "jq119q120*Sm119*Sp120", "jq64q65*Sp64*Sm65", "jq64q65*Sm64*Sp65", "jq54q64*Sp54*Sm64", "jq54q64*Sm54*Sp64", "jq32q36*Sp32*Sm36", "jq32q36*Sm32*Sp36", "jq5q6*Sp5*Sm6", "jq5q6*Sm5*Sp6", "jq60q61*Sp60*Sm61", "jq60q61*Sm60*Sp61", "jq14q18*Sp14*Sm18", "jq14q18*Sm14*Sp18", "jq87q88*Sp87*Sm88", "jq87q88*Sm87*Sp88", "jq97q98*Sp97*Sm98", "jq97q98*Sm97*Sp98", "jq1q2*Sp1*Sm2", "jq1q2*Sm1*Sp2", "jq112q126*Sp112*Sm126", "jq112q126*Sm112*Sp126", "jq28q29*Sp28*Sm29", "jq28q29*Sm28*Sp29", "jq45q54*Sp45*Sm54", "jq45q54*Sm45*Sp54", "jq36q51*Sp36*Sm51", "jq36q51*Sm36*Sp51", "jq88q89*Sp88*Sm89", "jq88q89*Sm88*Sp89", "jq120q121*Sp120*Sm121", "jq120q121*Sm120*Sp121", "jq15q22*Sp15*Sm22", "jq15q22*Sm15*Sp22", "jq24q34*Sp24*Sm34", "jq24q34*Sm24*Sp34", "jq84q85*Sp84*Sm85", "jq84q85*Sm84*Sp85", "jq29q30*Sp29*Sm30", "jq29q30*Sm29*Sp30", "jq61q62*Sp61*Sm62", "jq61q62*Sm61*Sp62", "jq70q74*Sp70*Sm74", "jq70q74*Sm70*Sp74", "jq121q122*Sp121*Sm122", "jq121q122*Sm121*Sp122", "jq2q3*Sp2*Sm3", "jq2q3*Sm2*Sp3", "jq122q123*Sp122*Sm123", "jq122q123*Sm122*Sp123", "jq117q118*Sp117*Sm118", "jq117q118*Sm117*Sp118", "jq62q63*Sp62*Sm63", "jq62q63*Sm62*Sp63", "jq94q95*Sp94*Sm95", "jq94q95*Sm94*Sp95", "jq109q114*Sp109*Sm114", "jq109q114*Sm109*Sp114", "jq37q52*Sp37*Sm52", "jq37q52*Sm37*Sp52", "jq3q4*Sp3*Sm4", "jq3q4*Sm3*Sp4", "jq58q59*Sp58*Sm59", "jq58q59*Sm58*Sp59", "jq33q39*Sp33*Sm39", "jq33q39*Sm33*Sp39", "jq95q96*Sp95*Sm96", "jq95q96*Sm95*Sp96", "jq68q69*Sp68*Sm69", "jq68q69*Sm68*Sp69", "jq63q64*Sp63*Sm64", "jq63q64*Sm63*Sp64", "jq71q77*Sp71*Sm77", "jq71q77*Sm71*Sp77", "jq111q122*Sp111*Sm122", "jq111q122*Sm111*Sp122", "jq4q5*Sp4*Sm5", "jq4q5*Sm4*Sp5", "jq59q60*Sp59*Sm60", "jq59q60*Sm59*Sp60", "jq96q109*Sp96*Sm109", "jq96q109*Sm96*Sp109", "jq124q125*Sp124*Sm125", "jq124q125*Sm124*Sp125", "jq69q70*Sp69*Sm70", "jq69q70*Sm69*Sp70", "jq35q47*Sp35*Sm47", "jq35q47*Sm35*Sp47", "jq101q102*Sp101*Sm102", "jq101q102*Sm101*Sp102", "jq0q1*Sp0*Sm1", "jq0q1*Sm0*Sp1", "jq65q66*Sp65*Sm66", "jq65q66*Sm65*Sp66", "jq10q11*Sp10*Sm11", "jq10q11*Sm10*Sp11", "jq37q38*Sp37*Sm38", "jq37q38*Sm37*Sp38", "jq28q35*Sp28*Sm35", "jq28q35*Sm28*Sp35", "jq102q103*Sp102*Sm103", "jq102q103*Sm102*Sp103", "jq92q102*Sp92*Sm102", "jq92q102*Sm92*Sp102", "jq6q7*Sp6*Sm7", "jq6q7*Sm6*Sp7", "jq43q44*Sp43*Sm44", "jq43q44*Sm43*Sp44", "jq98q99*Sp98*Sm99", "jq98q99*Sm98*Sp99", "jq52q56*Sp52*Sm56", "jq52q56*Sm52*Sp56", "jq125q126*Sp125*Sm126", "jq125q126*Sm125*Sp126", "jq39q40*Sp39*Sm40", "jq39q40*Sm39*Sp40", "jq8q16*Sp8*Sm16", "jq8q16*Sm8*Sp16", "jq11q12*Sp11*Sm12", "jq11q12*Sm11*Sp12", "jq66q67*Sp66*Sm67", "jq66q67*Sm66*Sp67", "jq76q77*Sp76*Sm77", "jq76q77*Sm76*Sp77", "jq83q92*Sp83*Sm92", "jq83q92*Sm83*Sp92", "jq74q89*Sp74*Sm89", "jq74q89*Sm74*Sp89", "jq7q8*Sp7*Sm8", "jq7q8*Sm7*Sp8", "jq53q60*Sp53*Sm60", "jq53q60*Sm53*Sp60", "omegad0*X1||U0", "omegad1*X2||U1", "omegad4*X3||U3", "omegad2*X3||U2", "omegad15*X4||U4", "omegad6*X5||U6", "omegad4*X5||U5", 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"label": "M_m112", "pulse_shape": "gaussian_square", "parameters": {"amp": [0.19432416916498313, 0.23130545463355281], "duration": 2240, "sigma": 64, "width": 1984}}, {"name": "delay", "t0": 2240, "ch": "m112", "duration": 1520}, {"name": "acquire", "t0": 0, "duration": 2240, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 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68}}]}], "meas_kernel": {"name": "hw_qmfk", "params": {}}, "discriminator": {"name": "hw_qmfk", "params": {}}, "_data": {}} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/quebec/fake_quebec.py b/qiskit_ibm_runtime/fake_provider/backends/quebec/fake_quebec.py new file mode 100644 index 000000000..3d72323b8 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/quebec/fake_quebec.py @@ -0,0 +1,28 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Quebec device (127 qubit). +""" + +import os +from qiskit_ibm_runtime.fake_provider import fake_backend + + +class FakeQuebec(fake_backend.FakeBackendV2): + """A fake 127 qubit backend.""" + + dirname = os.path.dirname(__file__) # type: ignore + conf_filename = "conf_quebec.json" # type: ignore + props_filename = "props_quebec.json" # type: ignore + defs_filename = "defs_quebec.json" # type: ignore + backend_name = "fake_quebec" # type: ignore diff --git a/qiskit_ibm_runtime/fake_provider/backends/quebec/props_quebec.json b/qiskit_ibm_runtime/fake_provider/backends/quebec/props_quebec.json new file mode 100644 index 000000000..a577d7270 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/quebec/props_quebec.json @@ -0,0 +1 @@ +{"backend_name": "ibm_quebec", "backend_version": "1.2.4", "last_update_date": "2024-02-28T08:33:13-05:00", "qubits": [[{"date": "2024-02-28T01:00:35-05:00", "name": "T1", "unit": "us", "value": 113.89152156836147}, {"date": "2024-02-28T01:03:34-05:00", "name": "T2", "unit": "us", "value": 76.12115586081512}, {"date": "2024-02-28T08:33:13-05:00", "name": "frequency", "unit": "GHz", "value": 4.786036049680476}, {"date": "2024-02-28T08:33:13-05:00", "name": "anharmonicity", "unit": "GHz", "value": -0.2852566341849986}, {"date": "2024-02-28T00:41:26-05:00", "name": "readout_error", "unit": "", "value": 0.01539999999999997}, {"date": "2024-02-28T00:41:26-05:00", "name": "prob_meas0_prep1", "unit": "", "value": 0.0152}, {"date": "2024-02-28T00:41:26-05:00", "name": "prob_meas1_prep0", "unit": "", "value": 0.015599999999999947}, {"date": "2024-02-28T00:41:26-05:00", 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62, 72, 81, 82, 83, 84, 85, 86, 87, 93, 106, 107, 108, 112, 126, 125, 124, 123, 122, 111, 104, 103, 102, 101, 100, 110, 118, 117, 116, 115, 114, 109, 96, 97, 98, 91, 79, 78, 77, 76, 75, 90]}]} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/backends/torino/__init__.py b/qiskit_ibm_runtime/fake_provider/backends/torino/__init__.py new file mode 100644 index 000000000..be2de5892 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/torino/__init__.py @@ -0,0 +1,17 @@ +# This code is part of Qiskit. +# +# (C) Copyright IBM 2023. +# +# This code is licensed under the Apache License, Version 2.0. You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Torino backend (133 qubit). +""" + +from .fake_torino import FakeTorino diff --git a/qiskit_ibm_runtime/fake_provider/backends/torino/conf_torino.json b/qiskit_ibm_runtime/fake_provider/backends/torino/conf_torino.json new file mode 100644 index 000000000..ac732e279 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/torino/conf_torino.json @@ -0,0 +1 @@ +{"backend_name": "ibm_torino", "backend_version": "1.0.4", "n_qubits": 133, "basis_gates": ["cz", "id", "rz", "sx", "x"], "gates": [{"name": "id", "parameters": [], "qasm_def": "gate id q { U(0, 0, 0) q; }", "coupling_map": [[0], [1], [2], [3], [4], [5], [6], 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[103], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m103", "label": "M_m103", "pulse_shape": "gaussian_square", "parameters": {"amp": [0.04363678194233676, -0.16750332563181233], "duration": 200, "sigma": 4, "width": 184}}, {"name": "delay", "t0": 200, "ch": "m103", "duration": 190}, {"name": "acquire", "t0": 0, "duration": 200, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 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122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132]}]}, {"name": "measure", "qubits": [109], "sequence": [{"name": "parametric_pulse", "t0": 0, "ch": "m109", "label": "M_m109", "pulse_shape": "gaussian_square", "parameters": {"amp": [-0.3587612882954419, 0.029838532480583043], "duration": 200, "sigma": 4, "width": 184}}, {"name": "delay", "t0": 200, "ch": "m109", "duration": 190}, {"name": "acquire", "t0": 0, "duration": 200, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132], 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"label": "M_m128", "pulse_shape": "gaussian_square", "parameters": {"amp": [0.12454904128080066, -0.14612164903269267], "duration": 200, "sigma": 4, "width": 184}}, {"name": "delay", "t0": 200, "ch": "m128", "duration": 190}, {"name": "acquire", "t0": 0, "duration": 200, "qubits": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132], "memory_slot": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 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You may +# obtain a copy of this license in the LICENSE.txt file in the root directory +# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0. +# +# Any modifications or derivative works of this code must retain this +# copyright notice, and modified files need to carry a notice indicating +# that they have been altered from the originals. + +""" +Fake Torino device (133 qubit). +""" + +import os +from qiskit_ibm_runtime.fake_provider import fake_backend + + +class FakeTorino(fake_backend.FakeBackendV2): + """A fake 133 qubit backend.""" + + dirname = os.path.dirname(__file__) # type: ignore + conf_filename = "conf_torino.json" # type: ignore + props_filename = "props_torino.json" # type: ignore + defs_filename = "defs_torino.json" # type: ignore + backend_name = "fake_torino" # type: ignore diff --git a/qiskit_ibm_runtime/fake_provider/backends/torino/props_torino.json b/qiskit_ibm_runtime/fake_provider/backends/torino/props_torino.json new file mode 100644 index 000000000..6b2e94da7 --- /dev/null +++ b/qiskit_ibm_runtime/fake_provider/backends/torino/props_torino.json @@ -0,0 +1 @@ +{"backend_name": "ibm_torino", "backend_version": "1.0.4", "last_update_date": "2024-02-28T08:48:51-05:00", "qubits": [[{"date": "2024-02-27T03:46:46-05:00", "name": "T1", "unit": "us", "value": 180.04100080673533}, {"date": "2024-02-28T01:05:21-05:00", "name": "T2", "unit": "us", "value": 77.18927425012103}, {"date": "2024-02-28T08:48:51-05:00", "name": "frequency", "unit": "GHz", "value": 0}, {"date": "2024-02-28T08:48:51-05:00", "name": "anharmonicity", "unit": "GHz", "value": 0}, {"date": "2024-02-28T00:46:02-05:00", "name": "readout_error", "unit": "", "value": 0.06830000000000003}, {"date": "2024-02-28T00:46:02-05:00", "name": "prob_meas0_prep1", "unit": "", "value": 0.06259999999999999}, {"date": "2024-02-28T00:46:02-05:00", "name": "prob_meas1_prep0", "unit": "", "value": 0.074}, {"date": "2024-02-28T00:46:02-05:00", "name": "readout_length", "unit": "ns", 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42, 43, 44, 35, 25, 26, 27, 28, 29, 36, 48, 47, 46, 55, 65, 64, 63, 73, 82, 81, 80, 92, 99, 100, 101, 111, 120, 121, 122, 123, 124, 125, 126, 127, 128, 113, 109, 108, 107, 106, 105, 104, 103, 93, 84, 85, 86, 87, 88, 89, 90, 75, 71, 70, 69, 56, 50, 51, 52, 37, 33, 32, 31, 18, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 15, 19, 20, 21, 22, 23]}]} \ No newline at end of file diff --git a/qiskit_ibm_runtime/fake_provider/fake_provider.py b/qiskit_ibm_runtime/fake_provider/fake_provider.py index ecd526168..dddb70ceb 100644 --- a/qiskit_ibm_runtime/fake_provider/fake_provider.py +++ b/qiskit_ibm_runtime/fake_provider/fake_provider.py @@ -88,6 +88,7 @@ def backends(self, name=None, **kwargs): # type: ignore def __init__(self) -> None: self._backends = [ + FakeAlgiers(), # type: ignore FakeAlmadenV2(), # type: ignore FakeArmonkV2(), # type: ignore FakeAthensV2(), # type: ignore @@ -95,18 +96,23 @@ def __init__(self) -> None: FakeBelemV2(), # type: ignore FakeBoeblingenV2(), # type: ignore FakeBogotaV2(), # type: ignore + FakeBrisbane(), # type: ignore FakeBrooklynV2(), # type: ignore FakeBurlingtonV2(), # type: ignore FakeCairoV2(), # type: ignore FakeCambridgeV2(), # type: ignore FakeCasablancaV2(), # type: ignore + FakeCusco(), # type: ignore FakeEssexV2(), # type: ignore FakeGeneva(), # type: ignore FakeGuadalupeV2(), # type: ignore FakeHanoiV2(), # type: ignore FakeJakartaV2(), # type: ignore FakeJohannesburgV2(), # type: ignore + FakeKawasaki(), # type: ignore FakeKolkataV2(), # type: ignore + FakeKyiv(), # type: ignore + FakeKyoto(), # type: ignore FakeLagosV2(), # type: ignore FakeLimaV2(), # type: ignore FakeLondonV2(), # type: ignore @@ -116,12 +122,15 @@ def __init__(self) -> None: FakeMontrealV2(), # type: ignore FakeMumbaiV2(), # type: ignore FakeNairobiV2(), # type: ignore + FakeOsaka(), # type: ignore FakeOslo(), # type: ignore FakeOurenseV2(), # type: ignore FakeParisV2(), # type: ignore + FakePeekskill(), # type: ignore FakePerth(), # type: ignore FakePrague(), # type: ignore FakePoughkeepsieV2(), # type: ignore + FakeQuebec(), # type: ignore FakeQuitoV2(), # type: ignore FakeRochesterV2(), # type: ignore FakeRomeV2(), # type: ignore @@ -129,6 +138,7 @@ def __init__(self) -> None: FakeSherbrooke(), # type: ignore FakeSingaporeV2(), # type: ignore FakeSydneyV2(), # type: ignore + FakeTorino(), # type: ignore FakeTorontoV2(), # type: ignore FakeValenciaV2(), # type: ignore FakeVigoV2(), # type: ignore diff --git a/qiskit_ibm_runtime/qiskit_runtime_service.py b/qiskit_ibm_runtime/qiskit_runtime_service.py index 681c49ef9..13dd02eb1 100644 --- a/qiskit_ibm_runtime/qiskit_runtime_service.py +++ b/qiskit_ibm_runtime/qiskit_runtime_service.py @@ -20,7 +20,7 @@ from collections import OrderedDict from typing import Dict, Callable, Optional, Union, List, Any, Type, Sequence -from qiskit.providers.backend import BackendV1 as Backend +from qiskit.providers.backend import BackendV2 as Backend from qiskit.providers.provider import ProviderV1 as Provider from qiskit.providers.exceptions import QiskitBackendNotFoundError from qiskit.providers.providerutils import filter_backends diff --git a/qiskit_ibm_runtime/sampler.py b/qiskit_ibm_runtime/sampler.py index c940880c9..80c621cce 100644 --- a/qiskit_ibm_runtime/sampler.py +++ b/qiskit_ibm_runtime/sampler.py @@ -154,17 +154,19 @@ class SamplerV1(BasePrimitiveV1, Sampler, BaseSampler): from qiskit_ibm_runtime import QiskitRuntimeService, Session, Sampler service = QiskitRuntimeService(channel="ibm_cloud") - quantum_register = QuantumRegister(2, name="qr") - classical_register = ClassicalRegister(2, name="cr") - bell = QuantumCircuit(quantum_register, classical_register, name="bell") - bell.h(quantum_register[0]) - bell.cx(quantum_register[0], quantum_register[1]) - bell.measure(quantum_register, classical_register) + + # Bell Circuit + qr = QuantumRegister(2, name="qr") + cr = ClassicalRegister(2, name="cr") + qc = QuantumCircuit(qr, cr, name="bell") + qc.h(qr[0]) + qc.cx(qr[0], qr[1]) + qc.measure(qr, cr) with Session(service, backend="ibmq_qasm_simulator") as session: sampler = Sampler(session=session) - job = sampler.run(bell, shots=1024) + job = sampler.run(qc, shots=1024) print(f"Job ID: {job.job_id()}") print(f"Job result: {job.result()}") diff --git a/qiskit_ibm_runtime/session.py b/qiskit_ibm_runtime/session.py index 81efdf98b..9ee14e2a7 100644 --- a/qiskit_ibm_runtime/session.py +++ b/qiskit_ibm_runtime/session.py @@ -21,7 +21,7 @@ from .utils.result_decoder import ResultDecoder from .ibm_backend import IBMBackend from .utils.default_session import set_cm_session -from .utils.deprecation import deprecate_arguments +from .utils.deprecation import deprecate_arguments, issue_deprecation_msg from .utils.converters import hms_to_seconds @@ -112,8 +112,14 @@ def __init__( else: self._service = service - if self._service.channel == "ibm_quantum" and not backend: - raise ValueError('"backend" is required for ``ibm_quantum`` channel.') + if not backend: + if self._service.channel == "ibm_quantum": + raise ValueError('"backend" is required for ``ibm_quantum`` channel.') + issue_deprecation_msg( + "Not providing a backend is deprecated", + "0.21.0", + "Passing in a backend will be required, please provide a backend.", + ) self._instance = None diff --git a/qiskit_ibm_runtime/utils/backend_converter.py b/qiskit_ibm_runtime/utils/backend_converter.py index 3db605d10..4f7051883 100644 --- a/qiskit_ibm_runtime/utils/backend_converter.py +++ b/qiskit_ibm_runtime/utils/backend_converter.py @@ -25,6 +25,8 @@ ECRGate, CZGate, ) +from qiskit.circuit.controlflow import CONTROL_FLOW_OP_NAMES +from qiskit.circuit import IfElseOp, WhileLoopOp, ForLoopOp, SwitchCaseOp from qiskit.circuit.parameter import Parameter from qiskit.circuit.delay import Delay from qiskit.circuit.gate import Gate @@ -56,6 +58,10 @@ def convert_to_target( "reset": Reset(), "ecr": ECRGate(), "cz": CZGate(), + "if_else": IfElseOp, + "while_loop": WhileLoopOp, + "for_loop": ForLoopOp, + "switch_case": SwitchCaseOp, } custom_gates = {} target = None @@ -128,6 +134,10 @@ def convert_to_target( target.min_length = configuration.timing_constraints.get("min_length") target.pulse_alignment = configuration.timing_constraints.get("pulse_alignment") target.acquire_alignment = configuration.timing_constraints.get("acquire_alignment") + supported_instructions = set(getattr(configuration, "supported_instructions", [])) + control_flow_ops = CONTROL_FLOW_OP_NAMES.intersection(supported_instructions) + for op in control_flow_ops: + target.add_instruction(name_mapping[op], name=op) # If pulse defaults exists use that as the source of truth if defaults is not None: faulty_qubits = set() diff --git a/qiskit_ibm_runtime/utils/json.py b/qiskit_ibm_runtime/utils/json.py index 2688ed60a..53ab980f2 100644 --- a/qiskit_ibm_runtime/utils/json.py +++ b/qiskit_ibm_runtime/utils/json.py @@ -63,6 +63,8 @@ load, dump, ) +from qiskit.primitives.containers.estimator_pub import EstimatorPub +from qiskit.primitives.containers.sampler_pub import SamplerPub from qiskit.qpy.binary_io.value import _write_parameter, _read_parameter from qiskit.primitives.containers.bindings_array import BindingsArray from qiskit.primitives.containers.observables_array import ObservablesArray @@ -73,8 +75,6 @@ PubResult, PrimitiveResult, ) -from qiskit.primitives.containers.estimator_pub import EstimatorPub -from qiskit.primitives.containers.sampler_pub import SamplerPub _TERRA_VERSION = tuple( int(x) for x in re.match(r"\d+\.\d+\.\d", _terra_version_string).group(0).split(".")[:3] diff --git a/qiskit_ibm_runtime/utils/utils.py b/qiskit_ibm_runtime/utils/utils.py index 057ff1de1..7f60c6970 100644 --- a/qiskit_ibm_runtime/utils/utils.py +++ b/qiskit_ibm_runtime/utils/utils.py @@ -17,7 +17,6 @@ import os import re import hashlib -import warnings from queue import Queue from threading import Condition from typing import List, Optional, Any, Dict, Union, Tuple, Sequence @@ -64,43 +63,25 @@ def is_isa_circuit(circuit: QuantumCircuit, target: Target) -> str: return "" -def validate_isa_circuits( - circuits: Sequence[QuantumCircuit], target: Target, raise_exc: bool = False -) -> None: +def validate_isa_circuits(circuits: Sequence[QuantumCircuit], target: Target) -> None: """Validate if all circuits are ISA circuits Args: - circuits: A list of QuantumCircuits + circuits: A list of QuantumCircuits. target: The backend target - - Raises: - IBMInputValueError if some of the circuits are not ISA circuits """ for circuit in circuits: message = is_isa_circuit(circuit, target) - if not message: - return - if raise_exc: + if message: raise IBMInputValueError( message - + " Circuits that do not match the target hardware definition will no longer be " - "supported after March 1, 2024. See the transpilation documentation " + + " Circuits that do not match the target hardware definition are no longer " + "supported after March 4, 2024. See the transpilation documentation " "(https://docs.quantum.ibm.com/transpile) for instructions to transform circuits and " "the primitive examples (https://docs.quantum.ibm.com/run/primitives-examples) to see " "this coupled with operator transformations." ) - warnings.warn( - message - + " Circuits that do not match the target hardware definition will no longer be " - "supported after March 1, 2024. See the transpilation documentation " - "(https://docs.quantum.ibm.com/transpile) for instructions to transform circuits and " - "the primitive examples (https://docs.quantum.ibm.com/run/primitives-examples) to see " - "this coupled with operator transformations.", - DeprecationWarning, - stacklevel=6, - ) - def validate_job_tags(job_tags: Optional[List[str]]) -> None: """Validates input job tags. diff --git a/releasenotes/notes/0.20/session-modes-5c22b68620f8d690.yaml b/releasenotes/notes/0.20/session-modes-5c22b68620f8d690.yaml index b9e887fe6..f885fca4c 100644 --- a/releasenotes/notes/0.20/session-modes-5c22b68620f8d690.yaml +++ b/releasenotes/notes/0.20/session-modes-5c22b68620f8d690.yaml @@ -1,10 +1,13 @@ --- features: - | - Sessions will now be started with a new ``/sessions`` endpoint that allows for different - execution modes. Batch mode is now supported through :class:`~qiskit_ibm_runtime.Batch`, and - :class:`~qiskit_ibm_runtime.Session` will work the same as way as before. + Sessions will now be started with a new ``/sessions`` endpoint that allows for different + execution modes. Batch mode is now supported through :class:`~qiskit_ibm_runtime.Batch`, and + :class:`~qiskit_ibm_runtime.Session` will work the same as way as before. Please see https://docs.quantum.ibm.com/run/sessions for more information. - Note that ``Session`` and ``Batch`` created from ``qiskit-ibm-runtime`` prior to this release will no longer be - supported after March 31, 2024. Please update your ``qiskit-ibm-runtime`` version as soon as possible before this date. + Note that ``Session`` and ``Batch`` created from ``qiskit-ibm-runtime`` prior to this release will no longer be + supported after March 31, 2024. Please update your ``qiskit-ibm-runtime`` version as soon as possible before this date. + + Also note that using simulators with sessions is no longer supported. Users can still start + sessions with simulators without any issues but a session will not actually be created. There will be no session ID. diff --git a/releasenotes/notes/fix-control-flow-d5a61dd5647acb42.yaml b/releasenotes/notes/fix-control-flow-d5a61dd5647acb42.yaml new file mode 100644 index 000000000..0031db5cc --- /dev/null +++ b/releasenotes/notes/fix-control-flow-d5a61dd5647acb42.yaml @@ -0,0 +1,6 @@ +--- +fixes: + - | + Fixed an issue with the :attr:`.IBMBackend.target` where it would + incorrectly exclude supported control flow operations (:class:`.IfElseOp`, + :class:`.WhileLoop`, etc.) if a given backend supported them. diff --git a/releasenotes/notes/isa-circuit-required-ed361bd65cef5ed8.yaml b/releasenotes/notes/isa-circuit-required-ed361bd65cef5ed8.yaml new file mode 100644 index 000000000..64301c557 --- /dev/null +++ b/releasenotes/notes/isa-circuit-required-ed361bd65cef5ed8.yaml @@ -0,0 +1,10 @@ +--- +upgrade: + - | + Circuits that do not match the target hardware definition are no longer + supported by Qiskit Runtime primitives, unless ``channel_strategy="q-ctrl"`` + is used. See the transpilation documentation + (https://docs.quantum.ibm.com/transpile) for instructions to transform + circuits and the primitive examples + (https://docs.quantum.ibm.com/run/primitives-examples) to see + this coupled with operator transformations. diff --git a/releasenotes/notes/require-cloud-backend-38a74144347c735d.yaml b/releasenotes/notes/require-cloud-backend-38a74144347c735d.yaml new file mode 100644 index 000000000..9326e4323 --- /dev/null +++ b/releasenotes/notes/require-cloud-backend-38a74144347c735d.yaml @@ -0,0 +1,10 @@ +--- +deprecations: + - | + In a future release, ``backend`` will be a required parameter for :class:`qiskit_ibm_runtime.Sampler`, and + :class:`qiskit_ibm_runtime.Estimator` if ``session`` is not specified, + even when using the ``ibm_cloud`` channel. + + It will also be a required parameter for + :class:`qiskit_ibm_runtime.Session` and + :class:`qiskit_ibm_runtime.Batch`. diff --git a/test/unit/test_backend.py b/test/unit/test_backend.py index 3eda26ed2..754236e98 100644 --- a/test/unit/test_backend.py +++ b/test/unit/test_backend.py @@ -16,11 +16,18 @@ import warnings from qiskit import transpile, qasm3, QuantumCircuit -from qiskit.providers.models import BackendStatus +from qiskit.circuit import IfElseOp +from qiskit.providers.models import ( + BackendStatus, + BackendConfiguration, + BackendProperties, + PulseDefaults, +) from qiskit_ibm_runtime.exceptions import IBMBackendValueError -from qiskit_ibm_runtime.fake_provider import FakeManila +from qiskit_ibm_runtime.fake_provider import FakeManila, FakeSherbrooke from qiskit_ibm_runtime.ibm_backend import IBMBackend +from qiskit_ibm_runtime.utils.backend_converter import convert_to_target from ..ibm_test_case import IBMTestCase from ..utils import ( @@ -305,3 +312,17 @@ def test_too_many_circuits(self): f"Number of circuits, {max_circs+1} exceeds the maximum for this backend, {max_circs}", str(err.exception), ) + + def test_control_flow_converter(self): + """Test that control flow instructions are properly added to the target.""" + backend = FakeSherbrooke() + backend._get_conf_dict_from_json() + backend._set_props_dict_from_json() + backend._set_defs_dict_from_json() + target = convert_to_target( + BackendConfiguration.from_dict(backend._conf_dict), + BackendProperties.from_dict(backend._props_dict), + PulseDefaults.from_dict(backend._defs_dict), + ) + self.assertTrue(target.instruction_supported("if_else", ())) + self.assertTrue(target.instruction_supported(operation_class=IfElseOp)) diff --git a/test/unit/test_ibm_primitives.py b/test/unit/test_ibm_primitives.py index 4b85774c6..5bfe96efc 100644 --- a/test/unit/test_ibm_primitives.py +++ b/test/unit/test_ibm_primitives.py @@ -18,17 +18,15 @@ from unittest.mock import MagicMock, patch from dataclasses import asdict from typing import Dict -import warnings from ddt import data, ddt from qiskit import transpile, pulse -from qiskit.circuit import QuantumCircuit +from qiskit.circuit import QuantumCircuit, QuantumRegister, ClassicalRegister from qiskit.pulse.library import Gaussian from qiskit.quantum_info import SparsePauliOp -from qiskit.providers.models.backendconfiguration import QasmBackendConfiguration from qiskit_aer.noise import NoiseModel -from qiskit_ibm_runtime.fake_provider import FakeManila +from qiskit_ibm_runtime.fake_provider import FakeManila, FakeSherbrooke from qiskit_ibm_runtime import ( Sampler, Estimator, @@ -37,6 +35,7 @@ ) from qiskit_ibm_runtime.ibm_backend import IBMBackend from qiskit_ibm_runtime.utils.default_session import _DEFAULT_SESSION +from qiskit_ibm_runtime.exceptions import IBMInputValueError from ..ibm_test_case import IBMTestCase from ..utils import ( @@ -853,7 +852,7 @@ def test_abstract_circuits(self, primitive): else: circ.measure_all() - with self.assertWarnsRegex(DeprecationWarning, "target hardware"): + with self.assertRaisesRegex(IBMInputValueError, "target hardware"): inst.run(**run_input) @data(Sampler, Estimator) @@ -863,7 +862,6 @@ def test_abstract_circuits_backend_no_coupling_map(self, primitive): config = FakeManila().configuration().to_dict() for gate in config["gates"]: gate.pop("coupling_map", None) - config = QasmBackendConfiguration.from_dict(config) backend = get_mocked_backend(configuration=config) inst = primitive(backend=backend) @@ -876,10 +874,7 @@ def test_abstract_circuits_backend_no_coupling_map(self, primitive): else: transpiled.measure_all() - with warnings.catch_warnings(record=True) as warns: - warnings.simplefilter("always") - inst.run(**run_input) - self.assertFalse(warns) + inst.run(**run_input) @data(Sampler, Estimator) def test_pulse_gates_is_isa(self, primitive): @@ -899,10 +894,60 @@ def test_pulse_gates_is_isa(self, primitive): else: circuit.measure_all() - with warnings.catch_warnings(record=True) as warns: - warnings.simplefilter("always") - inst.run(**run_input) - self.assertFalse(warns) + inst.run(**run_input) + + @data(Sampler, Estimator) + def test_dynamic_circuit_is_isa(self, primitive): + """Test passing dynmaic circuits is considered ISA.""" + # pylint: disable=not-context-manager + # pylint: disable=invalid-name + sherbrooke = FakeSherbrooke() + config = sherbrooke._get_conf_dict_from_json() + config["supported_instructions"] += ["for_loop", "switch_case", "while_loop"] + + backend = get_mocked_backend( + configuration=config, + properties=sherbrooke._set_props_dict_from_json(), + defaults=sherbrooke._set_defs_dict_from_json(), + ) + + inst = primitive(backend=backend) + + qubits = QuantumRegister(3) + clbits = ClassicalRegister(3) + circuit = QuantumCircuit(qubits, clbits) + (q0, q1, q2) = qubits + (c0, c1, c2) = clbits + + circuit.x(q0) + circuit.measure(q0, c0) + with circuit.if_test((c0, 1)): + circuit.x(q0) + + circuit.measure(q1, c1) + with circuit.switch(c1) as case: + with case(0): + circuit.x(q0) + with case(1): + circuit.x(q1) + + circuit.measure(q1, c1) + circuit.measure(q2, c2) + with circuit.while_loop((clbits, 0b111)): + circuit.rz(1.5, q1) + circuit.rz(1.5, q2) + circuit.measure(q1, c1) + circuit.measure(q2, c2) + + with circuit.for_loop(range(2)) as _: + circuit.x(q0) + + circuit = transpile(circuit, backend=backend) + run_input = {"circuits": circuit} + if isinstance(inst, Estimator): + run_input["observables"] = SparsePauliOp("ZZZ").apply_layout(circuit.layout) + + inst.run(**run_input) def _update_dict(self, dict1, dict2): for key, val in dict1.items(): @@ -982,3 +1027,20 @@ def test_qctrl_unsupported_values_for_options(self): _ = inst.run(self.qx, observables=self.obs, **bad_opt) self.assertIn(expected_message, str(exc.exception)) + + @data(Sampler, Estimator) + def test_qctrl_abstract_circuit(self, primitive): + """Test q-ctrl can still accept abstract circuits.""" + backend = get_mocked_backend() + backend._service._channel_strategy = "q-ctrl" + inst = primitive(backend=backend) + + circ = QuantumCircuit(3, 3) + circ.cx(0, 2) + run_input = {"circuits": circ} + if isinstance(inst, Estimator): + run_input["observables"] = SparsePauliOp("ZZZ") + else: + circ.measure_all() + + inst.run(**run_input) diff --git a/test/unit/test_sampler.py b/test/unit/test_sampler.py index b508019b5..db0fafc0f 100644 --- a/test/unit/test_sampler.py +++ b/test/unit/test_sampler.py @@ -18,15 +18,14 @@ from ddt import data, ddt import numpy as np -from qiskit import QuantumCircuit +from qiskit import QuantumCircuit, transpile from qiskit.primitives.containers.sampler_pub import SamplerPub from qiskit.circuit.library import RealAmplitudes from qiskit_ibm_runtime import Sampler, Session, SamplerV2, SamplerOptions from ..ibm_test_case import IBMTestCase -from ..utils import bell +from ..utils import bell, MockSession, dict_paritally_equal, get_mocked_backend from .mock.fake_runtime_service import FakeRuntimeService -from ..utils import MockSession, dict_paritally_equal class TestSampler(IBMTestCase): @@ -38,12 +37,13 @@ def test_unsupported_values_for_sampler_options(self): {"resilience_level": 2, "optimization_level": 3}, {"optimization_level": 4, "resilience_level": 1}, ] + backend = get_mocked_backend() + circuit = transpile(bell(), backend=backend) with Session( service=FakeRuntimeService(channel="ibm_quantum", token="abc"), backend="common_backend", ) as session: - circuit = bell() for bad_opt in options_bad: inst = Sampler(session=session) with self.assertRaises(ValueError) as exc: diff --git a/test/unit/test_session.py b/test/unit/test_session.py index b2b84fbd2..1f7bc9768 100644 --- a/test/unit/test_session.py +++ b/test/unit/test_session.py @@ -44,6 +44,13 @@ def test_missing_backend(self): with self.assertRaises(ValueError): Session(service=service) + def test_missing_backend_cloud_warning(self): + """Test warning if no backend provided on cloud channel.""" + service = MagicMock() + service.channel = "ibm_cloud" + with self.assertWarns(DeprecationWarning): + Session(service=service) + def test_passing_ibm_backend(self): """Test passing in IBMBackend instance.""" backend = MagicMock(spec=IBMBackend) diff --git a/test/utils.py b/test/utils.py index 187a487df..f47b33e4d 100644 --- a/test/utils.py +++ b/test/utils.py @@ -26,12 +26,16 @@ from qiskit.compiler import transpile from qiskit.providers.jobstatus import JOB_FINAL_STATES, JobStatus from qiskit.providers.exceptions import QiskitBackendNotFoundError -from qiskit.providers.models import BackendStatus, BackendProperties, BackendConfiguration +from qiskit.providers.models import ( + BackendStatus, + BackendProperties, + BackendConfiguration, +) from qiskit.providers.backend import Backend from qiskit.quantum_info import SparsePauliOp, Pauli +from qiskit_ibm_runtime import QiskitRuntimeService, Session, EstimatorV2 from qiskit_ibm_runtime.fake_provider import FakeManila from qiskit_ibm_runtime.hub_group_project import HubGroupProject -from qiskit_ibm_runtime import QiskitRuntimeService, Session, EstimatorV2 from qiskit_ibm_runtime.ibm_backend import IBMBackend from qiskit_ibm_runtime.runtime_job import RuntimeJob from qiskit_ibm_runtime.exceptions import RuntimeInvalidStateError @@ -278,22 +282,25 @@ def create_faulty_backend( def get_mocked_backend( - name: str = "ibm_gotham", configuration: Optional[BackendConfiguration] = None + name: str = "ibm_gotham", + configuration: Optional[Dict] = None, + properties: Optional[Dict] = None, + defaults: Optional[Dict] = None, ) -> IBMBackend: """Return a mock backend.""" - def _noop(*args, **kwargs): # pylint: disable=unused-argument - return None - mock_service = mock.MagicMock(spec=QiskitRuntimeService) mock_service._channel_strategy = None mock_api_client = mock.MagicMock() - if not configuration: - configuration = FakeManila().configuration() + configuration = ( + FakeManila().configuration() + if configuration is None + else BackendConfiguration.from_dict(configuration) + ) - mock_api_client.backend_properties = _noop - mock_api_client.backend_pulse_defaults = _noop + mock_api_client.backend_properties = lambda *args, **kwargs: properties + mock_api_client.backend_pulse_defaults = lambda *args, **kwargs: defaults mock_backend = IBMBackend( configuration=configuration, service=mock_service, api_client=mock_api_client ) diff --git a/tox.ini b/tox.ini index d4d7ea562..b4fcb0d68 100644 --- a/tox.ini +++ b/tox.ini @@ -10,6 +10,9 @@ setenv = VIRTUAL_ENV={envdir} LANGUAGE=en_US LC_ALL=en_US.utf-8 +passenv = + GITHUB_REF_NAME + GITHUB_BASE_REF deps = -r{toxinidir}/requirements.txt -r{toxinidir}/requirements-dev.txt