Update shadows workflow images #2142
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purva-thakre
commented
Dec 21, 2023
| @@ -256,7 +259,7 @@ The expectation value for a series of operators, denoted as $\{O_\iota\}_{\iota\ | |||
| \hat{o}_\iota &= \langle\!\langle O_\iota|{\hat{\rho}}\rangle\!\rangle \simeq \langle\!\langle O_\iota|\widehat{\mathcal{M}}^{-1}\widetilde{\mathcal{M}}|\rho\rangle\!\rangle=\sum_{b^{(1)}\in\{0,1\}^{n}}f_{b^{(1)}}^{-1}\left(\bigotimes_{i=1}^n \langle\!\langle P_i|\Pi_{b_i^{(1)}}\widehat{\mathcal{M}}_{P_i}\right)|\rho\rangle\!\rangle\nonumber\\ | |||
| &=\sum_{b^{(1)}\in\{0,1\}^{n}}f_{b^{(1)}}^{-1}\prod_{i=1}^n \langle\!\langle P_i|\Pi_{b^{(1)}_i}\bigg|U_i^{(2)\dagger}|b_i^{(2)}\rangle\langle b_i^{(2)}|U_i^{(2)}\bigg\rangle\!\bigg\rangle | |||
| \end{align} | |||
| where in the last equality, $\{P_i\}_{i\in n}$ represents Pauli operators, with $P=\{I,X,Y,Z\}$. And as we did previously, we use the lable $(1)$ as the subscript to distinguish the parameters of the calibration process from the parameters of the shadow estimation process, which is labelled by $(2)$. It is assumed that $O_\iota$ are Pauli strings acting on $supp(O_\iota)$ ($|supp(O_\iota)|\leq n$) sites of the system. It can be verified that the cross product over qubit sites within the summation of the final expression in the above equation is zero, except when all sites in $supp(O_\iota)^c$ have $\Pi_0$ acting on. Similarly, it can be verified that the cross product over qubit sites within the summation of the final expression in the above equation is zero, except when all sites in $supp(O_\iota)$ have $\Pi_1$ acting on, i.e. | |||
| where in the last equality, $\{P_i\}_{i\in n}$ represents Pauli operators, with $P=\{I,X,Y,Z\}$. And as we did previously, we use the label $(1)$ as the subscript to distinguish the parameters of the calibration process from the parameters of the shadow estimation process, which is labelled by $(2)$. It is assumed that $O_\iota$ are Pauli strings acting on $supp(O_\iota)$ ($|supp(O_\iota)|\leq n$) sites of the system. It can be verified that the cross product over qubit sites within the summation of the final expression in the above equation is zero, except when all sites in $supp(O_\iota)^c$ have $\Pi_0$ acting on. Similarly, it can be verified that the cross product over qubit sites within the summation of the final expression in the above equation is zero, except when all sites in $supp(O_\iota)$ have $\Pi_1$ acting on, i.e. | |||
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Apply the following comment to all .md files in this PR.
I did not make changes to all these lines, changed only a word or two when there was a typo. For some reason, it is being highlighted as a change of multiple lines.
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Thanks for correcting my spelling, unclear statements and grammar!
Codecov ReportAll modified and coverable lines are covered by tests ✅
Additional details and impacted files@@ Coverage Diff @@
## master #2142 +/- ##
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Coverage 98.20% 98.20%
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Files 88 88
Lines 4167 4167
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Hits 4092 4092
Misses 75 75 ☔ View full report in Codecov by Sentry. |
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@Min-Li I requested a review from you to look over the images in this PR. |
purva-thakre
commented
Dec 21, 2023
Comment on lines
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+105
| The Clifford measurement requires the depth of the circuit to grow linearly with system size, which is not currently feasible for large systems, so we are going to implement the local (Pauli) measurement and integrate it into Mitiq in the current stage. However, it is worth noting that there is an intermediate step of scrambling the circuits and combining the local and global measurement {cite}`hu2023classical`. | ||
| The Clifford measurement requires the depth of the circuit to grow linearly with system size, which is not currently feasible for large systems, which is why only the local (Pauli) measurement is implemented in Mitiq in the current stage. However, it is worth noting that this method involves an intermediate step of scrambling the circuits and combining the local and global measurement {cite}`hu2023classical`. |
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I made these changes here because the wording makes it sound like work on mitiq.shadows is still in the planning stage.
Min-Li
approved these changes
Dec 22, 2023
| @@ -256,7 +259,7 @@ The expectation value for a series of operators, denoted as $\{O_\iota\}_{\iota\ | |||
| \hat{o}_\iota &= \langle\!\langle O_\iota|{\hat{\rho}}\rangle\!\rangle \simeq \langle\!\langle O_\iota|\widehat{\mathcal{M}}^{-1}\widetilde{\mathcal{M}}|\rho\rangle\!\rangle=\sum_{b^{(1)}\in\{0,1\}^{n}}f_{b^{(1)}}^{-1}\left(\bigotimes_{i=1}^n \langle\!\langle P_i|\Pi_{b_i^{(1)}}\widehat{\mathcal{M}}_{P_i}\right)|\rho\rangle\!\rangle\nonumber\\ | |||
| &=\sum_{b^{(1)}\in\{0,1\}^{n}}f_{b^{(1)}}^{-1}\prod_{i=1}^n \langle\!\langle P_i|\Pi_{b^{(1)}_i}\bigg|U_i^{(2)\dagger}|b_i^{(2)}\rangle\langle b_i^{(2)}|U_i^{(2)}\bigg\rangle\!\bigg\rangle | |||
| \end{align} | |||
| where in the last equality, $\{P_i\}_{i\in n}$ represents Pauli operators, with $P=\{I,X,Y,Z\}$. And as we did previously, we use the lable $(1)$ as the subscript to distinguish the parameters of the calibration process from the parameters of the shadow estimation process, which is labelled by $(2)$. It is assumed that $O_\iota$ are Pauli strings acting on $supp(O_\iota)$ ($|supp(O_\iota)|\leq n$) sites of the system. It can be verified that the cross product over qubit sites within the summation of the final expression in the above equation is zero, except when all sites in $supp(O_\iota)^c$ have $\Pi_0$ acting on. Similarly, it can be verified that the cross product over qubit sites within the summation of the final expression in the above equation is zero, except when all sites in $supp(O_\iota)$ have $\Pi_1$ acting on, i.e. | |||
| where in the last equality, $\{P_i\}_{i\in n}$ represents Pauli operators, with $P=\{I,X,Y,Z\}$. And as we did previously, we use the label $(1)$ as the subscript to distinguish the parameters of the calibration process from the parameters of the shadow estimation process, which is labelled by $(2)$. It is assumed that $O_\iota$ are Pauli strings acting on $supp(O_\iota)$ ($|supp(O_\iota)|\leq n$) sites of the system. It can be verified that the cross product over qubit sites within the summation of the final expression in the above equation is zero, except when all sites in $supp(O_\iota)^c$ have $\Pi_0$ acting on. Similarly, it can be verified that the cross product over qubit sites within the summation of the final expression in the above equation is zero, except when all sites in $supp(O_\iota)$ have $\Pi_1$ acting on, i.e. | |||
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Thanks for correcting my spelling, unclear statements and grammar!
Comment on lines
-101
to
+105
| The Clifford measurement requires the depth of the circuit to grow linearly with system size, which is not currently feasible for large systems, so we are going to implement the local (Pauli) measurement and integrate it into Mitiq in the current stage. However, it is worth noting that there is an intermediate step of scrambling the circuits and combining the local and global measurement {cite}`hu2023classical`. | ||
| The Clifford measurement requires the depth of the circuit to grow linearly with system size, which is not currently feasible for large systems, which is why only the local (Pauli) measurement is implemented in Mitiq in the current stage. However, it is worth noting that this method involves an intermediate step of scrambling the circuits and combining the local and global measurement {cite}`hu2023classical`. |
|
@purva-thakre Thanks for correcting these documents! We can have a chat now if you like, or other time would be okay for me. My email address is [email protected] |
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Fixes #2141
Users GuideandExampleswhile I tried to understand the workflow formitiq.shadows.@Misty-W @natestemen Apologies for another patch!