Complete first section of Pauli Twirling user guide

[cosenal]

Description

Fullfills acceptance criteria of #2435.

Still a draft PR to discuss the noise model that should be used to highlight the effect of Pauli Twirling.
The noise model of choice is a coherent error introduced by applying a Rx(theta) gate on the output of each 2-qubit gate.

Imho this is a strict improvement on the current state of the guide, where the final and arguably the most important notebook cell was commented out and not working correctly.

⚠️ I renamed the API method pauli_twirl_circuit in the mitiq.pt.pt module to generate_pauli_twirl_variants, because it wasn't clear from the old name that it generate a list of twirled circuits (in fact the docstring itself was wrong on describing the output of the function.) Since the Pauli Twirling module is still under construction, I wouldn't consider this a breaking change. However, if you have objections, I can revert this renaming back.

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License

• I license this contribution under the terms of the GNU GPL, version 3 and grant Unitary Fund the right to provide additional permissions as described in section 7 of the GNU GPL, version 3.

Before opening the PR, please ensure you have completed the following where appropriate.

• I added unit tests for new code.
• I used type hints in function signatures.
• I used Google-style docstrings for functions.
• I updated the documentation where relevant.
• Added myself / the copyright holder to the AUTHORS file

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.70%. Comparing base (02ebc4b) to head (75359e6).
Report is 45 commits behind head on main.

Additional details and impacted files

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[purva-thakre]

What if you change depolarize to a coherent noise channel? As we can describe a depolarizing channel using paulis, I don't think pauli twirling is going to do anything to tailor the noise of the input circuit.

See section 2.1.3 of https://arxiv.org/pdf/1509.02921 If a Pauli Transfer Matrix of some noise channel has off-diagonal terms, we expect the noise to be tailored after twirling.

[cosenal]

I have now changed the noise to a coherent one, please take a look.

[purva-thakre]

LGTM! Made some minor suggestions on the wording.

[purva-thakre]

renamed the API method pauli_twirl_circuit in the mitiq.pt.pt module to generate_pauli_twirl_variants

Since the Pauli Twirling module is still under construction, I wouldn't consider this a breaking change. However, if you have objections, I can revert this renaming back

I am fine with the change. It's consistent with the pattern of how we named benchmarking circuits functions.

Thanks for catching the docstring leftovers!

[cosenal]

@purva-thakre Addressed your comments and made further improvements to the docstring. PTAL

[natestemen]

Good clean/elucidation! A few minor things from me.

[purva-thakre]

MWR!

[cosenal]

Merging, as the failing test test_with_observable_batched_factory is unrelated to those changes. We will investigate separately, see #2442.