Fixed commutation checking between two Pauli product measurements (backport #16023)

[mergify]

Summary

We have recently realized that checking commutativity between two PauliProductMeasurement instructions (introduced in #15359) is incorrect in the case that both measurements measure to the same classical bit. In this case, the later measurement overwrites the result of the earlier measurement, and thus the order of these instructions in the quantum circuit matters. This PR applies a simple fix of saying that two Pauli product measurement instruction do not commute unless they are completely identical (including pauli, qubits and clbits).

(Updated) This also handles "canonicalization": PPM(XZ, qubits=[0,1], clbits=[0]) is the same as PPM(ZX, qubits=[1,0], clbits=[0]), and so they are now also computed to commute.

Note: the current strategy of constructing sparse observable is in the spirit of the existing code, and I am trying to do minimal changes in order to backport a variant of this to 2.4. I have a followup PR #15815 that greatly increases the efficiency of commuting PPRs/PPMs among themselves (including canonicalization, but temporarily having the same problems as being fixed here).

This also updates commutativity checking tests to pass clbits when checking commutativity between two PPMs.

One other question: do we want to backport the fix to 2.4? If so, we would need to adjust this PR to the commutation checker version before #15488.

AI/LLM disclosure

• I didn't use LLM tooling, or only used it privately.
• I used the following tool to help write this PR description:
• I used the following tool to generate or modify code:

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This is an automatic backport of pull request #16023 done by [Mergify](https://mergify.com).

[mergify]

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Changes to be committed:
	new file:   releasenotes/notes/fix-ppm-commutation-ddcde0bf8b20a9f8.yaml

Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   crates/transpiler/src/commutation_checker.rs
	both modified:   test/python/circuit/test_commutation_checker.py

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

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[coveralls]

Coverage Report for CI Build 24451488591

Coverage increased (+0.01%) to 87.606%

Details

• Coverage increased (+0.01%) from the base build.
• Patch coverage: 19 of 19 lines across 1 file are fully covered (100%).
• 11 coverage regressions across 3 files.

Uncovered Changes

No uncovered changes found.

Coverage Regressions

11 previously-covered lines in 3 files lost coverage.

File	Lines Losing Coverage	Coverage
crates/qasm2/src/parse.rs	6	97.15%
crates/qasm2/src/lex.rs	4	91.26%
crates/qasm2/src/expr.rs	1	93.82%

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Coverage Stats

Relevant Lines:	118834
Covered Lines:	104106
Line Coverage:	87.61%
Coverage Strength:	1011381.81 hits per line

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💛 - Coveralls