docs: clarify method purpose

[boonware]

Summary

Fixes #13051.

Details and comments

Update the doc string for the Pauli operator method conjugate to clarify that it returns the complex conjugate and not the conjugate transpose.

[qiskit-bot]

Thank you for opening a new pull request.

Before your PR can be merged it will first need to pass continuous integration tests and be reviewed. Sometimes the review process can be slow, so please be patient.

While you're waiting, please feel free to review other open PRs. While only a subset of people are authorized to approve pull requests for merging, everyone is encouraged to review open pull requests. Doing reviews helps reduce the burden on the core team and helps make the project's code better for everyone.

One or more of the following people are relevant to this code:

• @Qiskit/terra-core

[CLAassistant]

All committers have signed the CLA.

[jakelishman]

Thanks for looking at this.

I think we'll maybe need a little bit more detail than this to properly describe the function. The complex conjugate of an arbitrary linear operator is only defined with regards to a particular matrix representation (unlike the adjoint, which is what this method was confused with), so I think we should highlight that here. (For example, if we use the $Y$-eigenstate basis, then $Y$ is real-valued and $X$ and $Z$ are complex instead.) It's sufficient to say that the conjugation is defined in terms of the matrix returned by to_matrix, or we can add a short comment that it's the matrix expressed in the $Z$-eigenstate basis.

[boonware]

Thanks for looking at this.

I think we'll maybe need a little bit more detail than this to properly describe the function. The complex conjugate of an arbitrary linear operator is only defined with regards to a particular matrix representation (unlike the adjoint, which is what this method was confused with), so I think we should highlight that here. (For example, if we use the Y -eigenstate basis, then Y is real-valued and X and Z are complex instead.) It's sufficient to say that the conjugation is defined in terms of the matrix returned by to_matrix, or we can add a short comment that it's the matrix expressed in the Z -eigenstate basis.

@jakelishman Thanks for the feedback. I have updated the comment.

[jakelishman]

Nice, thanks!

[coveralls]

Pull Request Test Coverage Report for Build 11331375663

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

• For more information on this, see Tracking coverage changes with pull request builds.
• To avoid this issue with future PRs, see these Recommended CI Configurations.
• For a quick fix, rebase this PR at GitHub. Your next report should be accurate.

Details

• 0 of 0 changed or added relevant lines in 0 files are covered.
• 560 unchanged lines in 18 files lost coverage.
• Overall coverage increased (+0.01%) to 88.666%

---

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/expr.rs	1	94.02%
crates/accelerate/src/error_map.rs	1	85.42%
crates/accelerate/src/barrier_before_final_measurement.rs	2	97.33%
crates/circuit/src/bit_data.rs	2	94.62%
crates/accelerate/src/commutation_checker.rs	2	97.14%
crates/accelerate/src/circuit_library/quantum_volume.rs	3	95.04%
crates/qasm2/src/lex.rs	4	91.98%
crates/accelerate/src/results/marginalization.rs	7	90.17%
crates/circuit/src/circuit_instruction.rs	8	76.04%
crates/accelerate/src/target_transpiler/mod.rs	8	79.11%

Totals
Change from base Build 11277520565:	0.01%
Covered Lines:	73197
Relevant Lines:	82554

---

💛 - Coveralls