Add dense matrix support for PauliProductRotation

[Adithyaphani]

AI tool used: ChatGPT (OpenAI GPT-5.4 Thinking) for understanding the issue clearly and not relying on it completely.

Fixes #15869.

Summary

This PR adds the missing dense Pauli-matrix helper required by the existing PauliProductRotation::matrix() implementation.

Details and comments

This PR is intentionally minimal and limited to:

• crates/circuit/src/gate_matrix.rs

It adds pauli_zx_to_matrix(z, x) so the existing PauliProductRotation::matrix() path in operations.rs can construct the dense Pauli-product matrix and return the dense rotation matrix correctly.

The resulting matrix follows:

cos(theta / 2) * I - i * sin(theta / 2) * P

Validation run locally:

• cargo fmt --all
• cargo check -p qiskit-circuit --lib --all-features
• cargo clippy -p qiskit-circuit --lib --all-features -- -D warnings

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[Adithyaphani]

Hi @ShellyGarion , just a gentle reminder on this PR whenever you have a chance to review it.

This is a follow-up focused only on the required PauliProductRotation matrix fix, with unrelated changes removed from the earlier attempt.

Thank you.

[Adithyaphani]

@1ucian0 and @ShellyGarion I’ve pushed a fix that clears the macOS CI failure. Could you please Re-run all jobs for this PR.

[Adithyaphani]

@1ucian0 thanks for the rerun. At this point the remaining failure appears limited to the macOS-15 / Python 3.10 install-dependencies step.

The log shows a runner/setup-side conflict while installing Rust tooling (clippy-preview-aarch64-apple-darwin / cargo-clippy) and then reports that it cannot find a Rust compiler, before the Python tests actually run.

I restored the accidental workflow-file change and have not made further source or workflow edits to avoid widening the PR scope again. If helpful, I’d appreciate another rerun or any guidance on the next step from your side. Thank you.

[Adithyaphani]

@1ucian0 .Unfortunately, the PR was closed earlier, but I have now reopened it. All required checks are passing in the latest commit. For reference, I’ve attached a screenshot in the comments.

Leaving this as a gentle follow-up for review whenever convenient. I hope the branch can be successfully merged after this re-run. If any further changes are needed, I’d be happy to make them.

Thank you.

[ShellyGarion]

This PR does not address the functionality requested in #15869 and does not add a to_matrix support to PauliProductRotation.
The suggested functionallyity in this PR (converting Paulis into a matrix) already exists in qiskit/crates/quantum_info/src/sparse_pauli_op.rs and is already implemented there in an efficient way, as alreay pointed out in the review of #15879.
The Qiskit team will handle issue #15869, so you're kindly asked not to open further PRs on this issue.

[Adithyaphani]

@ShellyGarion ,I’ll ensure better efficiency in future fixes. Thanks for your guidance!