Fix OptimizeCliffordT producing non-unitarily-equivalent output when basis excludes sx/sxdg (backport #16729)

[mergify]

Summary

OptimizeCliffordT's apply_ty closure re-expresses a Y-axis T-rotation without sx/sxdg using S, H, T(dg), H, Sdg -- but S and Sdg are swapped relative to the correct decomposition. As a result, the pass can emit a circuit that is not unitarily equivalent to its input (not even up to global phase) whenever basis_gates excludes sx/sxdg -- a normal, common Clifford+T target basis, not an edge case. No exception or warning is raised.

Verified two ways, not just with a custom offdiag computation: Qiskit's own Operator.equiv() (handles global phase correctly), and process_fidelity() (1.0 expected, 0.067-0.26 observed on affected cases).

Root cause

In the non-SX branch of apply_ty (see diff), S and Sdg are swapped at the two ends of the sequence. Verified numerically: SX*T*SXdg matches Sdg*H*T*H*S (offdiag 5.5e-17, correct) but not S*H*T*H*Sdg (offdiag 0.7071, wrong) -- and the same holds for the flip=true (Tdg) case.

Affected versions

Introduced in #15625 (merged 2026-03-19), first released in 2.4.0rc1. Confirmed affected: 2.4.0, 2.4.1, 2.4.2, 2.5.0, 2.5.0rc1, 2.5.1, and main prior to this fix. Not affected: 2.3.1 and earlier (the basis-aware Clifford+T pipeline didn't exist yet).

Fix verified end-to-end

Built from source (not just the algebraic argument) and re-ran every known reproduction at every optimization_level (0-3): all now come out Operator.equiv() == True (previously False at levels 1, 2, and/or 3 depending on the circuit).

Test plan

Added test_clifford_t_transpile_is_unitarily_equivalent to test_clifford_t_passmanager.py, parametrized over all four optimization levels, asserting Operator(qc).equiv(Operator(transpiled)). None of the existing tests in that file check unitary equivalence (only gate-set membership and T-count), which is consistent with how this went unnoticed across several releases.

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: Claude (Anthropic), OpenCode, ChatGPT (OpenAI), Gemini (Google)
• I used the following tool to help generate or modify code: Claude (Anthropic), OpenCode, ChatGPT (OpenAI), Gemini (Google)

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This is an automatic backport of pull request #16729 done by [Mergify](https://mergify.com).

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[coveralls]

Coverage Report for CI Build 31471417832

Coverage increased (+0.009%) to 87.685%

Details

• Coverage increased (+0.009%) from the base build.
• Patch coverage: 2 of 2 lines across 1 file are fully covered (100%).
• 11 coverage regressions across 4 files.

Uncovered Changes

No uncovered changes found.

Coverage Regressions

11 previously-covered lines in 4 files lost coverage.

File	Lines Losing Coverage	Coverage
crates/qasm2/src/lex.rs	6	91.52%
crates/circuit/src/parameter/symbol_expr.rs	3	76.03%
crates/circuit/src/parameter/parameter_expression.rs	1	90.36%
crates/qasm2/src/expr.rs	1	93.88%

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Coverage Stats

Relevant Lines:	128757
Covered Lines:	112900
Line Coverage:	87.68%
Coverage Strength:	997449.96 hits per line

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💛 - Coveralls