Clifford-only RXYXY2Q and RXY1Q reject theta = pi with pi/4 axes, and RXYXY2Q compares theta to exact zero

[ciaranra]

Summary

The Clifford-only entry points for the two XY-plane rotations reject some inputs that are Clifford, and one of them is inconsistent with its own single-angle helper about what "zero rotation" means.

try_rxyxy2q (crates/pecos-simulators/src/clifford_rotation.rs, added in #788)

1. The early return tests theta == Angle64::ZERO exactly, whereas try_rxx snaps theta within the Clifford tolerance. A theta within tolerance of zero combined with a non-Clifford phi is rejected even though the gate is the identity. try_simplify_rxy1q snaps theta before comparing; the same should happen here. The Selene stabilizer plugin (python/selene-plugins/pecos-selene-stabilizer/src/lib.rs) already snaps on its side, so it does not see this.

2. theta = pi with phi an odd multiple of pi/4 is Clifford: the gate is -i P(phi) (x) P(phi) and P(pi/4) = (X + Y) / sqrt(2) conjugates X to Y, Y to X and Z to -Z. Selene's own Stim simulator accepts these cases (see its rpp table). PECOS rejects them because the precheck asks for RZ(phi) to be Clifford, which is a sufficient condition, not a necessary one.

try_rxy1q / try_simplify_rxy1q (crates/pecos-core/src/clifford_simplify.rs)

The same gap as (2) exists for the single-qubit gate: RXY1Q(pi, pi/4) is -i (X + Y) / sqrt(2), a Clifford, and is rejected. The documented table in try_simplify_rxy1q lists only quarter-turn axes.

Expected

• Snap theta before the zero check in try_rxyxy2q.
• Accept theta = pi with phi any multiple of pi/4 in both gates, dispatching to the appropriate named Cliffords (SZdg; X; Z-style sequences per Selene's table, or whatever the tableau lookup gives). Phase must be tracked, not dropped; the existing phase-exactness tests are the gate for that.
• Extend try_rxyxy2q_matches_xx_and_yy_rotations and the RXY1Q tests with the new axes, using an independent oracle.

Provenance

Found during an AI-assisted review of #788 and deferred out of that PR so it can merge. Not a correctness bug: every rejected case fails loudly.

[ciaranra]

The zero-check half of this issue (snap theta before comparing to zero in try_rxyxy2q) is fixed in #811.

The remaining half, accepting theta = pi with phi an odd multiple of pi/4 in both try_rxyxy2q and try_rxy1q, is a design change rather than a patch: try_simplify_rxy1q returns Option<GateType> (one named Clifford), and -i (X + Y)/sqrt(2) is not a single named gate, so the return type would have to become a decomposition and snap_clifford_angle would need an eighth-turn grid, with every consumer of try_simplify_rxy1q updated. Leaving this issue open for that decision.