Speed up commutation-aware rewrite searches

[taalexander]

Fixes #5268 and #5269. QuakeSimplify currently scans every earlier operation when looking for a gate to combine. For example,

  S(q0)          possible match
  H(q0)          barrier
  H/X(q1) ...    unrelated gap
  S(q0)          search starts here

Previously, the search checked every q1 gate before reaching the H(q0) that stops it (as wires cannot always be followed due to a bunch of other issues noted below). Repeating this across a growing block can produce quadratic scan work.

This change builds a lazy interaction index for each known virtual qubit to operation. This is done on segment boundaries and when I say "virtual" qubit I mean a qubit that is statically knowable as equivalent to itself in the wire-flow chain:

  q0: S, H, S
  q1: H, X, ...

The q0 search now skips the q1 stream and reaches the same H(q0) immediately. Unsupported operations form segment boundaries, while unresolved qubit identities retain the existing block-order search.

All of the other commutation machinery has been kept the same.

Performance:

• Reduce performance cost of failed searches in CommutationAwareRewriteMatcher #5268 at 2,048 placements: 1.91 s → 0.038 s
• Reduce repeated QuakeSimplify scans across disjoint quantum support #5269 search work no longer grows with the size

I tried to keep it as simple as possible but it was still more LOC than I would have liked. A large portion of the difficulty with all of this work is we really can't "just" follow value form as there are loads of special cases of aliasing, reference form, unknown qubit values, etc., making the wire semantics non-trivial and causing the analysis "segment" within a block. Perhaps the right fix would be to simplify the IR/make the value form more strict, however, I don't think this is possible right now.

To review I recommend looking at it in this order:

1. find_nearest: unchanged matching rules and the handoff to indexed traversal.
2. LogicalQubitInteractionIndex: operation classification, segments, and ordered streams.

[github-actions]

CI Summary (push) — ✅ passed

Run #33029896942 · ✅ 7 · ⏩ 7 · ❌ 0 · ⛔ 0

Top-level jobs (14)

Job	Result
binaries	⏩ skipped
build_and_test	✅ success
changes	✅ success
config_devdeps	✅ success
config_source_build	⏩ skipped
config_wheeldeps	✅ success
devdeps	✅ success
docker_image	⏩ skipped
gen_code_coverage	⏩ skipped
metadata	✅ success
python_metapackages	⏩ skipped
python_wheels	⏩ skipped
source_build	⏩ skipped
wheeldeps	✅ success

⏩ Skipped jobs (7) — intentionally skipped on PR builds; run on merge_group / workflow_dispatch

Job
binaries
config_source_build
docker_image
gen_code_coverage
python_metapackages
python_wheels
source_build

All sub-jobs (43) — every matrix leg, with links

Job	Status	Link
Build and test (amd64, gcc12, openmpi) / Dev environment (Debug)	✅ success	view
Build and test (amd64, gcc12, openmpi) / Dev environment (Python)	✅ success	view
Build and test (amd64, llvm, openmpi) / Dev environment (Debug)	✅ success	view
Build and test (amd64, llvm, openmpi) / Dev environment (Python)	✅ success	view
Build and test (arm64, llvm, openmpi) / Dev environment (Debug)	✅ success	view
Build and test (arm64, llvm, openmpi) / Dev environment (Python)	✅ success	view
CI Summary	❔ in_progress	view
Check for stable CUDA-Q changes	✅ success	view
Configure build (devdeps)	✅ success	view
Configure build (source_build)	⏩ skipped	view
Configure build (wheeldeps)	✅ success	view
Create CUDA Quantum installer	⏩ skipped	view
Create Docker images	⏩ skipped	view
Create Python metapackages	⏩ skipped	view
Create Python wheels	⏩ skipped	view
Gen code coverage	⏩ skipped	view
Load dependencies (amd64, gcc12) / Caching	✅ success	view
Load dependencies (amd64, gcc12) / Finalize	✅ success	view
Load dependencies (amd64, gcc12) / Metadata	✅ success	view
Load dependencies (amd64, llvm) / Caching	✅ success	view
Load dependencies (amd64, llvm) / Finalize	✅ success	view
Load dependencies (amd64, llvm) / Metadata	✅ success	view
Load dependencies (arm64, gcc12) / Caching	✅ success	view
Load dependencies (arm64, gcc12) / Finalize	✅ success	view
Load dependencies (arm64, gcc12) / Metadata	✅ success	view
Load dependencies (arm64, llvm) / Caching	✅ success	view
Load dependencies (arm64, llvm) / Finalize	✅ success	view
Load dependencies (arm64, llvm) / Metadata	✅ success	view
Load source build cache	⏩ skipped	view
Load wheel dependencies (amd64, 12.6) / Caching	✅ success	view
Load wheel dependencies (amd64, 12.6) / Finalize	✅ success	view
Load wheel dependencies (amd64, 12.6) / Metadata	✅ success	view
Load wheel dependencies (amd64, 13.0) / Caching	✅ success	view
Load wheel dependencies (amd64, 13.0) / Finalize	✅ success	view
Load wheel dependencies (amd64, 13.0) / Metadata	✅ success	view
Load wheel dependencies (arm64, 12.6) / Caching	✅ success	view
Load wheel dependencies (arm64, 12.6) / Finalize	✅ success	view
Load wheel dependencies (arm64, 12.6) / Metadata	✅ success	view
Load wheel dependencies (arm64, 13.0) / Caching	✅ success	view
Load wheel dependencies (arm64, 13.0) / Finalize	✅ success	view
Load wheel dependencies (arm64, 13.0) / Metadata	✅ success	view
Prepare cache clean-up	❔ in_progress	view
Retrieve PR info	✅ success	view

✅ Required checks (6/6) — declared in .github/required-checks.yml for push

Required check	Status	Link
Build and test (amd64, llvm, openmpi) / Dev environment (Debug)	✅ success	view
Build and test (amd64, llvm, openmpi) / Dev environment (Python)	✅ success	view
Build and test (arm64, llvm, openmpi) / Dev environment (Debug)	✅ success	view
Build and test (arm64, llvm, openmpi) / Dev environment (Python)	✅ success	view
Build and test (amd64, gcc12, openmpi) / Dev environment (Debug)	✅ success	view
Build and test (amd64, gcc12, openmpi) / Dev environment (Python)	✅ success	view