Add Clifford-to-transvection decomposition from arXiv:2102.11380 - #118
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Marcus P S (marcusps) wants to merge 7 commits into
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Marcus P S (marcusps) wants to merge 7 commits into
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Implement a linear-size decomposition of a Clifford into Clifford transvections (pi/4 Pauli exponents) reproducing its symplectic (conjugation) action, plus the centralizer generators (the paper's headline application), in the paulimer crate. - paulimer::clifford::clifford_to_transvections: greedy O'Meara-style reduction producing O(n) factors that reproduce the symplectic action (signs and global phase are not tracked; contrast the sign-exact, O(n^2) clifford_to_pauli_exponents). Not guaranteed strictly minimal; exact r/r+1 minimality via congruence triangulation is a follow-up. - paulimer::clifford::clifford_centralizer: generators of Paulis fixed up to sign under conjugation (kernel of the residue map over GF(2), via binar). - Python bindings CliffordUnitary.to_transvections() / .centralizer() with .pyi stubs. - Extensive Rust (unit + proptest) and Python (hypothesis) tests: symplectic round trip, linear factor bound, no-shorter-than-minimum, and centralizer conjugation-fixedness. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com> Co-authored-by: Claude Opus 4.8 <noreply@anthropic.com>
This was referenced Jul 17, 2026
Marcus P S (marcusps)
marked this pull request as ready for review
July 17, 2026 04:34
Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Apply the conventions established while addressing @jmbr's review on the phased-outcome / decomposition stack (PRs microsoft#115/microsoft#116) to the transvection decomposition, anticipating the same feedback here: - Replace the seed + internal-RNG proptests (`seed in any::<u64>()` feeding `CliffordUnitary::random`) with a `Gate`-sequence `Strategy`, mirroring phased_clifford_dense.rs and measure_with_hint_sign_test.rs, so a failing input shrinks to a minimal gate sequence instead of an opaque seed. The deterministic sweep (which needs no shrinking) keeps using a seeded RNG. - Derive `qubit_count` inside `next_transvection` from `working.num_qubits()` instead of threading it as a parameter, matching the earlier "derive qubit count" tidy on the Gaussian-elimination decomposition. Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com> Copilot-Session: 16f923fe-a72a-4430-97b0-b7677f48dfb7
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Summary
Published reference
Implements the greedy O’Meara-style reduction from the transvection framework of Decomposition of Clifford Gates (arXiv:2102.11380). The contract is deliberately unphased: it reproduces the symplectic action, not Pauli-image signs or global phase.
Review series
This is the first of two dependent PRs for Clifford transvection decomposition and is independent of the phased outcome-complete simulation PRs. Review and merge this PR before the strict-minimum decomposition follow-up.