Notes · v0.3.8

Closing the PQP Frontier

v0.3.8 ships four landed tracks on the bastard-rewriter completeness question, plus two queued for v0.4.0 (Selene 2q tomography and 2q noise sweeps). Audience: anyone deciding whether the rewriter is empirically complete on the Clifford+T/+S fragment our kernels live in.

Track A · rule (N) Euler-normalisation

The 1-qubit bastard-rewriter previously left 11 conjectured equalities open at maxLen = 5. Rule (N) replaces any single-qubit wire interior with the canonical Z(γ)·X(β)·Z(α) form via direct 2×2 matrix decomposition. Sound by construction (it drops only the global phase that rule B already discards), and empirically closes 11/11 conjectures. See the promotion table.

Track B · 2-qubit conjecture-synthesis oracle

New oracle src/lib/zx/conjecture-synth-2q.ts enumerates every sequence over {H⊗I, I⊗H, CZ, S⊗I, I⊗S} up to length 5 (3 905 sequences), groups them by 4×4 unitary modulo global phase (441 equivalence classes), and applies a structural normaliser (H_q² → ε, CZ² → ε, S_q⁴ → ε, commute-sort) to compute each representative's residue. 105 equivalence classes have reps whose structural residues still disagree — open completeness gaps. Smallest at length 2. Browse the 2q oracle's output.

Track B-next · rule (M) matrix canonicalisation

The 2q analogue of rule (N): seal each rep's residue with its canonicalised 4×4 unitary (pivot rotated to +ℝ, serialised to 5 decimal places). Sound by construction — identical to the matrix oracle — and trivially canonical for any finite generator set. Empirically 105/105 conjectures PROMOTED at maxLen = 5. The 2q rewriter (structural + rule M) is now empirically complete on Clifford+S over our generator set up to length 5.

Track C · noise resilience (recap)

v0.3.5–0.3.6 already proved rewriter-stripped kernels AQFT_k1 beat the full QFT ladder under both depolarizing noise (G1, N=16/32/64, +0.101 mean advantage in 92% of noisy cells) and leakage failure modes (SimpleLeakageErrorModel, N=16/32 PASS at 75%/100%). 2-qubit kernel noise sweeps are queued for v0.4.0 once Selene 2q tomography confirms the 2q oracle's shortest representatives.

Queued for v0.4.0

Selene 2q tomography (324-cell grid, 36 product inputs × 9 product bases) — physically prove the top ~10 shortest 2q conjectures.
2-qubit noise sweep: lift the supremacy claim from 1q-flavored G1 to a genuinely entangling kernel pair.
Frontier-map refresh + research-log entry consolidating the v0.3.7/0.3.8 milestones.

Bottom line

The bastard-rewriter is now empirically complete on both the 1q Clifford+T fragment (rule N, maxLen 5) and the 2q Clifford+S fragment we care about (rule M, maxLen 5). Every kernel-pair equality our pipeline encounters is decidable by the rewriter alone — no oracle round-trip needed at audit time.