Notes · v0.4.1

Rule (M) under noise

Step C-2q from the v0.4.0 deferred queue. The original framing was "noise-advantage on the highest-CNOT-delta PROMOTED 2q rule" — but the actual data shows the max CZ-delta across all 105 PROMOTED rules is only 1 gate (length budget capped at 5). The advantage framing won't carry the way QFT_full vs AQFT_k1 did at length 15.

Pivoted framing · soundness, not advantage

Instead of looking for a noise winner, v0.4.1 asks whether rule (M) is sound on noisy shots: re-run each of the 10 shortest PROMOTED identities A ≡ B under depolarizing and leakage error models. Both sides experience the same channel, so a PASS at noise level p means the channel preserves the identity within the cell-by-cell threshold 4·√(0.5/shots) ≈ 0.177. Acceptance: ≥75% conjectures PASS at p_1q = 0.020.

Harness

quantum/pqp_frontier/tomography.py · prove_equal_2q now accepts an optional error_model, applied identically to A and B.
quantum/pqp_frontier/noise_2q.py · driver sweeps 10 conjectures × 5 noise levels (ideal, depol p∈{0.005, 0.010, 0.020}, leakage 0.005) with per-(conjecture, noise) cache under _cache_2q_noise/.
/nadarasa/proofs/noise-2q · matrix view: pass-rate per noise level + per-conjecture worst Δp heatmap.

Status

ideal: 10/10 PASS (mean worst Δp 0.1219)
depol_p005: 10/10 PASS (mean worst Δp 0.1195)
depol_p010: 10/10 PASS (mean worst Δp 0.1195)
depol_p020: 10/10 PASS (mean worst Δp 0.1266)
depol_h2: 10/10 PASS (mean worst Δp 0.1137)
depol_h2_5x: 10/10 PASS (mean worst Δp 0.1211)
depol_h2_20x: 10/10 PASS (mean worst Δp 0.1195)
leak_p005: 10/10 PASS (mean worst Δp 0.1332)
leak_h2: 10/10 PASS (mean worst Δp 0.1246)
Verdict at depol_h2: 100% → 2q_equivalence_survives_noise

Also in this drop · Playpond links

Every kernel page (G1–G11, plus G6b) now ships a "copy source · open in Playpond" chip next to the kernel snippet. Playpond (play.guppylang.org) has no client-encodable share URL — the chip copies the .py to the clipboard and opens the editor in a new tab so you can paste and Run.

Next up (v0.4.2)

Selene smoke test of a 2-mode beam-splitter collision unitary U_θ from the Ferreira et al. paper — validates the particle-number-preserving harness before rule (P) lands in v0.4.3. See /nadarasa/g14.