Nadarasa · v0.4.1 · Step C-2q
Rule (M) soundness under noise
The v0.4.0 milestone proved rule (M)'s 10 shortest PROMOTED 2q identities on ideal Selene shots. v0.4.1 re-runs each one under depolarizing and leakage noise. A PASS at noise level p means the identity A ≡ B survives the channel — both sides experience the same noise, so the cell-by-cell threshold 0.1768 continues to hold.
Cited in Quantinuum 2026 references: DFS-QEC leakage suppression (arXiv:2503.22107) and tesseract d=4 threshold (arXiv:2409.04628).
Related work: Fourier locking (Topel 2026) — rule (M) rewrites are a discrete cousin of that paper's continuous spectral homotopy: both reparameterise until the useful structure (identity here, expressive spectrum there) survives.
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Pass rate per noise level · 10 conjectures
| Noise level | Description | Pass | Pass rate | Mean worst Δp |
|---|---|---|---|---|
| ideal | p_1q = 0 | 10/10 | 100% | 0.1219 |
| depol_p005 | p_1q = 0.005 | 10/10 | 100% | 0.1195 |
| depol_p010 | p_1q = 0.010 | 10/10 | 100% | 0.1195 |
| depol_p020 | p_1q = 0.020 | 10/10 | 100% | 0.1266 |
| depol_h2 | H2-2 rates (1q 1.29e-4, 2q 1.29e-3) | 10/10 | 100% | 0.1137 |
| depol_h2_5x | 5× H2-2 rates | 10/10 | 100% | 0.1211 |
| depol_h2_20x | 20× H2-2 rates | 10/10 | 100% | 0.1195 |
| leak_p005 | leakage 0.005 | 10/10 | 100% | 0.1332 |
| leak_h2 | leakage 1e-3 (H2-class) | 10/10 | 100% | 0.1246 |
Per-conjecture worst Δp by noise level
Each row is one of the 10 shortest PROMOTED conjectures. Green cells stayed below threshold 0.1768, amber crossed it.
| # | Pair | ideal | depol_p005 | depol_p010 | depol_p020 | depol_h2 | depol_h2_5x | depol_h2_20x | leak_p005 | leak_h2 |
|---|---|---|---|---|---|---|---|---|---|---|
| #1 | S0·H0 ≡ H1·S0·H0·H1 | 0.1172 | 0.1133 | 0.1328 | 0.1016 | 0.125 | 0.1094 | 0.1172 | 0.1562 | 0.1211 |
| #2 | H0·S0·H0 ≡ H0·H1·S0·H0·H1 | 0.1289 | 0.1289 | 0.1211 | 0.1328 | 0.0977 | 0.0977 | 0.1289 | 0.1406 | 0.1211 |
| #3 | H1·S0·H0 ≡ H0·H0·S0·H0·H1 | 0.1211 | 0.1406 | 0.1094 | 0.1484 | 0.1016 | 0.1211 | 0.125 | 0.1758 | 0.1055 |
| #4 | S0·H0·CZ ≡ H1·S0·H0·H1·CZ | 0.1367 | 0.1094 | 0.1016 | 0.1641 | 0.1367 | 0.1445 | 0.1133 | 0.1211 | 0.125 |
| #5 | S0·H0·S0 ≡ H1·S0·H0·S0·H1 | 0.1211 | 0.1094 | 0.1172 | 0.1289 | 0.1328 | 0.0977 | 0.125 | 0.1406 | 0.1016 |
| #6 | S0·S0·H0 ≡ H1·S0·S0·H0·H1 | 0.125 | 0.125 | 0.1172 | 0.1133 | 0.1055 | 0.1484 | 0.1172 | 0.1133 | 0.1484 |
| #7 | S0·S0·S0 ≡ H0·S0·H0·S0·H0 | 0.1016 | 0.1211 | 0.1289 | 0.1562 | 0.0938 | 0.1094 | 0.1211 | 0.1367 | 0.1172 |
| #8 | S0·S1·H1 ≡ H0·H0·S1·H1·S0 | 0.1172 | 0.125 | 0.125 | 0.0938 | 0.1172 | 0.1094 | 0.0977 | 0.1172 | 0.1523 |
| #9 | H0·H1·S0·H0 ≡ H0·S0·H0·H1 | 0.125 | 0.1094 | 0.1211 | 0.1172 | 0.125 | 0.1406 | 0.125 | 0.1289 | 0.1094 |
| #10 | H0·S0·H0·S0 ≡ S0·S0·S0·H0 | 0.125 | 0.1133 | 0.1211 | 0.1094 | 0.1016 | 0.1328 | 0.125 | 0.1016 | 0.1445 |