ZNE Healing-Branch Sigma Provenance: a Confound, Not a New Win¶
dense_evolution.zero_noise_extrapolation's "healing-adapted" branch (sigma_at_base_noise, see docs/api/healing.md) perturbs the 3 Richardson coefficients via calculate_delta_preemp(sigma_at_base_noise, target_sigma_ideal). The library's own calculate_advanced_sigma (kappa*H*Psi*Omega_sync*tau_K) was meant to produce that sigma, but its 5 inputs have no defined provenance in a ZNE context: dashboard_core's run_zne_mitigation only ever has scalar Pauli expectation values, never a density matrix, so entropy/purity-style inputs have no real data to come from at that integration point -- deliberately left unwired rather than plumbed in speculatively.
What's being tested: bypass the unresolved calculate_advanced_sigma provenance question entirely and test the mechanism directly with the most literal, oracle-free candidate for "sigma at the base noise level" -- the real empirical standard deviation of the n_trials stochastic Kraus-draw ensemble at noise_factor=1. No density matrix, no ideal-state comparison (uhlmann_fidelity's own docstring bans that: "never to feed into" a correction).
Setup¶
2-qubit Bell state, <ZZ> (ideal = 1.0), 3 noise channels (depolarizing, bitflip, amplitude_damping) x 3 noise levels (p=0.02/0.05/0.10) x 5 seeds x 300 trials per noise scale -- 45 configurations total. target_sigma_ideal is measured per-config (empirical std at the sweep's smallest real noise level, independently seeded), not guessed.
Result: looks like a win at first¶
| mean error delta (plain − healing) | win rate | |
|---|---|---|
Real pairing (real base_std) |
+0.000458 | 88.9% (40/45) |
Every single (noise_model, noise_p) combination came out net positive -- exactly the shape of result that looked convincing before Experiment 25's own JSD-ZNE nudge turned out to be a confound.
Negative control: shuffle sigma_at_base_noise across runs¶
Same 45 configurations, same means/ideal pairs, but base_std permuted at random across rows before being fed into the healing branch:
| mean error delta | win rate | |
|---|---|---|
Negative control (shuffled base_std) |
+0.000491 | 86.7% (39/45) |
Statistically indistinguishable from the real pairing. The win doesn't depend on base_std reflecting anything real about that specific run -- any positive-valued sigma produces essentially the same small structural nudge to the Richardson coefficients.
Verdict¶
Confound, not a real effect -- the same failure mode as Experiment 25, on a different part of the codebase. The healing-adapted branch's coefficient perturbation (c1 = 3.0 - 0.01*delta_p, c2 = -3.0 + 0.02*delta_p, c3 = 1.0 - 0.01*delta_p) is a small enough nudge away from the exact-interpolation Richardson coefficients that it mildly regularizes the extrapolation regardless of what delta_p actually is -- consistent with polynomial_extrapolate's own documented finding that exact 3-point Richardson coefficients are numerically fragile under real statistical noise. The apparent benefit is about perturbing away from the exact coefficients at all, not about what the perturbation is driven by.
What this means for calculate_advanced_sigma: even a fully-designed, physically-grounded set of kappa/H/Psi/Omega_sync/tau_K inputs would not make the healing-adapted ZNE branch meaningfully better than feeding it any other positive scalar -- the consumer doesn't discriminate signal from noise at the tested scale. Completing calculate_advanced_sigma's provenance is not blocked on missing inputs anymore; it's blocked on the downstream mechanism itself not using its input, which is a different (and more fundamental) problem than the one originally suspected.
Status¶
Not promoted. calculate_advanced_sigma remains publicly exported (backward-compat) but unused by any real pipeline, same as before this experiment -- now with a verified reason why completing its provenance wouldn't help, rather than an open question.