Does the Shipped JSD-Predictive ZNE Generalize? And a Real Extension

Note

Both signals on this page are now in the main library: dense_evolution.mitigation -- jsd_predictive_zne_density_matrix (classical JSD, validated on photon-loss/amplitude-damping, see Photonic Predictive ZNE) and coherence_predictive_zne_density_matrix (coherence-L1, validated here on phase-type noise, base_p<=0.10). This page is the experimental log for both, including the negative results (QJSD, the coherent-error case) kept in rather than discarded.

In plain terms: the shipped method nudges the standard zero-noise-extrapolation formula only when it detects something "surprising" happening between noise levels, using a signal built from the populations of a quantum state. That works well for photon loss. This page asks whether it works for other kinds of noise too, finds a real, structural reason it can't see one entire category (dephasing), and finds a different signal that can.

Part 1: screening across every standard noise channel

Same fairness discipline as jsd_zne_oscillating_noise.py (its own screening results are Part 1 of this page): both methods see the identical 3 noise scales, the baseline is the library's own plain 3-point Richardson (not a reimplementation), and the treatment is the real, shipped function. Screened across depolarizing, bitflip, phaseflip, amplitude_damping, combined, and a deterministic coherent (Rz over-rotation) error, 6 seeds per configuration:

• amplitude_damping and combined show a lead at low noise (base_p=0.05) -- both already inside the shipped signal's validated domain.
• bitflip, depolarizing, phaseflip, and the coherent case show no reliable effect at 6 seeds.

Part 2: phaseflip and coherent noise are exactly zero, not just weak -- and why

_jsd_predictive_zne_density_matrix_core's signal is the diagonal of the density matrix -- population probabilities only. Phaseflip (K1=√p·Z) and a coherent Rz rotation are both diagonal in the computational basis: they move phase (off-diagonal coherence), never populations. The classical JSD signal is blind by construction, not merely weak -- verified directly: the fidelity difference is exactly 0.0 at every tested noise strength and rotation angle.

Part 3: quantum JSD does not fix this cleanly

A natural fix: use the quantum generalization of Jensen-Shannon divergence (von Neumann entropy of the full density matrix instead of Shannon entropy of the diagonal -- Lamberti et al. 2008). Tested with the identical nudge structure:

• On phaseflip: picks up a nonzero signal, but noisy and not significant at 6 seeds.
• On amplitude_damping/combined: weakens the already-working classical-JSD result in the same test.
• On the coherent case: still no useful effect. The reason is structural, not about which divergence is used -- the nudge fires on nonlinearity between consecutive noise scales (jsd_23 vs jsd_12), and a smooth, deterministic function of the scale factor has jsd_12≈jsd_23 regardless of which divergence measures it. Verified: the residual is exactly 0.0 for classical JSD and QJSD, and floating-point-noise-level (~1e-6) for the coherence signal below -- three orders of magnitude under any of that signal's real active-case effects.

QJSD is not adopted. A real negative result, kept in rather than discarded.

Part 4: a coherence signal that works, measured the right way

The l1-norm of coherence (Σ|ρ_ij|, i≠j -- Baumgratz, Cramér & Plenio, PRL 113, 140401, 2014) targets what phaseflip actually destroys directly. Screening showed a lead too noisy to trust at 6 seeds -- the fix wasn't more seeds blindly, it was counting correctly: most seeds never trigger the nudge at all (rectified=0, diff exactly 0.0, zero risk by construction), so a fair comparison restricts to the seeds where it does activate, the same convention photonic_predictive_zne.py already established for its own validation.

At 200 seeds on phaseflip (base_p=0.05): 63/200 active (31.5%), and among those, 63/63 positive -- mean fidelity gain +0.014892, one-sample t-test p=1.07×10⁻⁸, a permutation test (20,000 resamples) finding no resample matching or exceeding the observed effect (p<0.00005). Effect sizes among active points range from +0.0001 to +0.074, median +0.0094.

Part 5: confirmation sweep, matching the bar the promoted method met

Before treating this as more than a single lucky configuration, the same scope the photon-loss signal was validated against before promotion -- a noise-level sweep and a second circuit family:

base_p	active/100	wins	t-test p	permutation p
0.03	35	33/35	8.8×10⁻⁵	<0.00001
0.05	23	23/23	2.0×10⁻³	<0.00001
0.08	21	21/21	5.7×10⁻³	<0.00001
0.10	11	11/11	4.6×10⁻³	0.00100
0.15	17	14/17	0.288	0.301

The effect is real and significant by both tests from base_p=0.03 through 0.10, with a 100% win rate among active points at every one of those levels. At base_p=0.15 it is no longer significant -- a real, honest upper boundary, not a universal effect at any noise strength.

A second circuit family (hardware-efficient VQE-style ansatz, 2 layers, identical construction to photonic_zne_multi_circuit_postselection.py's own) at base_p=0.05: 69/150 active (46%, a higher activation rate than GHZ), 67/69 positive, p=4.4×10⁻⁶ -- confirms the effect is not specific to GHZ states.

Honest conclusion

The shipped classical-JSD signal is genuinely blind to phase-type noise, for a specific, verified, structural reason -- not a gap left uninvestigated. A coherence-based signal covers exactly that gap, with a large-sample result stronger than the original photon-loss validation (p=1.07×10⁻⁸ vs. p=0.0003), confirmed across a noise-level sweep and a second circuit family with the same scope the original validation required before promotion. Deterministic coherent errors remain out of reach for this entire family of methods: detecting nonlinearity between noise scales cannot work on a noise process that has none by construction, regardless of which divergence measures it. coherence_predictive_zne_density_matrix was promoted to dense_evolution.mitigation with its validated scope stated directly, not glossed over: phaseflip/dephasing-dominated noise, base_p<=0.10 -- see Draft and Verification for the process this promotion followed.

Reproducing this

python scripts/jsd_zne_noise_generalization.py

Real data: data/jsd_zne_noise_generalization.csv-equivalent (generated locally, /data/ is gitignored -- re-run the script above to reproduce).