Nadarasa · v0.4.2 · Selene experiment

G17 — Ethylene QPDE under H2-class noise

G16 showed the ethylene QPDE interference law holds cell-by-cell on a noiseless emulator. The question a chemistry user actually asks is different: how much gate error can the gap fit absorb before the answer stops being chemistry? This run re-executes the maximum-slope β = π/2 column at a ladder of depolarizing error rates anchored on Quantinuum's published H2 numbers, and re-fits the eigenvalue gap at each rung.

verdict verifiedqpde_noise_ladder_verified2/2 criteria

Each criterion below is recomputed from the committed rows by quantum/verdicts.py; this chip reads the result rather than restating it.

passideal_cells_match_oracle
every ideal-noise cell agrees with the exact statevector value inside the 4*sqrt(0.5/shots) envelope
measured 0.018863 · threshold 0.044194
passdegradation_is_monotone
the gap-fit error grows monotonically with the noise multiplier
measured [0.042412,0.075355,0.211628] · threshold non-decreasing

Reference gap

0.800 Ha

Fit @ 1× H2

0.758 Ha

Error @ 1× H2

5.3%

Error @ 20× H2

26.5%

The noise ladder

Selene's DepolarizingErrorModel is driven from the H2 numbers reported in the SoftBank / Quantinuum white paper: p_2q = 0.00129, p_1q = 0.00003, p_meas = 0.00135 (the midpoint of the asymmetric readout rates). Each rung multiplies all three together, so the ladder is a single-parameter stress test rather than a per-channel ablation.

Only k ∈ 1, 2, 4 enters the fit. k = 8 is the mod-1 aliasing control from G16 and carries no gradient, so it would only add noise to the average.

Measured p(q1 = 1) and recovered gap

Noise	p_2q	k = 1	k = 2	k = 4	Gap (Ha)	Rel. error
Ideal (control)	—	0.2898 / 0.3087	0.1416 / 0.1464	0.0000 / 0.0000	0.8327	4.08%
H2 baseline · 1×	1.29e-3	0.3159 / 0.3087	0.1531 / 0.1464	0.0056 / 0.0000	0.7576	5.30%
H2 baseline · 5×	6.45e-3	0.3127 / 0.3087	0.1619 / 0.1464	0.0259 / 0.0000	0.7246	9.42%
H2 baseline · 20×	2.58e-2	0.3352 / 0.3087	0.2195 / 0.1464	0.0989 / 0.0000	0.5884	26.45%

Each cell shows measured / noiseless-ideal p(q1 = 1) at 4096 shots.

Reading the result

Degradation is monotone and one-sided: depolarizing noise pushes every probability toward 0.5, which compresses the recovered phase and therefore underestimates the gap. The bias is systematic, not statistical — more shots will not remove it.
The k = 4 cell is the canary. Its ideal value is exactly 0, so its measured value is a direct readout of accumulated error: 0.0056 at 1×, 0.0259 at 5×, 0.0989 at 20×.
At 1× H2 the fit lands within about 5% of the reference gap — the same order as the shot-noise-limited ideal control, so at this depth the published error rates are not the binding constraint.
At 20× the fit collapses to 26% error. Between 5× and 20× is where zero-noise extrapolation or an error-corrected encoding stops being optional for this protocol.

Zero-noise extrapolation

verdict verifiedqpde_zne_recovers_gap3/3 criteria

Each criterion below is recomputed from the committed rows by quantum/verdicts.py; this chip reads the result rather than restating it.

passmitigation_beats_worst_rung
the quadratic extrapolation is closer to the reference gap than the worst unmitigated rung
measured 3.656 · threshold 26.453
passquadratic_fits_better_than_linear
the quadratic Richardson fit has the smaller residual RMS
measured 0.009294 · threshold 0.012187
passrecovers_majority_of_collapse
the extrapolation recovers more than half of the noise-induced collapse in the gap
measured 74.66 · threshold 50

The ladder above is also a mitigation dataset. Densifying it with 2× and 10× rungs gives five noisy points; fitting the recovered gap against the noise multiplier λ and evaluating at λ = 0 asks how much of the collapse a Richardson-style extrapolation buys back — without ever running an error-corrected circuit.

Rung (λ)	Gap (Ha)	Rel. error
0 (control)	0.8327	4.08%
1×	0.7576	5.30%
2×	0.7356	8.05%
5×	0.7246	9.42%
10×	0.6476	19.05%
20×	0.5884	26.45%
ZNE · linear → λ = 0	0.7586	5.17%
ZNE · quadratic → λ = 0	0.7708	3.66%

Both extrapolators recover most of the damage: the quadratic fit returns 74.66% of the 0.244 Ha collapse, landing at 0.7708 Ha — 3.7% from the 0.800 Ha reference.
Neither reaches the measured ideal control (0.8327 Ha). The λ = 0 intercepts sit below it, which is what a slightly non-polynomial error profile looks like: the linear fit's residual RMS (0.012187) is a third larger than the quadratic's (0.009294).
Practical reading: extrapolation converts a 26% error at 20× into roughly a 4% error, i.e. it buys about one order of magnitude of gate quality on this protocol — useful, but not a substitute for encoding once the active space grows.

Caveats

Depolarizing noise is a coarse stand-in. Selene ships no coherent / T1–T2 memory model, so the slow-dephasing channel that dominates long idle windows on real traps is absent here.
The ideal control itself carries ~4% error at these shot counts, so the 1× rung is not resolved against shot noise. Separating them needs more shots, not more noise levels.
This is a two-qubit active space. Nothing here extrapolates to the depth of a production chemistry instance without redoing the ladder at that depth.
Results are committed static JSON. Nothing quantum runs at request time.

Reproduce

pip install --target .pydeps -r quantum/requirements.txt
PYTHONPATH=.pydeps python -m quantum.qpde.noise
PYTHONPATH=.pydeps python -m quantum.qpde.zne

Backend: selene-sim Quest. Each (noise, k) cell caches under quantum/qpde/_cache_qpde_noise/, so the sweep is resumable across sandbox sessions. Total runtime 25s.

G16 Ethylene QPDE 2q noise resilience Quantinuum 2026 refs