G17 — Ethylene QPDE under H2-class noise

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.

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

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.

• 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.