v0.4.2 — noise ladders, extrapolation, and spectral moments

Gate 8A — noise ladder and zero-noise extrapolation

The ethylene QPDE gap fit was re-run under depolarizing noise anchored on Quantinuum's published H2 rates. The recovered gap degrades monotonically, reaching 26% error at 20× H2 — a one-sided bias, since depolarizing channels pull every probability toward 0.5 and compress the estimated phase. Richardson extrapolation over a densified ladder recovers most of that collapse. /nadarasa/g17

Gate 8B — shot budget vs fit bias

The 4% residual in the ideal G16 fit turned out to be statistics, not bias: with the arcsine branch handled correctly (k ≤ 4, so 2φ stays inside π/2) the error falls to 0.27% at 4096 shots and keeps falling. k = 6 and k = 8 are branch and aliasing controls, not fit data. /nadarasa/g16

Gate 8C — Laplacian moments on a WL-blind pair

A Hadamard test over all eight computational basis states estimates tr(e^(−iΔτ))/N for two graphs that 1-WL refinement cannot tell apart. Subtracting the measured curves gives χ²/dof = 110 over 24 points. Attributing the separation to a single moment is harder: on this shot budget the T₃ gap sits inside its own error bar at fit order 8, and only the truncated order-6 fit resolves it — reported as an open limitation rather than smoothed over. /nadarasa/g18

Operational lessons

• Budget many-circuit sweeps up front. The G18 grid is 384 circuits at roughly 4 seconds each — half an hour of emulator time, far past a single sandbox command. The per-circuit resumable cache is what made it finishable.
• For Taylor-series fits, conditioning beats sampling. The τ grid and truncation order moved σ(T₃) by a factor of four at fixed shots; quadrupling the shot count would only have halved it.
• Everything ships as committed static JSON. No quantum code runs at request time.