Fix reset-window and final-round data-qubit priors in precompute_dem

[ivanbasov]

Summary

Follow-up to #85 (see the review discussion there). Auditing build_single_p_marginal with the same isolated-channel Stim methodology used to validate #85 surfaced two more circuit-vs-sampler mismatches in the explicit 25-parameter noise-model path. Both predate #85 and were invisible to its validation only because the affected channels were zeroed in that isolation.

1. Reset-window data idles were overcounted with p_idle_cnot_*

In NoiseModel mode the circuit applies no idle noise to data qubits during the ancilla prep/reset window — that idle is deliberately folded into the measurement-window SPAM idle (MemoryCircuit: "IGNORE data-idle during ancilla prep/reset"; the config calibration p_idle_spam = 2p/3 − 4p²/9 reflects the combined window). But the marginal builder let intermediate-round data locations at tt == 0 fall through to the bulk-idle branch and assigned p_idle_cnot_*.

Isolating p_idle_cnot_X/Y/Z = 0.002 (d=3, r=4, X basis, 400k shots), per-round mean syndrome densities:

Round	Sampler (before)	Stim	Sampler (after)
0	0.01087	0.01079	0.01087
1	0.03291	0.02165	0.02171
2	0.03294	0.02177	0.02168
3	0.01092	0.01102	0.01095

With the full public 25-parameter values (r13 config), intermediate-round syndrome densities were ~10% hotter than Stim (0.1020 vs 0.0924).

Fix: intermediate-round data locations at tt == 0 get probability 0. Boundary rounds are unaffected (their tt == 0 data locations are consumed by is_data_prep).

2. Final-round data injection used the preparation rates

The circuit represents noisy data readout as a fake data-measurement flip injected at the start of the final perfect round, at the measurement rates: Z_ERROR(p_meas_X) for X-basis readout, X_ERROR(p_meas_Z) for Z-basis. The sampler's is_data_prep branch assigned p_prep_X/Z instead (its is_final_round split had identical arms — this change makes the split carry the intended distinction).

All shipped configs use p_prep == p_meas, so this cancels numerically today, but it breaks as soon as the two families are calibrated separately. Isolating the channels makes the mirror image visible in the final round (d=3, r=4, 400k shots): with only p_meas_* = 0.004, Stim shows 0.0099 vs the sampler's 0.0040; with only p_prep_* = 0.004, the sampler showed 0.0099 vs Stim's 0.0040. After the fix both isolations agree with Stim.

Tests

Extends test_precompute_dem_probabilities.py (added in #85):

• Unit tests asserting the exact prior at both locations (reset-window zeros, final-round p_meas_* with the basis-correct Pauli), plus a guard that round-0 data preparation keeps p_prep_*. The two new location tests fail on main with the expected signatures.
• A seeded, deterministic end-to-end guard (TestSamplerMatchesStimSyndromeDensities): per-round syndrome densities from Bernoulli(p) errors pushed through the precomputed H must match direct Stim sampling of the same MemoryCircuit within 5 standard errors, for cnot-idle-only, measurement-only, and full-25-parameter noise. Runs in ~1 s at d=3/r=4 (CPU, no cuStabilizer needed), so it sits in the short tier and will catch any future circuit-vs-sampler prior drift.

Impact

Only the explicit-NoiseModel path of build_single_p_marginal is touched; the legacy scalar path is untouched (its circuit emits a genuine reset-window idle, which it already accounts for). Training data generated after this change has intermediate-round syndrome densities ~10% lower than before, now matching the Stim reference; models trained on previously generated bundles are unaffected functionally but were trained against slightly hotter priors.

[ivanbasov]

@jolle-ag one focused question for review, since this pins down the intended noise-model semantics: is the Stim circuit the reference on both counts — (1) the data-qubit reset-window idle carries no separate noise location because it is folded into the measurement-window SPAM idle (consistent with the p_idle_spam = 2p/3 − 4p²/9 calibration in the configs), and (2) the final-round data injection is a fake data-measurement flip at p_meas_X/p_meas_Z? This PR makes the precomputed priors match the circuit on both; if either circuit behavior itself doesn't reflect the intended physical model, the fix belongs on the circuit side instead.

[bmhowe23]

LGTM. It would be good to get Jan's answer to your question before merging.

[jolle-ag]

Thanks for catching this. What you spotted and how you fixed it is the intended behavior.