A quantum error correction decoder runs on a model of "how this machine breaks." Point that model at itself: it predicts that roughly one in a hundred measurement records will be hard to explain. On IBM's Boston and Kingston processors, 25.7% of actual records crossed that line.
A team led by Pacific Northwest National Laboratory turned this failure mode into a filter. The paper appeared on arXiv on September 24, under number 2609.29018.
The number decoders compute and throw away
Minimum-weight perfect matching decoders compute more than the correction they report. For each possible logical answer, they find the cheapest set of physical faults that could explain the observed syndrome, returning with two costs. Their difference is the so-called logical gap, proposed by Bombín, Pant, Roberts and Seetharam in 2024 as a confidence measure. It answers which answer the model prefers. Records with small gaps are the ambiguous ones; discarding them buys fidelity at the cost of throughput.
English, Williamson and Bartlett proved last year in Physical Review Letters that, if the decoder knows the device's true noise distribution, confidence-ranked post-selection is the optimal rejection rule at a fixed acceptance rate.
The problem is that premise. No frozen decoder can hold the true distribution of a living machine, for long.
This paper picks up the smaller of the two costs, which the authors call W. After computing the gap, W is usually discarded. W carries information the gap cannot reach: it says whether either answer can explain the record at all. Two records can have identical gaps while one is perfectly ordinary under the model and the other is nearly inexplicable.
Measuring one month of drift
The team generated repetition-code circuits with Stim, compiled them via Qiskit, and submitted them to IBM Quantum over roughly a month. The result: 163 physical implementations across code distances 5, 7, and 9, distributed over regions of two chips, each with about 2 million held-out shots—305 million in total.
Each implementation built its detector error model from the IBM calibration snapshot taken at collection time, was decoded with PyMatching, and then the decoder was frozen and applied to the held-out half. Everything the machine did afterward shows up relative to a fixed reference, not absorbed by refitting.
The machine did move. The most stable implementation held its detector event rate near 1.1% throughout. The least stable distance-9 layout swung between 8.9% and 34.5%, with logical error rates shifting in plateaus per 10,000-shot windows—stepwise drift, not isolated spikes.
Superconducting qubits drift by nature: relaxation times fluctuate with the spectral dynamics of microscopic two-level-system defects, and a single cosmic-ray event can spray quasiparticles across the whole chip, pulling down many qubits' T1s at once.
They then compared the measured W distribution against records sampled from the calibration model itself. Taking each model's own 99th percentile as the threshold, hardware costs at that percentile were a median 2.30 times higher, and 25.7% of held-out hardware shots fell above the line the model reserved for its own most bizarre one percent.
What the filter buys
The method adds only one scalar coefficient, fit on earlier validation data in chronological order and then frozen—no held-out shots enter the fit. At a 15% rejection rate, the combined score reduced retained logical error rate by an additional 10.6% over gap-only rejection at code distance 7 (bootstrap interval 8.35–16.18), and 28.8% at distance 9 (interval 26.84–30.20).
The same construction held on a machine the team had no involvement with. Google's published below-threshold memory data from the 72-qubit Willow processor shows the same deviation: on ten rounds of distance-5 XZZX surface-code memory, the filter cut retained logical error probability by 75.4%—though the 95% interval ran from 50.8% to 100%, and this operating point discards nine of ten shots. The gain stacks on top of Google's own reinforcement-learning-tuned decoder priors.
Where the bill actually gets paid: magic states
A fault-tolerant machine spends enormous area and time manufacturing magic states—the non-Clifford resource that lets circuits go beyond Clifford. Magic state cultivation, proposed by Gidney, Shutty and Jones in 2024, grows an encoded T state through rounds of fault-tolerant checks and rejections, then grafts it onto a larger code before ordinary uncorrected cycles destroy it. Google has run this protocol on a superconducting processor and published the records, with the grafting stage decoded by Tesseract, an A*-based maximum-likelihood error decoder.
Hoyt's group added the likelihood-aware score at the grafting stage, after Google's own hard acceptance checks. On three-cycle data, discarding a further 30% of records reduced the infidelity of accepted states by 34.7%. Read the other way: fixing output quality at 97% fidelity, the same information yielded 30.4% more accepted states per attempt. Two-cycle data showed the same trend with wider intervals: 19.2% and 15.5%.
For a factory whose output is consumed downstream, yield is the number that matters. The authors keep their claim tight: converting acceptance-rate improvements into end-to-end compute throughput requires modeling factory parallelism, buffering, and magic state consumption—all left to future work.
The proxy's limits, written by the authors themselves
The first reason W holds up is that it is free: it already exists inside the sector-constrained decoding problem, and the whole method adds one fitting step using data the experiment already collected. The team also compared simpler alternatives on the same 163 implementations: W alone, the raw fraction of detector bit flips, and a normalized combination of gap and detector density.
Their own assessment of W is that it "should be viewed as a plausible proxy rather than an optimal metric."
Model mismatch is not exclusive to matching decoders, either. Any decoder reporting confidence from an assumed noise model can have that confidence go wrong as the machine drifts. Neural-network decoders and belief-propagation decoders now being installed in real-time control stacks return likelihoods, clustering scores, and learned features—no compatibility analogue has been written for these quantities yet. The drift will be there in the next run; what is missing is the number that reads it.
References
- Aaron C. Hoyt et al., "Decoder Model Compatibility Provides Information beyond the Logical Gap under Drifting and Correlated Quantum Noise," arXiv:2609.29018, submitted 2026-09-24. Institutions include Pacific Northwest National Laboratory, University of Washington, Lawrence Berkeley National Laboratory, NASA Ames Research Center, and Fordham University
- Héctor Bombín et al., PRX Quantum 5, 010302 (2024), the logical gap as a post-selection confidence measure
- Lucas H. English et al., Physical Review Letters 135, 120603 (2025), optimality of confidence-ranked post-selection under a correctly specified noise model
- Craig Gidney et al., "Magic state cultivation" (arXiv:2409.17595); experimental records on Google's superconducting processor (arXiv:2512.13908)
- Google Quantum AI, Nature 638, 920–926 (2025), Willow public memory data
- Quantum Brief, 2026-09-28