An internal disagreement signal in a quantum error-correction decoder picked out the simulated shots most likely to fail a fast decoding pass. When researchers sent only the 20% of shots with the largest disagreement to a deeper search, the test recovered 91.9%, 91.5% and 84.9% of the improvement available from running that search on every shot at three noise settings. The result is reported in an arXiv preprint dated 29 September 2026.
The study asks a practical question: how much extra post-processing search should each decoded shot receive after a fast decoder produces an answer? Its adaptive pipeline runs BP for at most 20 iterations, then applies OSD-0. BP supplies a hard decision, while OSD-0 produces a correction consistent with the observed syndrome. The disagreement score counts the positions where those two answers differ. Shots at or above a chosen cutoff go to a truncated one-free-variable search with K = 1000 candidates; the rest keep the OSD-0 result.
The strongest results came in simulation
The main benchmark used the [[144, 12, 12]] bivariate bicycle code over 24 syndrome-extraction rounds. Researchers tested three noise settings, p = 0.006, 0.007 and 0.008, with 20,000 shots at each operating point. A shot counted as a logical failure when any of the code's 12 logical Z observables was misidentified.
Disagreement was a strong ranking signal. The area under the receiver operating characteristic curve, or AUROC, measures how well a score separates two outcomes, with higher values indicating cleaner separation. For the primary code, AUROC was 0.958 at p = 0.006, 0.958 at p = 0.007 and 0.937 at p = 0.008. The reported 95% bootstrap intervals were 0.941-0.974, 0.951-0.965 and 0.930-0.943, respectively.
Most of the gain came from a minority of shots
The full one-free-variable reference search produced lower reported logical error rates than OSD-0 alone. At p values 0.006, 0.007 and 0.008, OSD-0 rates were 0.00475, 0.01990 and 0.06275. The corresponding full-search rates were 0.00105, 0.00410 and 0.01865, described in the study as improvement factors of 4.52, 4.85 and 3.36.
The adaptive test used the disagreement ranking to spend that extra effort selectively. Escalating the top 20% produced logical error rates of 0.00135, 0.00545 and 0.02530 at the same three noise points, recovering 91.9%, 91.5% and 84.9% of the full-search improvement. At p = 0.007 and the same 20% budget, disagreement routing reported 0.00545, compared with 0.01140 for BP-residual routing, 0.01385 for syndrome-weight routing and 0.01687 for random routing.
That accuracy result was paired with a large timing difference in the study's serial measurements. At 20% escalation, mean decoding cost was 36.3 milliseconds per shot, with a bootstrap interval of 32.9 to 39.9 milliseconds, versus 131.9 milliseconds when the K = 1000 branch ran on every shot. The reported saving factor was 3.6.
The advantage depended on the code and noise
The advantage was smaller when the stronger search had less room to improve the fast answer. In the [[72, 12, 6]] code, disagreement still separated outcomes with AUROC 0.831 and 0.839 at p = 0.006 and 0.008. But 20% routing produced rates of 0.0358 and 0.1140, only slightly above the full-sweep rates of 0.0350 and 0.1101; the fast-path rates were 0.0406 and 0.1339.
The ranking also appeared in a different code family. The cross-family test used a radial n = 90, k = 8 instance in a 12-round circuit-level Z-memory, with 20,000 test shots and 5,000 independent calibration shots at each of p = 0.008 and 0.009. Disagreement AUROC was 0.951 and 0.940, versus 0.832 and 0.809 for BP residual and 0.707 and 0.701 for syndrome weight. Routing the highest-disagreement 20% gave rates of 0.02275 and 0.05390 and recovered 93.9% and 86.6% of available improvement.
Hardware kept the warning signal, not the accuracy gain
The hardware check was more mixed. It used a full-CSS Z-memory with the [[12, 2, 2]] construction on 22 physical qubits over 12 rounds, producing 300 shots. OSD-0 failed on 83 of them, for a logical error rate of 0.277, with an interval of 0.229 to 0.330. Disagreement still ranked failures, with AUROC 0.853, compared with 0.886 in preflight simulation; the hardware interval was 0.804 to 0.897.
But the ranking did not translate into a net accuracy gain in that hardware test. The full search rescued three shots while turning three shots that had been correct into logical failures, leaving the logical error rate unchanged.
What the preprint establishes so far
The results separate two questions: whether disagreement can identify risky shots, and whether a deeper search can repair those shots. The first answer was strong in the primary simulation and remained positive on hardware; the second produced no net hardware improvement. The paper is an arXiv preprint, version 1, dated 29 September 2026, and reports results from the tested simulations and one hardware experiment.
Uncertainty estimates were calculated with nonparametric bootstrap 95% intervals using 800 resamples. Comparator routing used exact top-k budgets, while random routing was averaged over 200 seeds. The paper states that its decoding and analysis code and supporting data are available in the cited repository. It reports UK EPSRC funding through the SEAVEA project, Grant No. EP/W007711/1, and acknowledges Quantinuum access to the H2 processor.
Paper data and sources
Original title: Adaptive decoding of quantum LDPC codes through decoder disagreement
Authors: Maida Wang, Peter V. Coveney
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-09-29
DOI: Not available
Original paper · Full text