Speculative window decoders hide quantum error-correction decoder latency by guessing the cross-boundary decisions that link adjacent decoding windows, running downstream work on the guess, and verifying lazily. SWIPER and ARTERY each build one predictor, about 90% accurate; neither built the verifier side. We build it on a reconstructed SWIPER harness (Stim rotated surface code, minimum-weight matching). A predictor-only bracket shows the cross-boundary decision is local, the achievable accuracy reaching about 0.999 within three rounds, with small, diffuse headroom over SWIPER. We establish a worst-case temporal blast-radius bound, its probability core machine-checked in Lean4 and conditional on a modeling reduction we then test: a misprediction's effect decays exponentially in the commit width, so the radius is one and speculation adds no error floor. We falsify that reduction shot by shot and find the real mechanism, clearest at near-threshold noise, is a global minimum-weight re-pairing. A compiler pass derives SWIPER's restart policy from these numbers; a runtime executor confirms on the harness that the loop recovers exactly and removes the serial commit-chain stall up to a small penalty. A second decoder (union-find) settles which results are decoder-agnostic: the predict-verify-recover wrapper and the structural phenomenology, while the absolute magnitudes and the min-weight mechanism are matching-specific.
Speculative window decoders hide quantum error-correction decoder latency by guessing the cross-boundary decisions that link adjacent decoding windows, running downstream work on the guess, and verifying lazily. SWIPER and ARTERY each build one predictor, about 90% accurate; neither built the verifier side. We build it on a reconstructed SWIPER harness (Stim rotated surface code, minimum-weight matching). A predictor-only bracket shows the cross-boundary decision is local, the achievable accuracy reaching about 0.999 within three rounds, with small, diffuse headroom over SWIPER. We establish a worst-case temporal blast-radius bound, its probability core machine-checked in Lean4 and conditional on a modeling reduction we then test: a misprediction's effect decays exponentially in the commit width, so the radius is one and speculation adds no error floor. We falsify that reduction shot by shot and find the real mechanism, clearest at near-threshold noise, is a global minimum-weight re-pairing. A compiler pass derives SWIPER's restart policy from these numbers; a runtime executor confirms on the harness that the loop recovers exactly and removes the serial commit-chain stall up to a small penalty. A second decoder (union-find) settles which results are decoder-agnostic: the predict-verify-recover wrapper and the structural phenomenology, while the absolute magnitudes and the min-weight mechanism are matching-specific.
Real-time decoding is a key ingredient in future fault-tolerant quantum systems, yet many decoders are too slow to run in real time.Prior work has shown that parallel window decoding can scalably meet throughput requirements in the presence of increasing decoding times.However, windowed decoding require that some decoding tasks be delayed until others have completed, which can be problematic during time-sensitive operations such as T gate teleportation, leading to suboptimal program runtimes.To alleviate this, we introduce SWIPER, a speculative window decoder.Taking inspiration from branch prediction in classical computer architecture, SWIPER utilizes a light-weight speculation step to predict data dependencies between adjacent decoding windows, allowing multiple layers of decoding tasks to be resolved simultaneously.Through a state-of-the-art compilation pipeline and a detailed open-source simulator, we find that SWIPER reduces application runtimes by 40% on average compared to prior parallel window decoders.
Real-time quantum error correction requires a classical decoder to consume syndrome measurements at the rate the quantum hardware produces them, roughly one round per microsecond on supercon-ducting devices. The standard stability requirement is a utilization condition: the mean decode time per round must be less than the round period, ρ < 1. We show that this condition is inadequate for windowed decoders whose per-window cost grows superlinearly in the number of detection events, which is the empirical shape of matching-based decoders under burst-like syndrome content. For this class, stability is not a threshold but a basin. The deterministic backlog dynamics have a stable operating point and an unstable boundary B∗. Noise erodes that boundary downward, and sufficiently superlinear decoders escape spontaneously. In discrete-event simulations paired under common random numbers, a decoder with cost exponent γ = 1.5 and mean utilization ρ0 = 0.6 (forty percent nominal headroom) fails without provocation, with a mean time to failure of 1,344 ± 289 rounds, about 1.3 ms of wall clock at a 1 μs cycle. These Poisson times are upper bounds: modulating the arrival rate at fixed mean load shortens them monotonically with the measured dispersion index of the arrivals, fourfold by D ≈ 3, and a dispersion excess of twelve percent already uncensors the ρ0 = 0.5 ensemble. We measure the cost exponent of a production decoder (PyMatching 2, sparse blossom) and find it anisotropic: near-linear (γ ≈ 1.1–1.2) when a window grows in length at fixed syndrome density, but approximately quadratic (γ ≈ 2) when the same window grows denser. Bursts travel along the dangerous axis, where the basin is 2–4 rounds deep for ρ0 between 0.5 and 0.8. Spatially clustered event content, the syndrome footprint of leakage and cosmic-ray bursts, is worse still: at matched event count, clustered windows cost 7.6× length-grown ones and 4.8× uniformly densified ones, so the quadratic density exponent is a conservative proxy for burst content. The anisotropy is a property of the matching class rather than of one implementation, since a second exact-MWPM decoder reproduces the density exponent, while a BP+OSD decoder is nearly event-independent: no basin, but orders of magnitude more cost per window. The basin is the price of event-adaptive decoding. Greedy catch-up (“decode everything queued”) is precisely the divergent policy. A bounded decoding window restores stability, and the measured stability edge lands on a closed-form line. The rule survives finite memory: under greedy service a queue cap acts as an implicit window, and a cap on the unstable side of the same line pins at the cap and sheds rounds indefinitely, so adding buffer memory makes the greedy policy strictly worse. The simulation model is cross-validated against Stim at the level of individual fault mechanisms.
Real-time quantum error correction requires a classical decoder to consume syndrome measurements at the rate the quantum hardware produces them, roughly one round per microsecond on superconducting devices. The standard stability requirement is a utilization condition: the mean decode time per round must be less than the round period, ρ < 1. We show that this condition is inadequate for windowed decoders whose per-window cost grows superlinearly in the number of detection events, which is the empirical shape of matching-based decoders under burst-like syndrome content. For this class, stability is not a threshold but a basin. The deterministic backlog dynamics have a stable operating point and an unstable boundary B∗. Noise erodes that boundary downward, and sufficiently superlinear decoders escape spontaneously. In discrete-event simulations paired under common random numbers, a decoder with cost exponent γ = 1.5 and mean utilization ρ0 = 0.6 (forty percent nominal headroom) fails without provocation, with a mean time to failure of 1,344 ± 289 rounds, about 1.3ms of wall clock at a 1µs cycle. We measure the cost exponent of a production decoder (PyMatching 2, sparse blossom) and find it anisotropic: near-linear (γ ≈ 1.1–1.2) when a window grows in length at fixed syndrome density, but approximately quadratic (γ ≈ 2) when the same window grows denser. Bursts travel along the dangerous axis, where the basin is 2–4 rounds deep for ρ0 between 0.5 and 0.8. Spatially clustered event content, the syndrome footprint of leakage and cosmic-ray bursts, is worse still: at matched event count, clustered windows cost 7.6× length-grown ones and 4.8× uniformly densified ones, so the quadratic density exponent is a conservative proxy for burst content. Greedy catch-up (“decode everything queued”) is precisely the divergent policy. A bounded decoding window restores stability, and the measured stability edge lands on a closed-form line. The simulation model is cross-validated against Stim at the level of individual fault mechanisms.
Real-time decoding is a major bottleneck in scaling quantum error correction (QEC) from noisy intermediate-scale quantum (NISQ) devices to fault-tolerant quantum computing. We present an adaptive confidence-gated decoding framework for the rotated surface code that treats decoding as a two-stage inference problem. A lightweight feed-forward neural network performs fast-path decoding for the majority of syndrome measurements, while only low-confidence predictions are escalated to a minimum-weight perfect matching (MWPM) refinement stage. We benchmark the framework on rotated surface codes with distances d∈{3,5,7,9,11} under circuit-level depolarising noise using the Stim stabiliser simulator. The evaluation characterises logical accuracy, confidence-controlled accuracy-latency trade-offs, decoding throughput, per-shot latency, and decoding-graph resource scaling. Routing only 3.3%-6.2% of syndromes to the refinement stage improves logical accuracy from 99.21% for the neural-only baseline to 99.81% at a confidence threshold of 0.95 while incurring only a bounded increase in average decoding cost. Neural-decoder throughput saturates near 4.6×105 samples s−1 at batch size 512 on commodity CPU hardware, indicating that the neural fast path is not the dominant throughput bottleneck beyond code distance d=7. We release the complete benchmarking pipeline, trained models, raw benchmark data, and source code, and explicitly distinguish the experimentally validated contributions from the broader hardware-aware QEC co-design roadmap, including hardware-constrained code discovery, GPU-accelerated inference, and multi-noise optimisation, which remain directions for future work.
This registration describes a preregistered confirmatory study of heterogeneous pre-decoder conditioning in a rotated surface-code quantum error-correction workflow. Its purpose is to test whether, at a fixed total conditioning budget, heterogeneously distributed upstream conditioning produces lower logical error than budget-matched uniform conditioning, whether a single frozen conditioned representation remains effective across an architecture-diverse downstream decoder set, and whether performance varies nontrivially across a preregistered ordered target:non-target ratio grid. The study is conducted under frozen distances, frozen operating points, frozen seed and shot schedules, preregistered pooled metrics, and locked success criteria so that any supported effect can be interpreted as evidence about the architecture under test rather than post hoc tuning. The design contains four preregistered arms: untreated control, budget-matched uniform conditioning, budget-matched differential conditioning, and an ordered ratio-sweep arm with fixed total burden. A central feature of the protocol is that the conditioned representation is formed once upstream and then passed unchanged to each confirmatory decoder family, with no decoder-specific retuning, remapping, or auxiliary adaptation permitted after formation. The minimum confirmatory decoder set is minimum-weight perfect matching, Union-Find, and BP+OSD, selected to evaluate transfer across structurally different decoder families. Expected outcomes are defined in confirmatory terms. The primary pooled causal endpoint tests whether budget-matched differential conditioning outperforms budget-matched uniform conditioning, while the primary pooled transfer endpoint tests whether the same frozen conditioned representation improves performance relative to untreated control across decoder families. Additional preregistered questions address tunability through the ordered ratio response and persistence of favorable pooled effects across more than one primary code distance. A strong confirmatory outcome requires favorable pooled results with two-sided 95% bootstrap confidence intervals excluding 1 in the favorable direction, plus distance persistence at two or more primary distances; mixed, null, and thesis-changing outcomes are also explicitly predefined. This registration is limited to architecture-level evaluation and reproducible public inference. It does not claim that the frozen partition rule is uniquely optimal, that any specific targeting heuristic is the sole source of benefit, that threshold or asymptotic scaling is established, or that the exact coupling law, score function, or targeting recipe is disclosed. The confirmatory claim is bounded to whether budget-matched heterogeneous upstream conditioning improves logical performance and transfers across decoder families when the upstream representation is held fixed.
A quantum error correction decoder is a library other people's results depend on, judged in one dominant way. Sample errors, decode, and count wrong logical observables. We ask what else can be checked there. Our conformance contract needs no oracle. One check asks that a returned correction explain the syndrome in the caller's index space. The other hands a decoder one instance under two presentations differing only in bookkeeping, where two feasible corrections of different weight prove the heavier is not minimum-weight. Verdicts are gated on what each library declares, so a firing contradicts a published guarantee. Nine configurations from five public libraries give three results. Documentation answers 4 of 54 capability questions. Bounded-distance correctness, the property callers most depend on, has a direct declaration yield of 0.0%, though its hypotheses hold in 62.1% of cases. Presentation sensitivity is real but shallow. One solver moved to a 26% heavier correction under a different numbering, which reaches the logical class at most once in twenty thousand shots. Established evaluation misses corruptions that preserve logical parity, while one summation over the caller's weights catches every one we injected. All 639 certificates ship as bundles a standalone verifier re-derives from first principles.