Resgru, a lightweight recurrent neural decoder that maps time-ordered detection events to a binary logical-class prediction for each shot, is proposed, a lightweight recurrent neural decoder that maps time-ordered detection events to a binary logical-class prediction for each shot.
Abstract
Decoding is a central bottleneck in near-term quantum error correction (QEC), where repeated syndrome extraction must be translated into reliable logical outcomes under realistic noise and hardware constraints. We study heavy-hexagon (HH) quantum memory experiments and propose Resgru, a lightweight recurrent neural decoder that maps time-ordered detection events to a binary logical-class prediction for each shot. We benchmark Resgru against a standard minimum-weight perfect matching (MWPM) decoder instantiated on the same detector error model for HH code at code distances d∈{3,5,7} under circuit-level depolarizing noise with physical error rate p=0.1%. Resgru consistently achieved higher logical fidelity than MWPM decoder and yields lower per-round logical error rates, including a 28% reduction for d=5 and a 14% reduction for d=7. Despite being trained only on short sequences, Resgru maintains an advantage when evaluated on longer simulated memory experiments up to 300 QEC rounds.
Fault-tolerant quantum computing (FTQC) relies on quantum error correction to suppress physical errors and preserve logical information at scale. In practice, however, performance is constrained not only by physical noise but also by the latency of classical decoders processing rapidly generated syndrome data. This challenge is exacerbated by hardware noise that is strong, heterogeneous, and nonstationary, as well as by the simulation-to-hardware distribution shift that can substantially degrade fixed neural decoders. We present QAdapt, a noise-adaptive neural pre-decoding framework for surface-code quantum error correction. QAdapt captures local spatiotemporal correlations in syndrome data, sequentially adapts to evolving noise conditions while mitigating catastrophic forgetting, and forwards the residual syndrome to a conventional global decoder. Across 110 synthetic out-of-distribution noise configurations for rotated surface-code memory circuits, QAdapt consistently reduces the logical error rate relative to the neural pre-decoding baseline. On Google's Willow benchmark data, without target-domain fine-tuning, it achieves reductions of up to 5.79 percent in logical error rate and 9.32 percent in backend decoding latency on the residual syndrome. These results demonstrate that QAdapt provides a practical and decoder-compatible approach to improving the robustness and backend decoding efficiency of quantum error correction under evolving hardware noise.
Ran Miao, Rui Luo, Xiaohan Shan et al.· 0 citations
Real-time quantum error correction requires classical decoders to process growing syndrome workloads with low and predictable latency. For quantum low-density parity-check (qLDPC) codes, iterative belief propagation (BP) repeatedly updates messages over sparse Tanner graphs, creating substantial memory-access and data-movement demands. We map normalized Min-Sum BP decoding of the [[144,12,12]] Bivariate Bicycle qLDPC code onto a DPU-based Processing-in-Memory (PIM) architecture. Within each DPU, 11 tasklets cooperatively decode one syndrome, while multiple DPUs process independent syndrome instances in parallel. Using uPIMulator and a data-qubit Pauli error model with ideal syndrome measurements, we compare throughput, per-syndrome processing time, logical error rate (LER), and single-syndrome tail latency against a 16-logical-CPU baseline. At a component-wise physical error probability of p=0.001 and one BP iteration, the projected aggregate kernel throughput of 2,560 DPUs reaches 1.071 x 10^7 decodes/s, compared with 1.22 x 10^6 decodes/s for the CPU, an 8.8x improvement. From two iterations onward, the measured LER remains below the physical error probability for every evaluated value of p. For one to five iterations, the maximum sampled serialized X+Z DPU compute latency remains below the 1 ms decoder-side reference for trapped-ion QEC, reaching approximately 0.873 ms at five iterations. These results show that near-memory processing can provide high aggregate throughput and sub-millisecond compute latency for qLDPC BP decoding under the evaluated conditions.
Jeong-mae Seo, Youngsun Han, Leanghok Hour et al.· 0 citations
Quantum error correction can be enhanced by post-selecting out runs that are likely to produce a logical failure, but the most accurate measures for that require costly decoder-level information. We introduce a practical, decoder-agnostic post-selection method that learns directly from syndrome data. The method trains a supervised classifier to distinguish between syndromes from low- and high-noise regimes, and then uses the classifier's output as an abort score for new runs, without requiring logical-error labels, correction operators, or code-specific likelihood calculations. We validate the approach in three complementary settings: circuit-level simulations of the Gross bivariate-bicycle code, code-capacity simulations of the surface code, and experimental logical magic-state distillation data from the QuEra neutral-atom processor. In the Gross and surface codes, learned syndrome post-selection reduces the conditional logical error rate at a fixed acceptance rate, with performance comparable to syndrome-weight filtering. For the surface code, the learned classifier reveals a post-selection transition distinct from the conventional decoding threshold. In the experimental data, the machine-learning score outperforms syndrome-weight post-selection and, when combined with logical-gap filtering, improves the output fidelity beyond using the logical gap alone. These results show that syndrome-only learning provides a scalable and hardware-compatible route to improving the reliability of quantum error correction.
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 $d \in \{3,5,7,9,11\}$ 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 $4.6 \times 10^{5}$ 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.
Suppressing errors is the central challenge for useful large-scale quantum computing. While quantum error correction promises a viable solution to this challenge, existing codes typically suffer from trade-offs among encoding efficiency, error threshold, and hardware feasibility. Here, we introduce Cornucopia codes, a family of practical, hardware-efficient quantum low-density parity-check codes that achieve an ultra-high encoding rate exceeding $1/2$ while maintaining a pseudo-threshold exceeding $0.4\%$ under the standard circuit-level noise model. Inspired by recent affine-permutation-based code constructions and the long-range connectivity available in reconfigurable neutral-atom arrays, we adopt a structured code geometry in which the code layout, atom rearrangement, and syndrome-extraction schedule are co-designed. This structure enables nonlocal syndrome measurements through simple, parallel atom rearrangements. A complete syndrome extraction cycle measures all $X$- and $Z$-type checks in parallel with $12$ entangling layers, independent of the code size. The resulting threshold is comparable to those of the surface code and bivariate bicycle codes. In particular, a single code block $[[2844,1426,18]]$ encodes $1{,}426$ distance-$18$ logical qubits, achieving an extrapolated logical error rate of $2.6\times10^{-16}$ ($1.9\times10^{-31}$) per logical qubit per cycle, assuming the physical error rate of $0.1\%$ ($0.01\%$). By comparison, a bivariate bicycle code implementation would require more than $68{,}000$ physical qubits to encode the same number of logical qubits at a comparable logical error rate. These results bring demonstrations of ultra-low-overhead quantum error correction within the reach of near-term quantum processors.
Decoding is an essential component of quantum error correction (QEC), translating stabilizer measurement outcomes into corrective actions that suppress logical errors and preserve logical quantum information. Building fault-tolerant architectures requires increasing the code distance, which in turn places growing demands on decoding accuracy, scalability, and practical deployability. While a wide range of decoding algorithms have been proposed and demonstrated, achieving reliable, scalable, and real-time decoding remains a significant challenge. Machine-learning (ML) approaches are particularly well suited to this setting, as quantum error decoding is fundamentally a problem of processing large volumes of classical data with complex spatiotemporal correlations. This chapter surveys ML-based methods for quantum error decoding, with a focus on topological codes and an emphasis on architectural principles, practical performance, and real-time considerations. We first frame decoding as a learning problem and outline key paradigms, including discriminative, generative, and reinforcement-learning formulations. We then introduce the neural network building blocks that underpin most contemporary neural decoders and discuss how these components can be integrated to balance expressivity, scalability, and latency. Building on this architectural perspective, we review recent progress and benchmarks in neural decoding for memory experiments, and discuss real-time decoding, open challenges, and future directions toward scalable fault-tolerant quantum computing.
Changwon Lee, Tak Hur, Jeongwoo Jae et al.· 0 citations