Fast and accurate neural triage decoding of ultra-high-rate quantum LDPC codes

Hong-Ye Hu; Zhenlai Wang; Binzhao Luo; Tao Xiang; Chen Zhao

quant-phOct 29, 2026

Fast and accurate neural triage decoding of ultra-high-rate quantum LDPC codes

Authors: Hong-Ye Hu, Zhenlai Wang, Binzhao Luo, Tao Xiang, Chen Zhao

Organizations: Institute of Physics, Chinese Academy of Sciences, Beijing 100910, China · School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China · School of Mathematical Sciences, Eastern Institute of Technology, Ningbo, Zhejiang 315200, China

Abstract

Quantum error correction is essential for fault-tolerant quantum computing. High-rate quantum low-density parity-check (qLDPC) codes have emerged as a promising approach to reducing the substantial physical qubit overhead of quantum error correction, enabling encoding rates exceeding $1/2$ in blocks of approximately one thousand physical data qubits. However, their practical implementation requires decoders that combine high accuracy with low latency to keep pace with quantum hardware. Existing decoders of high-rate qLDPC codes can achieve high accuracy but often incur substantial computational latency, whereas neural network decoders have yet to be demonstrated for high-rate qLDPC codes. Here, we introduce neural triage decoding, a framework that uses syndrome consistency to adaptively allocate neural computation. A local neural message-passing network rapidly predicts error corrections, additional iterations reduce residual syndrome violations, and a rarely invoked diversification stage searches for consistent corrections to the remaining shots. We demonstrate that the Triage decoder can decode ultra-high-rate qLDPC codes encoding a few hundred logical qubits, including lifted-product and Kasai codes, achieving state-of-the-art accuracy comparable to the near optimal algorithmic decoders while reducing decoding latency by approximately one to two orders of magnitude. Our framework is inspired by a rigorous analysis of the exact bitwise marginal decoder, revealing a distance-independent syndrome-inconsistent error floor. In addition, we show the robustness of neural network decoders to mismatched error priors. Our results establish adaptive neural decoding as a promising route towards fast, accurate, and scalable quantum error correction in the near term.

Figures & tables

Figure 1: Neural triage decoding for high-rate quantum LDPC codes. ( a ) The Triage decoder combines a fast NeuralMP local decoder with iterative decoding strategy. For rare cases when proposed errors cannot resolve all syndrome, it enters diversification stage. The Triage decoder allocate computation resources adaptively to achieve high accuracy, high speed and being versatile simultaneously. ( b ) NeuralMP performs $R$ internal MP-rounds per evaluation. Then iterative decoding repeatedly applies the network to the residual syndrome for up to $K$ outer iterations. Remaining shots enter diversification stage, which uses prior perturbations, symmetric permutations and syndrome flips to explore alternative correction trajectories with the same trained network. ( c ) High-rate qLDPC codes are represented by data qubits (red circles), $X$ checks (blue squares) and $Z$ checks (green diamonds). Under the phenomenological error model, data qubits experience Pauli $X$ , $Y$ or $Z$ errors each per measurement round for multiple measurement rounds, while measurement outcomes are flipped with probability $p_{\mathrm{m}}$ . ( d ) Schematic comparison of decoding latency and logical error rate for neural and algorithmic decoders. Logical error rates are expressed on a per-qubit-per-round basis; the arrow indicates the desired direction of improvement.

Figure 2: NeuralMP architecture, failure-aware training and residual-syndrome scaling. ( a ) The Tanner graph of the DEM connects fault mechanisms (red circles) to detectors (blue squares) through

H_{vf}=1

. Red colored bars represent node states encoding mechanism priors together with positions embedding and blue colored bars represent detector outcomes embedding. ( b ) Each MP-round first updates fault states using neighbouring detector states, then updates detector states using the updated fault states. Aggregated messages enter residual multilayer perceptrons (MLPs) with layer normalization. After

R

MP-rounds, a linear readout followed by a sigmoid produces one marginal estimate per mechanism. ( c ) Training combines fresh online simulations, including error-weight-conditioned samples, with symmetry-augmented replay from an evolving mistake bank. Logical failures enter the bank, while repeatedly corrected examples are removed. The joint objective supervises fault predictions, logical observables and syndrome consistency. ( d ) Probability of a nonzero residual syndrome after a single pass of NeuralMP versus physical error rate

p

for the LP20 and Kasai codes. Orange dashed lines indicate

p^{4}=p^{w_{\min}/2}

reference scaling with

w_{\min}

as minimal weight of space-time degeneracy. Pale blue and pale red regions highlight regimes dominated by low-weight and high-weight errors, respectively. Error bars show 95% confidence intervals.

Figure 3: Decoding accuracy and amortized latency on LP20 and Kasai codes. ( a ) Logical error rate (LER) per-qubit-per-round versus physical error rate $p$ , using approximately $0.04$ – $40.96$ million shots per point for LP20 code and $0.24$ – $20.48$ million for Kasai code. Error bars quantify finite-sampling uncertainty using 95% Clopper–Pearson intervals. ( b ) Amortized decoding latency. We benchmark the latency using NVIDIA H200 GPU. NeuralMP ( Triage ’s frontend) reports the asymptotic frontend cost, whereas Triage shows the composed full-decoder cost at batch size 64, including handoff and diversification. CPU baseline timing uses 1,000–5,000 shots per point. Timing error bars, where shown, are 95% bootstrap confidence intervals from 2,000 resamples and indicate uncertainty in the estimated mean latency. CPU baselines use one thread, except the eight-thread COPT stage [ 26 ] .

Figure 4: Robustness to mismatched error priors. Block-LER ratio relative to correctly specified priors versus nominal mismatch strength $\sigma_{r}$ for ( a ) LP20 code at $p=0.024$ , and ( b ) Kasai code at $p=0.0175$ . NeuralMP uses four decoding iterations. Each prior realization is evaluated on $9\times 10^{5}$ shots for LP20 code and $6\times 10^{5}$ shots for Kasai code, sharing the same noise samples with the matched-prior baseline. Two prior realizations are used per $\sigma_{r}$ , except LP20 at $\sigma_{r}=0.1$ and $0.3$ , which use four. Markers show geometric means of the per-realization LER ratios. Error bars span the per-realization ratio intervals obtained by transforming conditional 95% Clopper–Pearson intervals.

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Rethink the Role of Neural Decoders in Quantum Error Correction

Ge Yan, Shanchuan Li, Yuxuan Du

College of Computing and Data Science, Nanyang Technological University, Singapore 639798, Singapore · Department of Electrical Engineering and Computer Science, Tokyo University of Agriculture & Technology, Koganei, Tokyo, 184-8588, Japan · School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798, Singapore

Neural Decoding Quantum Error Correction Quantum Error Correction Decoding

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Quantum error correction (QEC) is essential for enabling quantum advantages, with decoding as a central algorithmic primitive. Owing to its importance and intrinsic difficulty, substantial effort has been made to QEC decoder design, among which neural decoders have recently emerged as a promising data-driven paradigm. Despite this progress, practical deployment remains hindered by a fundamental accuracy-latency tradeoff, often on the microsecond timescale. To address this challenge, here we revisit neural decoders for surface-code decoding under explicit accuracy-latency constraints, considering code distances up to d=9 (161 physical qubits). We unify and redesign representative neural decoders into five architectural paradigms and develop an end-to-end compression pipeline to evaluate their deployability and performance on FPGA hardware. Through systematic experiments, we reveal several previously underexplored insights: (i) near-term decoding performance is driven more by data scale than architectural complexity; (ii) appropriate inductive bias is essential for achieving high decoding accuracy; and (iii) INT4 quantization is a prerequisite for meeting microsecond-scale latency requirements on FPGAs. Together, these findings provide concrete guidance toward scalable and real-time neural QEC decoding.

Abstract

Quantum Error Correction Decoding

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