用超图神经网络提升量子纠错码解码性能
HyperNQ: A Hypergraph Neural Network Decoder for Quantum LDPC Codes
- 引入超边捕捉更高阶稳定子约束，突破传统图模型限制
- 在伪阈值以下逻辑错误率比BP降低84%，比GNN提升50%
- 适合研究量子纠错与机器学习融合的学者
量子计算需要有效的错误纠正策略来缓解噪声和退相干问题。量子低密度奇偶校验（QLDPC）码因其支持恒定编码率和稀疏奇偶校验结构，成为可扩展量子误差纠正（QEC）应用的有前途方案。然而，传统的贝叶斯传播（BP）等解码方法在存在短环时收敛性差。基于图神经网络（GNN）的机器学习方法虽利用节点特征上的学习消息传递，但受限于塔纳图上的成对交互，难以捕捉高阶相关性。本文提出首个基于超图神经网络（HGNN）的QLDPC解码器HyperNQ，通过超边捕获更高阶稳定子约束，实现高度表达且紧凑的解码。采用两阶段消息传递机制，在伪阈值区域进行评估。低于伪阈值时，HyperNQ将逻辑错误率（LER）相比BP降低最高达84%，相比基于GNN的策略提升50%，展现出对现有最先进解码器的显著性能优势。
原文摘要 · Abstract (English)
Quantum computing requires effective error correction strategies to mitigate noise and decoherence. Quantum Low-Density Parity-Check (QLDPC) codes have emerged as a promising solution for scalable Quantum Error Correction (QEC) applications by supporting constant-rate encoding and a sparse parity-check structure. However, decoding QLDPC codes via traditional approaches such as Belief Propagation (BP) suffers from poor convergence in the presence of short cycles. Machine learning techniques like Graph Neural Networks (GNNs) utilize learned message passing over their node features; however, they are restricted to pairwise interactions on Tanner graphs, which limits their ability to capture higher-order correlations. In this work, we propose HyperNQ, the first Hypergraph Neural Network (HGNN)- based QLDPC decoder that captures higher-order stabilizer constraints by utilizing hyperedges-thus enabling highly expressive and compact decoding. We use a two-stage message passing scheme and evaluate the decoder over the pseudo-threshold region. Below the pseudo-threshold mark, HyperNQ improves the Logical Error Rate (LER) up to 84% over BP and 50% over GNN-based strategies, demonstrating enhanced performance over the existing state-of-the-art decoders.
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