用神经网络动态调整量子纠错匹配权重，提升纠错性能。
Neural Minimum Weight Perfect Matching for Quantum Error Codes
- 融合图神经网络与Transformer，捕捉局部和全局错误特征
- 在去极化噪声下达到17.9%纠错阈值，接近最优极限18.9%
- 适合研究量子纠错码、神经网络与经典算法结合方向的读者
实现量子计算潜力需依赖量子误差纠正（QEC）。QEC通过冗余物理量子比特编码逻辑信息，使错误可被检测与修正。常用解码器为最小权重完美匹配（MWPM），一种基于边权重识别最可能错误链的图算法。本文提出数据驱动解码器神经最小权重完美匹配（NMWPM），采用混合架构：图神经网络提取局部校验特征，Transformer捕捉长程全局依赖，进而预测MWPM的动态边权重。为克服非可微的MWPM带来的训练难题，设计新型代理损失函数，实现端到端优化。在去极化噪声下的环面码实验表明，纠错阈值达17.9%与10.95%，接近最大似然上限18.9%与11.0%，凸显结合神经网络预测能力与经典匹配结构的混合解码优势。
原文摘要 · Abstract (English)
Realizing the full potential of quantum computation requires Quantum Error Correction (QEC). QEC reduces error rates by encoding logical information across redundant physical qubits, enabling errors to be detected and corrected. A common decoder used for this task is Minimum Weight Perfect Matching (MWPM) a graph-based algorithm that relies on edge weights to identify the most likely error chains. In this work, we propose a data-driven decoder named Neural Minimum Weight Perfect Matching (NMWPM). Our decoder utilizes a hybrid architecture that integrates Graph Neural Networks (GNNs) to extract local syndrome features and Transformers to capture long-range global dependencies, which are then used to predict dynamic edge weights for the MWPM decoder. To facilitate training through the non-differentiable MWPM algorithm, we formulate a novel proxy loss function that enables end-to-end optimization. Our findings on the toric code under depolarizing noise demonstrate thresholds of 17.9% and 10.95%, nearing the 18.9% and 11.0% maximum likelihood bounds, highlighting the advantage of hybrid decoders that combine the predictive capabilities of neural networks with the algorithmic structure of classical matching.
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