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 demonstrate significant performance reduction in the Logical Error Rate (LER) over standard baselines, highlighting the advantage of hybrid decoders that combine the predictive capabilities of neural networks with the algorithmic structure of classical matching.

翻译：实现量子计算的全部潜力需要量子纠错（QEC）。QEC通过将逻辑信息编码到冗余的物理量子比特中来降低错误率，从而能够检测并纠正错误。用于此任务的常见解码器是最小权重完美匹配（MWPM），这是一种基于图的算法，依赖边权重来识别最可能的错误链。在本工作中，我们提出了一种名为神经最小权重完美匹配（NMWPM）的数据驱动解码器。我们的解码器采用混合架构，集成图神经网络（GNN）以提取局部校验子特征，并利用Transformer捕获长程全局依赖关系，进而用于预测MWPM解码器的动态边权重。为了通过不可微的MWPM算法进行训练，我们构建了一种新颖的代理损失函数，实现了端到端优化。我们的研究结果表明，在逻辑错误率（LER）方面，相比标准基线方法，性能显著降低，突显了将神经网络的预测能力与经典匹配算法结构相结合的混合解码器的优势。