Quantum error correction (QEC) is essential for scalable quantum computing, yet decoding errors via conventional algorithms result in limited accuracy (i.e., suppression of logical errors) and high overheads, both of which can be alleviated by inference-based decoders. To date, such machine-learning (ML) decoders lack two key properties crucial for practical fault tolerance: reliable uncertainty quantification and robust generalization to previously unseen codes. To address this gap, we propose \textbf{QuBA}, a Bayesian graph neural decoder that integrates attention to both dot-product and multi-head, enabling expressive error-pattern recognition alongside calibrated uncertainty estimates. Building on QuBA, we further develop \textbf{SAGU }\textbf{(Sequential Aggregate Generalization under Uncertainty)}, a multi-code training framework with enhanced cross-domain robustness enabling decoding beyond the training set. Experiments on bivariate bicycle (BB) codes and their coprime variants demonstrate that (i) both QuBA and SAGU consistently outperform the classical baseline belief propagation (BP), achieving a reduction of on average \emph{one order of magnitude} in logical error rate (LER), and up to \emph{two orders of magnitude} under confident-decision bounds on the coprime BB code $[[154, 6, 16]]$; (ii) QuBA also surpasses state-of-the-art neural decoders, providing an advantage of roughly \emph{one order of magnitude} (e.g., for the larger BB code $[[756, 16, \leq34]]$) even when considering conservative (safe) decision bounds; (iii) SAGU achieves decoding performance comparable to or even outperforming QuBA's domain-specific training approach.

翻译：量子纠错（QEC）是实现可扩展量子计算的关键，然而传统解码算法在解码错误时存在精度有限（即逻辑错误抑制不足）和开销高昂的问题，这两者均可通过基于推断的解码器得到缓解。迄今为止，此类机器学习（ML）解码器缺乏对实际容错至关重要的两个关键特性：可靠的不确定性量化以及对未见编码的鲁棒泛化能力。为弥补这一差距，我们提出了 **QuBA**，一种贝叶斯图神经解码器，它整合了对点积与多头注意力的关注，从而在提供校准的不确定性估计的同时实现富有表达力的错误模式识别。基于QuBA，我们进一步开发了 **SAGU**（**不确定性下的序列聚合泛化**），这是一个具有增强跨域鲁棒性的多码训练框架，能够对训练集之外的编码进行解码。在双变量自行车（BB）码及其互质变体上的实验表明：（i）QuBA与SAGU均持续超越经典基线置信传播（BP）算法，在逻辑错误率（LER）上平均实现了 **一个数量级** 的降低，并在互质BB码 $[[154, 6, 16]]$ 的置信决策边界下最高达到 **两个数量级** 的降低；（ii）QuBA也超越了最先进的神经解码器，即使在考虑保守（安全）决策边界时，仍能提供约 **一个数量级** 的优势（例如，对于更大的BB码 $[[756, 16, \leq34]]$）；（iii）SAGU实现的解码性能与QuBA的领域特定训练方法相当，甚至在某些情况下更优。