arXiv:2510.06257v3 Announce Type: replace-cross Abstract: 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 QEC codes. To address this gap, we propose a Quantum Bayesian graph Attention decoder \textbf{(QuBA)} that enables expressive error-pattern recognition alongside calibrated uncertainty estimates. Building on QuBA, we further develop a multi-phase training framework with enhanced cross-domain robustness enabling decoding beyond the training set called Sequential Aggregate Generalization under Uncertainty \textbf{(SAGU)}. Experiments on bivariate bicycle (BB) codes and their coprime variants demonstrate that (i)QuBA consistently outperforms the classical baseline belief propagation (BP), achieving up to a \emph{two orders of magnitude} reduction in logical error rate (LER) under confident-decision bounds on the coprime BB code $[[154,6,16]]$; (ii) SAGU achieves decoding performance comparable to or even outperforming QuBA's domain-specific training approach.