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Paper 1

Belief Propagation Convergence Prediction for Bivariate Bicycle Quantum Error Correction Codes

Anton Pakhunov

Year

2026

Journal

arXiv preprint

DOI

arXiv:2604.07995

arXiv

2604.07995

Decoding Bivariate Bicycle (BB) quantum error correction codes typically requires Belief Propagation (BP) followed by Ordered Statistics Decoding (OSD) post-processing when BP fails to converge. Whether BP will converge on a given syndrome is currently determined only after running BP to completion. We show that convergence can be predicted in advance by a single modulo operation: if the syndrome defect count is divisible by the code's column weight w, BP converges with high probability (100% at p <= 0.001, degrading to 87% at p = 0.01); otherwise, BP fails with probability >= 90%. The mechanism is structural: each physical data error activates exactly w stabilizers, so a defect count not divisible by w implies the presence of measurement errors outside BP's model space. Validated on five BB codes with column weights w = 2, 3, and 4, mod-w achieves AUC = 0.995 as a convergence classifier at p = 0.001 under phenomenological noise, dominating all other syndrome features (next best: AUC = 0.52). The false positive rate scales empirically as O(p^2.05) (R^2 = 0.98), confirming the analytical bound from Proposition 2. Among BP failures on mod-w = 0 syndromes, 82% contain weight-2 data error clusters, directly confirming the dominant failure mechanism. The prediction is invariant under BP scheduling strategy and decoder variant, including Relay-BP - the strongest known BP enhancement for quantum LDPC codes. These results apply directly to IBM's Gross code [[144, 12, 12]] and Two-Gross code [[288, 12, 18]], targeted for deployment in 2026-2028.

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Paper 2

Toward Uncertainty-Aware and Generalizable Neural Decoding for Quantum LDPC Codes

Xiangjun Mi, Frank Mueller

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.06257

arXiv

2510.06257

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.

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