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Paper 1

Analytical Theory of Greedy Peeling for Bivariate Bicycle Codes and Two-Shot Streaming Decoding

Anton Pakhunov

Year

2026

Journal

arXiv preprint

DOI

arXiv:2604.11352

arXiv

2604.11352

We present an analytical theory of greedy peeling decoding for bivariate bicycle (BB) codes under circuit-level noise. The deferred greedy decoder achieves 330x latency reduction over belief propagation (BP) at p = 10^{-3} while maintaining identical logical error rate. Our main theoretical contribution is a closed-form collision resolution factor A_0 = |true collisions| / |birthday collisions|, derived from XOR syndrome analysis with no free parameters, that quantifies the fraction of detector-sharing fault pairs genuinely blocking iterative peeling. For the [[144,12,12]] Gross code, A_0 = 0.8685 (within 0.5% of the empirical value), with shared-2 pairs (4-cycles) always resolving under peeling. We show A_0 depends on the mean fault-graph degree d-bar rather than code size: A_0 = 0.87 for d-bar = 52 (Gross family) versus A_0 = 0.76 for d-bar = 17 ([[32,8,6]]). We establish a syndrome code stopping distance d_S = n/4.5 for the Gross family and demonstrate that [[32,8,6]] (d_S = 4) enables two-shot streaming decoding: T = 2 rounds achieve 89% peeling success with 1.29 +/- 0.03 LER ratio versus T = 12, at estimated latency ~50 ns. The full formula P_peel = exp(-A_0 * gamma_analytic * exp(-BTp) * n * p^2) is validated across five BB codes, four noise levels, and four values of T with R^2 = 0.86. Cross-platform reproduction of the Kunlun [[18,4,4]] experiment matches their hardware LER within 0.73 percentage points.

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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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