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Paper 1

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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Paper 2

Subsystem many-hypercube codes: High-rate concatenated codes with low-weight syndrome measurements

Ryota Nakai, Hayato Goto

Year

2025

Journal

arXiv preprint

DOI

arXiv:2510.04526

arXiv

2510.04526

Quantum error-correcting codes (QECCs) require high encoding rate in addition to high threshold unless a sufficiently large number of physical qubits are available. The many-hypercube (MHC) codes defined as the concatenation of the [[6,4,2]] quantum error-detecting code have been proposed as high-performance and high-encoding-rate QECCs. However, the concatenated codes have a disadvantage that the syndrome weight grows exponentially with respect to the concatenation level. To address this issue, here we propose subsystem quantum codes based on the MHC codes. In particular, we study the smallest subsystem MHC codes, namely, subsystem codes derived from the concatenated [[4,2,2]] error-detecting codes. The resulting codes have a constant syndrome-measurement weight of 4, while keeping high encoding rates. We build the block-MAP and neural-network decoders and show that they demonstrate superior performance to the bounded-distance decoder.

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