标题： 线性规划解码器在量子LDPC码中的性能与局限性 显示英文标题

标题： Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

摘要： 解码量子纠错码是实现容错量子计算的关键挑战。 在经典情况下，线性规划（LP）解码器提供可证明的性能保证，并可以利用快速的实际优化算法。 尽管已经提出了用于量子码的LP解码器，但它们的性能和限制仍然相对未被深入研究。 在本工作中，我们揭示了量子低密度奇偶校验（LDPC）码LP解码的一个关键限制：某些固定重量的错误模式会导致无法通过独立舍入解决的模糊分数解。 为了解决这个问题，我们引入了一种称为有序统计解码（OSD）的后处理技术，这在实践中显著提高了LP解码的性能。 我们的结果表明，当与OSD结合时，LP解码在最多数百个量子比特的中等码长下，可以优于具有相同后处理的置信传播。 这些发现表明，配备有效后处理的基于LP的解码器，为解码近期量子LDPC码提供了一个有前景的方法。 显示英文摘要

摘要： Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.