量子LDPC码的局部自主推理机
Local autonomous inference machines for quantum LDPC codes
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中文总结 AI 辅助
提出一种基于置信传播的局部自主推理框架，通过局部信念驱动缺陷移动配对湮灭，实现量子LDPC码的高效并行解码，并在环面码及双变量自行车码中验证阈值行为。
中文摘要 AI 辅助
我们提出了一种用于解码量子LDPC码的局部分布式框架。该架构基于置信传播（BP），将综合征信息的严格局部处理、局部反馈、自主操作以及高度并行化解码相结合。我们在两个互补层面建立该框架。首先，我们证明任何在迭代BP解码下具有阈值的码都可以被提升为自主的局部测量-反馈动力学，同时保持该阈值。然后，我们转向朴素BP本身不表现出阈值行为的码。我们的关键观察是，BP仍然可以提供足够准确的局部边缘信息：活跃的综合征缺陷利用这些局部信念通过异步反馈进行移动、配对和湮灭。我们通过数值演示表明，在二维和三维环面码的点状扇区中，该构造表现出阈值行为，而传统BP解码在这些扇区中失效。利用BP的图通用性，我们进一步研究了三维环面码膜状扇区以及一族双变量自行车量子LDPC码中的推理动力学。
英文摘要
We introduce a local and distributed framework for decoding quantum LDPC codes. Built atop belief propagation (BP), the architecture combines strictly local processing of syndrome information, local feedback, autonomous operation, and highly parallelized decoding. We establish the framework at two complementary levels. First, we show that any code exhibiting a threshold under iterative BP decoding can be promoted to an autonomous local measurement-and-feedback dynamics while preserving that threshold. We then turn to codes for which naive BP does not itself exhibit threshold behavior. Our key observation is that BP can nevertheless provide sufficiently accurate \emph{local} marginal information: active syndrome defects use these local beliefs to \emph{move}, pair, and annihilate through asynchronous feedback. We demonstrate numerically that this construction exhibits threshold behavior in the point-like sectors of the two- and three-dimensional toric codes, where conventional BP decoding fails. Exploiting the graph-generality of BP, we then study the inference dynamics on the membrane-like sector of the three-dimensional toric code and in a family of bivariate-bicycle quantum LDPC codes.
发表机构
- Princeton University（普林斯顿大学）
- École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。
