低密度奇偶校验（LDPC）码玻璃态景观中的稳定谷
Stable valleys in the glassy landscape of a low-density parity-check (LDPC) code
浏览论文内容
中文总结 AI 辅助
研究低密度奇偶校验码在玻璃态景观中的稳定谷，借助局部树状扩展图的cLDPC码案例，用树上递归技术及数值研究，揭示其稳定谷特性及微正则与正则系综不等价性。
中文摘要 AI 辅助
定义在扩展图上的经典低密度奇偶校验（cLDPC）码是构建良好量子LDPC码的基本要素，这是量子纠错的一个近期里程碑。它们本身也定义了有趣的统计力学模型。通过对局部树状扩展图上的cLDPC码进行案例研究来展开调查。利用局部树状特性实现的树上递归技术，探测了在低温下施加不同边界条件所诱导的一系列稳定且不一致的谷。对封闭有限图上谷的补充数值研究揭示了某些谷的微正则系综和正则系综的不等价性。
英文摘要
Classical low-density parity-check (cLDPC) codes defined on expander graphs are a fundamental ingredient in the construction of good quantum LDPC codes, a recent milestone in quantum error correction. They also define interesting statistical mechanics models in their own right, as they include examples of spin glass order without quenched randomness or frustration. We investigate this via a case study of a cLDPC code on a locally tree-like expander graph. Recursive techniques on trees, made possible by the locally tree-like property, probe a menagerie of stable, incongruent valleys induced by imposing different boundary conditions at low temperature. Analysis of stable and unstable fixed points within the cavity method, complemented by a numerical study of the valleys on closed finite graphs, reveals the inequivalence of the microcanonical and canonical ensemble for certain valleys.
发表机构
- Princeton University（普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。
