发表机构
Technical University of Munich; Munich Center for Quantum Science and Technology; University of Cambridge; Universität Tübingen（慕尼黑工业大学; 慕尼黑量子科学与技术中心; 剑桥大学; 蒂宾根大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究严格证明了Haah三维立方码在任意正温度下快速热化，否定了其作为自校正量子记忆的候选资格，并首次给出分形码快速混合的解析证明。
AI 中文摘要
Haah的三维立方码最初被提出作为三维中自校正量子记忆的候选方案，其利用不存在弦状逻辑算子的特性来阻碍热致错误。它是否是一种自校正量子记忆一直是一个长期悬而未决的问题。尽管记忆时间已被数值探索，但此前没有任何解析上界。在此，我们严格地解决了这一问题，并证明立方码在任意正温度下都会快速热化。我们的证明依赖于[Commun. Math. Phys. 407, 195 (2026)]中的框架，将关联衰减条件转化为针对Davies生成元的修正对数Sobolev不等式。据我们所知，这是首次针对任意分形码在所有正温度下快速混合的解析证明。
英文摘要
Haah's 3D cubic code was introduced as a candidate for a self-correcting quantum memory in three dimensions, using the absence of string logical operators to obstruct thermal errors. It has been a long-standing open question whether it is a self-correcting quantum memory. Even though the memory time was explored numerically, no analytical upper bound was known. Here, we settle this question rigorously and show that the cubic code thermalizes rapidly at every positive temperature. Our proof relies on the framework of [Commun. Math. Phys. 407, 195 (2026)] to turn a decay-of-correlations condition into a modified logarithmic Sobolev inequality for the Davies generator. To the best of our knowledge, this is the first analytic proof of rapid mixing for all positive temperatures for any fracton code.
Comments28 pages, 11 figures
