任意维度下平移不变量子码的分类
A Classification of Translation-Invariant Quantum Codes in Any Dimension
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中文总结 AI 辅助
本文针对基于长度D链复形的D维平移不变量子码展开研究，证明其等价于D维环面码的复制，推广了二维平移不变量子码的分类结果。
中文摘要 AI 辅助
二维平移不变的量子纠错码已知等价于二维环面码的复制。由于存在多种类型的环面码以及无限族的分形子码，对于更高维平移不变的量子码，无法实现如此简单的分类。本文聚焦于基于长度为D的链复形的D维平移不变量子码，其中包含变量数等于循环数的多元多循环码。研究表明这类码等价于D维环面码的复制，直接推广了二维平移不变码的分类结果。
英文摘要
Quantum error-correcting codes with two-dimensional translation invariance are known to be equivalent to copies of the two-dimensional toric code. Such a simple classification is not possible for quantum codes with higher dimensional translation invariance due to the existence of multiple types of toric codes and infinite families of fracton codes. Here, we focus on D-dimensional translation-invariant quantum codes based on length-D chain complexes. This includes multivariate multicycle codes where the number of variables equals the number of cycles. We show that such codes are equivalent to copies of D-dimensional toric codes. This directly generalizes the classification result for two-dimensional translation-invariant codes.
