We define code maps between Calderbank-Shor-Steane (CSS) codes using maps between chain complexes, and describe code surgery between such codes using a specific colimit in the category of chain complexes. As well as describing a surgery operation, this gives a general recipe for new codes. As an application we describe how to `merge' and `split' along a shared $\overline{X}$ or $\overline{Z}$ operator between arbitrary CSS codes in a fault-tolerant manner, so long as certain technical conditions concerning gauge fixing and code distance are satisfied. We prove that such merges and splits on LDPC codes yield codes which are themselves LDPC.

中文翻译：

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CSS 代码手术作为通用构造

我们使用链复合体之间的映射来定义 Calderbank-Shor-Steane (CSS) 代码之间的代码映射，并使用链复合体类别中的特定 colimit 来描述此类代码之间的代码手术。除了描述外科手术之外，这还提供了新代码的一般配方。作为一个应用程序，我们描述了如何在任意 CSS 代码之间以容错的方式沿着共享的 $\overline{X}$ 或 $\overline{Z}$ 运算符“合并”和“拆分”，只要满足某些技术条件关于量规固定和码距的要求均得到满足。我们证明了 LDPC 码上的这种合并和分裂产生的代码本身就是 LDPC。