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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 or 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.

生成讲解博客的中文版本

生成AI智能校验的中文版本