CSS code surgery as a universal construction

• URL: http://arxiv.org/abs/2301.13738v6
• Date: Tue, 7 May 2024 09:50:06 GMT
• Title: CSS code surgery as a universal construction
• Authors: Alexander Cowtan, Simon Burton,
• Abstract summary: We define code maps between Calderbank-Shor-Steane (CSS) codes using maps between chain complexes. We describe code surgery between such codes using a specific colimit in the category of chain complexes.
• Score: 51.63482609748332
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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