Towards surgery with good quantum LDPC codes

TL;DR

This paper explores the use of good quantum LDPC codes for quantum surgery, demonstrating conditions under which surgery can be performed with minimal or no asymptotic penalty on code parameters.

Contribution

It shows that quantum LDPC codes can be used for surgery with or without asymptotic penalties, advancing the understanding of their practical applicability.

Findings

Surgery with any logical qubits is possible but incurs an asymptotic penalty.

Three of four conditions for penalty-free surgery can be satisfied.

All conditions met, code parameters remain linear in code length.

Abstract

We show that the good quantum LDPC codes of Panteleev-Kalachev \cite{PK} allow for surgery using any logical qubits, albeit incurring an asymptotic penalty which lowers the rate and distance scaling. We also prove that we can satisfy 3 of the 4 conditions for performing surgery \textit{without} incurring an asymptotic penalty. If the last condition is also satisfied then we can perform code surgery while maintaining $k, d\in \Theta(n)$.