Towards surgery with good quantum LDPC codes

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 $k,d\in \Theta (n)$.

arXiv commentCritical error in the proof of Thm 4.5: a surjective chain map does not imply a surjective map between homology groups