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∈Θ(n).
Cite
@article{arxiv.2309.16406,
title = {Towards surgery with good quantum LDPC codes},
author = {Alexander Cowtan},
journal= {arXiv preprint arXiv:2309.16406},
year = {2024}
}
Comments
Critical error in the proof of Thm 4.5: a surjective chain map does not imply a surjective map between homology groups