Distance bounds for generalized bicycle codes [article]

Renyu Wang, Leonid P. Pryadko
2022 arXiv   pre-print
Generalized bicycle (GB) codes is a class of quantum error-correcting codes constructed from a pair of binary circulant matrices. Unlike for other simple quantum code ansätze, unrestricted GB codes may have linear distance scaling. In addition, low-density parity-check GB codes have a naturally overcomplete set of low-weight stabilizer generators, which is expected to improve their performance in the presence of syndrome measurement errors. For such GB codes with a given maximum generator
more » ... w, we constructed upper distance bounds by mapping them to codes local in D≤ w-1 dimensions, and lower existence bounds which give d≥ O(n^1/2). We have also done an exhaustive enumeration of GB codes for certain prime circulant sizes in a family of two-qubit encoding codes with row weights 4, 6, and 8; the observed distance scaling is consistent with A(w)n^1/2+B(w), where n is the code length and A(w) is increasing with w.
arXiv:2203.17216v1 fatcat:q6elh3qmizhv3lctb5zu5ol3dm