Papers › Distance bounds for generalized bicycle codes
Distance bounds for generalized bicycle codes
Renyu Wang, Leonid P. Pryadko
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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 ans\"atze, 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 weight 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.
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