Distance bounds for generalized bicycle codes

• URL: http://arxiv.org/abs/2203.17216v1
• Date: Thu, 31 Mar 2022 17:43:34 GMT
• Title: Distance bounds for generalized bicycle codes
• Abstract summary: Generalized bicycle (GB) codes is a class of quantum error-correcting codes constructed from a pair of binary circulant matrices. We have 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 $A(w)n1/2+B(w)$, where $n$ is the code length and $A(w)$ is increasing with $w$.
• Score: 0.7513100214864644
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: 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 $D\le w-1$ dimensions, and lower existence bounds which give $d\ge {\cal O}({n}^{1/2})$. 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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