论文标题
广义自行车代码的距离界限
Distance bounds for generalized bicycle codes
论文作者
论文摘要
广义自行车（GB）代码是由一对二进制循环矩阵构建的一类量子误差校正代码。与其他简单的量子代码Ansätze不同，无限制的GB代码可能具有线性距离缩放。此外，低密度奇偶校验检查GB代码具有自然过度的低重量稳定器发电机，该集有望在存在综合征测量误差的情况下提高其性能。对于具有给定最大发电机重量$ W $的此类GB代码，我们通过将它们映射到$ d \ le W-1 $尺寸的局部代码来构建上距离界限，而下的存在界限则给出了$ d \ ge {\ ge {\ cal o}（{n} {n}^{1/2}）$。我们还对具有行重4、6和8的双Quibit编码代码的家族中的某些主要循环尺寸进行了详尽的GB代码列举；观察到的距离缩放与$ a（w）{n}^{1/2}+b（w）$一致，其中$ n $是代码长度，$ a（w）$随着$ w $而增加。
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 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 $w$.
