发表机构
Institute of Science Tokyo（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为量子比特CSS码构造低权重规范逻辑基，通过四元系数与配对多项式实现，并在多个码上验证了权重优势。
AI 中文摘要
我们通过将四元系数分配给二进制循环置换矩阵配对划分（CPM-PP）校验，构造并归一化逻辑代表，并将结果展开为二进制矩阵，为量子比特CSS码构造完整的规范逻辑基。当两个校验系统在不相交的列集上具有可逆子矩阵时，辅因子代表通过单一配对多项式的逆被规范地配对。所得配对张成整个逻辑空间。当配对多项式是系数为一的循环移位单项式时，归一化保持代表的二进制权重。我们陈述了一般块维数和CPM大小的构造，通过一个相应的例子进行说明，并报告了七个二进制码的参数、校验秩和基权重。代表性示例的参数为[[320,80,14]]、[[448,112,18]]和[[2048,512,24]]。这三个在X和Z两侧的最大校验权重均为10。它们的规范逻辑代表在X和Z两侧的二进制权重分别为25、27和27。
英文摘要
We construct complete canonical logical bases for qubit CSS codes by assigning quaternary coefficients to binary circulant permutation matrix pair-partition (CPM-PP) checks, constructing and normalizing logical representatives, and expanding the result into binary matrices. When the two check systems have invertible submatrices on disjoint column sets, cofactor representatives are canonically paired by the inverse of a single pairing polynomial. The resulting pairs span the entire logical space. When the pairing polynomial is a cyclic-shift monomial with coefficient one, normalization preserves the binary weights of the representatives. We state the construction for general block dimensions and CPM size, work through a corresponding example, and report the parameters, check ranks, and basis weights of seven binary codes. Representative examples have parameters $[[320,80,14]]$, $[[448,112,18]]$, and $[[2048,512,24]]$. All three have maximum check weight 10 on both the X and Z sides. Their canonical logical representatives have binary weights 25, 27, and 27, respectively, on both the X and Z sides.
Comments13 pages, 2 tables
