基于循环置换矩阵（CPM）的量子LDPC码的对划分构造
Pair-Partition Constructions for CPM-Based Quantum LDPC Codes
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中文总结 AI 辅助
该研究从循环置换矩阵构造量子LDPC码，由列权重J、行权重L和素数提升大小P参数化，通过对划分数组施加方程给出CSS正交性，给出多个正则围长为6的码的实例及速率等信息，还确定了距离。
中文摘要 AI 辅助
我们从循环置换矩阵（CPM）构造二进制Calderbank - Shor - Steane（CSS）量子低密度奇偶校验（LDPC）码。该构造由列权重J、行权重L和素数提升大小P参数化。J×J的对划分数组对CPM指数施加线性配对差分方程，这些方程给出CSS正交性。本文报告的主要有限示例包括（J，L）=（4,12）的正则围长为6的码[[372,130,16]]，速率为0.349，以及（J，L）=（4,14）的正则围长为6的码[[518,228,16]]，速率为0.440。我们还记录了（J，L）=（3,8）的正则围长为6的实例[[472,122,14]]和[[488,126,14]]，提升大小P分别为59和61。通过详尽的低权重排除和明确的非稳定器见证为固定矩阵确定了所述距离。
英文摘要
We introduce the pair-partition (PP) construction of binary Calderbank--Shor--Steane quantum low-density parity-check codes from circulant permutation matrices. A square array of pair partitions imposes linear paired-difference equations on the CPM exponents and thereby guarantees CSS orthogonality. Pairing graphs derived from this array allow the combinatorial design to be screened before exponent search. We further give and prove a complete algorithm for verifying lower bounds on the quantum minimum distance of a fixed CSS lift. The algorithm searches for zero-syndrome vectors outside the opposing stabilizer row space, uses only rigorously valid pruning rules, and finds no vector through a prescribed weight if and only if the corresponding distance exceeds that weight. For fixed column weight, row weight, and search limit, cyclic symmetry makes the combinatorial support-enumeration bound independent of the lift size, although matrix preprocessing and row-space tests can still depend on the lift size. Thus the construction stage and the distance-verification stage are both specified by directly checkable finite procedures.
