AI 中文总结
研究利用LDGM码构建CSS码族用于容错量子计算，通过行运算实现量子速率，迭代解码并结合DDE优化性能，设计灵活，能控制稳定子权重，纠错能力出色，适合容错量子计算。
AI 中文摘要
我们使用低密度生成矩阵（LDGM）码的生成矩阵和校验矩阵构建了一个新的Calderbank-Shor-Steane（CSS）码族。对两个矩阵进行行运算以实现所需的量子速率。通过在相关图上应用消息传递进行迭代解码，并使用离散密度演化（DDE）在去极化信道中优化性能。该构造在设计上具有高度灵活性和简便性，产生的量子码具有出色的纠错能力。通过适当设计码结构，能将稳定子生成元的权重控制并限制在较小值，特别适合容错量子计算，同时在纠错能力方面表现出色。
英文摘要
We construct a new family of Calderbank-Shor-Steane (CSS) codes using the generator and parity-check matrices of Low-Density Generator Matrix (LDGM) codes, with row operations applied to both matrices in order to achieve the desired quantum rate. Decoding is performed in an iterative manner, by applying message passing over the associated graph, and discrete Density Evolution (DDE) is used to optimize performance in the depolarizing channel. The proposed construction offers high flexibility and easiness in the design, producing quantum codes that possess excellent error correction capabilities. By properly designing the structure of the code, we are able to control and bound the weight of the stabilizer generators to a small value, which results in codes particularly well suited for fault-tolerant quantum computation. At the same time, these codes achieve very good performance in terms of error correction capability.
