高速率准二元量子LDPC码
High-Rate Quasi-Dyadic Quantum LDPC Codes
- Università Politecnica delle Marche（马尔凯理工大学）
- Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出基于准二元矩阵的高速率CSS量子LDPC码，其Tanner图围长至少为6，并精确计数四元表示中4环数量，模拟显示其有限长度逻辑错误率性能与最先进码相当。
AI中文摘要：
本文提出了一种基于准二元矩阵的高速率Calderbank-Shor-Steane（CSS）量子低密度奇偶校验（QLDPC）码的新型设计。用于构造所提出的CSS码的两个分量经典码相关的Tanner图具有至少为6的围长。我们还推导了奇偶校验矩阵的四元表示中长度为4的环的精确计数。在码容量和现象学噪声模型下的蒙特卡洛模拟表明，与最先进的码相比，所提出的码在这两种设置下都具有有竞争力的有限长度逻辑错误率性能。
英文摘要：
In this work, we propose a novel design of high-rate Calderbank--Shor--Steane (CSS) quantum low-density parity-check (QLDPC) codes based on quasi-dyadic matrices. The Tanner graphs associated with the two component classical codes used to construct the proposed CSS codes are characterized by a girth of at least $6$. We also derive an exact count of length-$4$ cycles in the quaternary representation of the parity-check matrix. Monte Carlo simulations under code-capacity and phenomenological noise models show that the proposed codes have competitive finite-length logical error rate performance compared with state-of-the-art codes in both these settings.
