Quantum low-density parity-check (QLDPC) codes are among the most promising candidates for future quantum error correction schemes. However, a limited number of short to moderate-length QLDPC codes have been designed and their decoding performance is sub-optimal with a quaternary belief propagation (BP) decoder due to unavoidable short cycles in their Tanner graphs. In this paper, we propose a novel joint code and decoder design for QLDPC codes. The constructed codes have a minimum distance of about the square root of the block length. In addition, it is, to the best of our knowledge, the first QLDPC code family where BP decoding is not impaired by short cycles of length 4. This is achieved by using an ensemble BP decoder mitigating the influence of assembled short cycles. We outline two code construction methods based on classical quasi-cyclic codes and finite geometry codes. Numerical results demonstrate outstanding decoding performance over depolarizing channels.

翻译：量子低密度奇偶校验码是未来量子纠错方案中最有前途的候选者之一。然而，由于Tanner图中不可避免的短环，目前已设计的短至中等长度量子LDPC码数量有限，且其四进制置信传播解码器的解码性能欠佳。本文提出一种针对量子LDPC码的新型联合码字与解码器设计方法。所构造码字的最小距离约为码块长度的平方根。此外，据我们所知，这是首个BP解码不受4环短环影响的量子LDPC码族，其核心机制在于采用集成BP解码器以缓解组合短环的影响。我们概述了基于经典准循环码和有限几何码的两种码字构造方法。数值结果表明，该方法在去极化信道上具有卓越的解码性能。