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 letter, 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（QLDPC）码是未来量子纠错方案中最有前景的候选之一。然而，由于坦纳图中不可避免的短环，现有中短码长的QLDPC码设计数量有限，且采用四进制置信传播（BP）译码器时性能次优。本文提出一种新型的量子LDPC码联合码与译码器设计方案。所构造的码字具有约为码长平方根的最小距离。此外，据我们所知，这是首个BP译码不受长度为4的短环影响的QLDPC码族。该成果通过采用一种集成BP译码器来减轻集结短环的影响实现。我们基于经典准循环码和有限几何码概述了两种码构造方法。数值结果表明，该方案在去极化信道上具有卓越的译码性能。