In this paper we analyse the performance of quantum low-density parity-check (LDPC) codes over quantum memory channels for correcting correlated errors, where the quantum LDPC codes we use are the hypergraph product quantum LDPC codes. We generalize the classical Gilbert-Elliot markovian memory channel to the quantum Gilbert-Elliot channel and use it to model the memory effect in quantum memory channels. The simulation results show the memory effects in quantum GE channels has a bad effect to the performance of hypergraph product quantum LDPC codes. Then we propose a concatenation scheme by serially concatenating two hypergraph product quantum LDPC codes and it is shown that the serial concatenation scheme can improve the performance of hypergraph product quantum LDPC codes and lower down the error floor over quantum GE channels.

中文翻译：

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用于纠正相关错误的量子低密度奇偶校验码的性能分析

在本文中，我们分析了量子存储通道上的量子低密度奇偶校验 (LDPC) 码用于纠正相关错误的性能，其中我们使用的量子 LDPC 码是超图乘积量子 LDPC 码。我们将经典的 Gilbert-Elliot 马尔可夫记忆通道推广到量子 Gilbert-Elliot 通道，并用它来模拟量子记忆通道中的记忆效应。仿真结果表明，量子GE通道中的记忆效应对超图乘积量子LDPC码的性能有不良影响。然后我们提出了通过串联两个超图乘积量子 LDPC 码的串联方案，结果表明，串联串联方案可以提高超图乘积量子 LDPC 码的性能并降低量子 GE 信道上的错误底线。