Quantum low-density-generator-matrix (QLDGM) codes are known to exhibit great error correction capabilities, surpassing existing quantum low-density-parity-check (QLDPC) codes and other sparse-graph schemes over the depolarizing channel. Most of the research on QLDPC codes and quantum error correction (QEC) is conducted for the symmetric instance of the generic Pauli channel, which incurs bit flips, phase flips, or a combination of both with the same probability. However, due to the behavior of the materials they are built from, some quantum devices must be modelled using a different channel model capable of accurately representing asymmetric scenarios in which the likelihood of a phase flip is higher than that of a bit flip. In this work, we study the design of QLDGM CSS codes for such Pauli channels. We show how codes tailored to the depolarizing channel are not well suited to these asymmetric environments and we derive methods to aptly design QLDGM CSS codes for this paradigm.

中文翻译：

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基于低密度发生器矩阵的非对称量子通道量子代码设计

众所周知，量子低密度发生器矩阵（QLDGM）代码具有强大的纠错能力，在去极化通道上超越了现有的量子低密度奇偶校验（QLDPC）代码和其他稀疏图方案。对QLDPC码和量子错误校正（QEC）的大多数研究都是针对通用Pauli通道的对称实例进行的，该实例会以相同的概率发生比特翻转，相位翻转或两者的组合。但是，由于制造它们的材料的行为，某些量子器件必须使用能够准确表示不对称情况的不同通道模型进行建模，在这些不对称情况中，相移的可能性高于位翻转的可能性。在这项工作中，我们研究了此类Pauli频道的QLDGM CSS代码的设计。