In this work, we develop a reduced complexity maximum likelihood (ML) decoder for quantum low-density parity-check (QLDPC) codes over erasures. Our decoder combines classical inactivation decoding, which integrates peeling with symbolic guessing, with a new dual peeling procedure. In the dual peeling stage, we perform row operations on the stabilizer matrix to efficiently reveal stabilizer generators and their linear combinations whose support lies entirely on the erased set. Each such stabilizer identified allows us to freely fix a bit in its support without affecting the logical state of the decoded result. This removes one degree of freedom that would otherwise require a symbolic guess, reducing the number of inactivated variables and decreasing the size of the final linear system that must be solved. We further show that dual peeling combined with standard peeling alone, without inactivation, is sufficient to achieve ML for erasure decoding of surface codes. Simulations across several QLDPC code families confirm that our decoder matches ML logical failure performance while significantly reducing the complexity of inactivation decoding, including more than a 20% reduction in symbolic guesses for the B1 lifted product code at high erasure rates.

翻译：本文针对擦除信道下的量子低密度奇偶校验（QLDPC）码，提出了一种降低复杂度的最大似然（ML）译码器。该译码器将经典的非激活译码（结合了剥离与符号猜测）与一种新的对偶剥离过程相结合。在对偶剥离阶段，我们对稳定子矩阵执行行运算，以高效地揭示其支撑集完全位于擦除集合上的稳定子生成元及其线性组合。每一个被识别出的此类稳定子，都允许我们自由地固定其支撑集中的一个比特，而不影响译码结果的逻辑状态。这消除了原本需要通过符号猜测来确定的自由度，从而减少了非激活变量的数量，并缩小了最终需要求解的线性系统的规模。我们进一步证明，对于表面码的擦除译码，仅将对偶剥离与标准剥离结合（无需非激活步骤）即足以实现最大似然译码。对多个QLDPC码族的仿真实验证实，我们的译码器在保持与最大似然译码相同的逻辑失败性能的同时，显著降低了非激活译码的复杂度，例如在高擦除率下，B1提升积码的符号猜测次数减少了超过20%。