Quantum low-density parity-check (LDPC) codes are a promising family of quantum error-correcting codes for fault tolerant quantum computing with low overhead. Decoding quantum LDPC codes on quantum erasure channels has received more attention recently due to advances in erasure conversion for various types of qubits including neutral atoms, trapped ions, and superconducting qubits. Belief propagation with guided decimation (BPGD) decoding of quantum LDPC codes has demonstrated good performance in bit-flip and depolarizing noise. In this work, we apply BPGD decoding to quantum erasure channels. Using a natural modification, we show that BPGD offers competitive performance on quantum erasure channels for multiple families of quantum LDPC codes. Furthermore, we show that the performance of BPGD decoding on erasure channels can sometimes be improved significantly by either adding damping or adjusting the initial channel log-likelihood ratio for bits that are not erased. More generally, our results demonstrate BPGD is an effective general-purpose solution for erasure decoding across the quantum LDPC landscape.

翻译：量子低密度奇偶校验（LDPC）码是一类极具前景的量子纠错码，能够以较低开销实现容错量子计算。随着中性原子、囚禁离子和超导量子比特等多种量子比特擦除转换技术的进展，量子擦除信道上的量子LDPC码译码近期受到更多关注。采用引导确定化的置信传播（BPGD）译码方案已在比特翻转与去极化噪声中展现出良好性能。本工作中，我们将BPGD译码应用于量子擦除信道。通过一种自然的改进，我们证明BPGD在多种量子LDPC码族上对量子擦除信道具有竞争优势。此外，我们发现通过引入阻尼因子或调整未擦除比特的初始信道对数似然比，有时能显著提升BPGD在擦除信道上的译码性能。更广泛而言，我们的结果表明BPGD是适用于量子LDPC码体系的一种高效通用擦除译码解决方案。