Decoding low-density parity-check codes is critical in many current technologies, such as fifth-generation (5G) wireless networks and satellite communications. The belief propagation algorithm allows for fast decoding due to the low density of these codes. However, there is scope for improvement to this algorithm both in terms of its computational cost when decoding large codes and its error-correcting abilities. Here, we introduce the quantum-enhanced belief propagation (QEBP) algorithm, in which the Quantum Approximate Optimization Algorithm (QAOA) acts as a pre-processing step to belief propagation. We perform exact simulations of syndrome decoding with QAOA, whose result guides the belief propagation algorithm, leading to faster convergence and a lower block error rate (BLER). In addition, through the repetition code, we study the possibility of having shared variational parameters between syndromes and, in this case, code lengths. We obtain a unique pair of variational parameters for level-1 QAOA by optimizing the probability of successful decoding through a transfer matrix method. Then, using these parameters, we compare the scaling of different QAOA post-processing techniques with code length.

翻译：低密度奇偶校验码的解码在第五代（5G）无线网络和卫星通信等众多现代技术中至关重要。置信传播算法因其低密度特性可实现快速解码，但在处理大规模码字时的计算成本及纠错能力方面仍有改进空间。本文提出量子增强置信传播算法，其中量子近似优化算法作为置信传播的预处理步骤。我们通过QAOA对校验子解码进行精确模拟，其运算结果引导置信传播算法，从而获得更快的收敛速度与更低的误块率。此外，通过重复码结构，我们研究了在校验子间（以及特定码长条件下）共享变分参数的可能性。采用转移矩阵方法优化解码成功率，我们得到一组适用于一级QAOA的独特变分参数。基于这些参数，我们比较了不同QAOA后处理技术随码长变化的扩展特性。