发表机构
University of Ulsan; Pohang University of Science and Technology (POSTECH); Ben-Gurion University of the Negev; Gyeongsang National University（蔚山科学技术院; 浦项科技大学; 内盖夫本古里安大学; 庆尚国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出逻辑神经置信传播（L-NBP）解码器，结合BP与神经权重，在保持线性复杂度的同时，在表面码解码上性能优于或相当于BP-OSD、MWPM，电路级噪声下复杂度仅为BP-OSD的0.2%
AI 中文摘要
量子纠错（QEC）需要解码器在实现高逻辑精度的同时，随码长高效扩展。置信传播（BP）因具有线性解码复杂度而具吸引力，但传统BP解码器在表面码上往往无法达到足够的逻辑精度。我们提出逻辑神经置信传播（L-NBP），这是一种基于BP的神经解码器，其将解码目标从物理级解码重定向至逻辑级解码。L-NBP首先运行神经BP（NBP）模块以生成后验置信度，随后逻辑分类器将这些置信度转换为连续值的软校验子并预测逻辑算子。由于L-NBP的所有组件均可通过反向传播训练，因此L-NBP以端到端方式进行训练，使NBP模块能够学习提取有利于逻辑分类的软校验子。在表面码上，L-NBP在保持BP线性复杂度的同时，性能与有序统计解码BP（BP-OSD）及最小权完美匹配（MWPM）相当或更优，且在去极化噪声下达到17.5%的阈值。此外，在电路级噪声下，L-NBP在距离为9的表面码上的精度与BP-OSD相当，而仅需其0.2%的复杂度。这些结果表明，将BP、神经权重与逻辑级解码相结合，可实现可扩展且高精度的量子解码。
英文摘要
Quantum error correction (QEC) requires accurate and efficient decoders, yet belief propagation (BP), despite its linear decoding complexity, often provides insufficient logical accuracy on surface codes. We propose Logical Neural Belief Propagation (L-NBP), a BP-based neural decoder that redirects the decoding objective from physical-level to logical-level decoding. L-NBP uses a neural BP (NBP) module to produce posterior beliefs, which a logical classifier transforms into a continuous-valued soft syndrome for logical-operator prediction. Trained end-to-end by backpropagation, the NBP module learns soft syndromes that are favorable for logical classification. On surface codes, L-NBP matches or outperforms BP with ordered-statistics decoding (BP-OSD) and minimum-weight perfect matching (MWPM) while retaining the linear complexity of BP, and achieves a threshold of $17.5\%$ under depolarizing noise. Under circuit-level noise, L-NBP matches the accuracy of BP-OSD on the distance-$9$ surface code while requiring only $0.2\%$ of its complexity.
Comments15 pages, 8 figures
