We present a new decoder for the surface code, which combines the accuracy of the tensor-network decoders with the efficiency and parallelism of the belief-propagation algorithm. Our main idea is to replace the expensive tensor-network contraction step in the tensor-network decoders with the blockBP algorithm - a recent approximate contraction algorithm, based on belief propagation. Our decoder is therefore a belief-propagation decoder that works in the degenerate maximal likelihood decoding framework. Unlike conventional tensor-network decoders, our algorithm can run efficiently in parallel, and may therefore be suitable for real-time decoding. We numerically test our decoder and show that for a large range of lattice sizes and noise levels it delivers a logical error probability that outperforms the Minimal-Weight-Perfect-Matching (MWPM) decoder, sometimes by more than an order of magnitude.

翻译：我们提出了一种针对表面码的新型解码器，该解码器融合了张量网络解码器的精度与置信传播算法的高效性和并行性。核心思路是用块BP算法（一种基于置信传播的近期近似缩并算法）替代传统张量网络解码器中昂贵的张量网络缩并步骤。因此，我们的解码器是一种在简并最大似然解码框架下运行的置信传播解码器。与传统张量网络解码器不同，该算法可高效并行执行，有望适用于实时解码。通过数值测试，我们证明该解码器在大范围晶格尺寸和噪声水平下，其逻辑错误概率优于最小权重完美匹配（MWPM）解码器，有时甚至提升一个数量级以上。