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：我们提出了一种新型表面码译码器，该译码器结合了张量网络译码器的准确性以及置信传播算法的高效性与并行性。我们的核心思想是用blockBP算法（一种基于置信传播的近期近似收缩算法）替代张量网络译码器中计算成本高昂的张量网络收缩步骤。因此，我们的译码器是一种在退化最大似然译码框架下运行的置信传播译码器。与传统张量网络译码器不同，我们的算法能够高效并行运行，可能适用于实时译码。我们通过数值测试表明，在广泛的晶格尺寸和噪声水平范围内，该译码器实现的逻辑错误概率优于最小权重完美匹配（MWPM）译码器，有时甚至高出超过一个数量级。