We introduce the spanning tree matching (STM) decoder for surface codes, which guarantees the error correction capability up to the code's designed distance by first employing an instance of the minimum spanning tree on a subset of ancilla qubits within the lattice. Then, a perfect matching graph is simply obtained, by selecting the edges more likely to be faulty. A comparative analysis reveals that the STM decoder, at the cost of a slight performance degradation, provides a substantial advantage in decoding time compared to the minimum weight perfect matching (MWPM) decoder. Finally, we propose an even more simplified and faster algorithm, the Rapid-Fire (RFire) decoder, designed for scenarios where decoding speed is a critical requirement.

翻译：我们提出了一种用于表面码的生成树匹配（STM）译码器。该译码器首先利用格点内一组辅助量子比特上的最小生成树实例，从而保证了达到码字设计距离的纠错能力。随后，通过选择更可能出错的边来简单构建一个完美匹配图。对比分析表明，与最小权重完美匹配（MWPM）译码器相比，STM译码器在性能略有下降的同时，在译码时间上具有显著优势。最后，我们提出了一种更简化且速度更快的算法——速射（RFire）译码器，专门针对译码速度要求严苛的场景设计。