Quantum error correction (QEC) is essential for operating quantum computers in the presence of noise. Here, we accurately decode arbitrary Calderbank-Shor-Steane (CSS) codes via the maximum satisfiability (MaxSAT) problem. We show how to map quantum maximum likelihood problem of CSS codes of arbitrary geometry and parity check weight into MaxSAT problems. We incorporate the syndrome measurements as hard clauses, while qubit and measurement error probabilities, including biased and non-uniform, are encoded as soft MaxSAT clauses. For the code capacity of color codes on a hexagonal lattice, our decoder has a higher threshold and superior scaling in noise suppression compared to belief propagation with ordered statistics post-processing (BP-OSD), while showing similar scaling in computational cost. Further, we decode surface codes and recently proposed bivariate quantum low-density parity check (QLDPC) codes where we find lower error rates than BP-OSD. Finally, we connect the complexity of MaxSAT decoding to a computational phase transition controlled by the clause density of the MaxSAT problem, where we show that our mapping is always in the computationally ''easy`` phase. Our MaxSAT decoder can be further parallelised or implemented on ASICs and FPGAs, promising potential further speedups of several orders of magnitude. Our work provides a flexible platform towards practical applications on quantum computers.

翻译：量子纠错（QEC）对于在存在噪声的情况下运行量子计算机至关重要。本文通过最大可满足性（MaxSAT）问题，精确解码任意Calderbank-Shor-Steane（CSS）码。我们展示了如何将任意几何结构和校验子权重的CSS码的量子最大似然问题映射为MaxSAT问题。我们将综合征测量编码为硬子句，而量子比特和测量误差概率（包括有偏和非均匀分布）则编码为软MaxSAT子句。对于六角晶格上颜色码的码容量模型，与采用有序统计后处理的置信传播（BP-OSD）解码器相比，我们的解码器具有更高的阈值和更优的噪声抑制缩放特性，同时计算成本的缩放行为相似。此外，我们解码了表面码以及近期提出的二元量子低密度奇偶校验（QLDPC）码，在这些码中我们的方法获得了比BP-OSD更低的误码率。最后，我们将MaxSAT解码的复杂度与由MaxSAT问题子句密度控制的计算相变联系起来，并证明我们的映射始终处于计算上的“简单”相。我们的MaxSAT解码器可进一步并行化或在ASIC和FPGA上实现，有望获得数个数量级的潜在加速。本工作为量子计算机的实际应用提供了一个灵活的平台。