In classical computing, error-correcting codes are well established and are ubiquitous both in theory and practical applications. For quantum computing, error-correction is essential as well, but harder to realize, coming along with substantial resource overheads and being concomitant with needs for substantial classical computing. Quantum error-correcting codes play a central role on the avenue towards fault-tolerant quantum computation beyond presumed near-term applications. Among those, color codes constitute a particularly important class of quantum codes that have gained interest in recent years due to favourable properties over other codes. As in classical computing, $decoding$ is the problem of inferring an operation to restore an uncorrupted state from a corrupted one and is central in the development of fault-tolerant quantum devices. In this work, we show how the decoding problem for color codes can be reduced to a slight variation of the well-known $\texttt{LightsOut}$ puzzle. We propose a novel decoder for quantum color codes using a formulation as a MaxSAT problem based on this analogy. Furthermore, we optimize the MaxSAT construction and show numerically that the decoding performance of the proposed decoder achieves state-of-the-art decoding performance on color codes. The implementation of the decoder as well as tools to automatically conduct numerical experiments are publicly available as part of the $\textit{Munich Quantum Toolkit}$ (MQT) on GitHub.

中文翻译：

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使用 MaxSAT 解码量子颜色代码


在经典计算中，纠错码已经非常成熟，并且在理论和实际应用中都无处不在。对于量子计算，纠错也是必不可少的，但更难实现，这伴随着大量的资源开销，并且伴随着对大量经典计算的需求。量子纠错码在实现容错量子计算的道路上发挥着核心作用，超越了假定的近期应用。其中，颜色代码构成了一类特别重要的量子代码，由于优于其他代码的特性，近年来引起了人们的兴趣。与经典计算一样，$decoding$ 是推断操作以从损坏的状态恢复未损坏状态的问题，是容错量子设备开发的核心。在这项工作中，我们展示了如何将颜色代码的解码问题简化为著名的 $\texttt{LightsOut}$ 谜题的轻微变化。基于这个类比，我们提出了一种新的量子颜色代码解码器，使用公式作为 MaxSAT 问题。此外，我们优化了 MaxSAT 结构，并以数值方式表明，所提出的解码器的解码性能在颜色代码上实现了最先进的解码性能。解码器的实现以及自动进行数值实验的工具作为 GitHub 上 $\textit{Munich Quantum Toolkit}$ （MQT） 的一部分公开提供。