Quantum technologies have the potential to solve certain computationally hard problems with polynomial or super-polynomial speedups when compared to classical methods. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build near term error corrected qubits given their two-dimensional architecture, the requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that they can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art decoding algorithms for surface codes is provided. The target audience of this work are both readers with an introductory understanding of the field as well as those seeking to further their knowledge of the decoding paradigm of surface codes. We describe the core principles of these decoding methods as well as existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface codes decoding is also provided.

中文翻译：

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表面代码的解码算法


与传统方法相比，量子技术有可能通过多项式或超多项式加速来解决某些计算难题。不幸的是，量子信息的不稳定性质使其容易出错。因此，量子纠错是使量子信息可靠并实现容错量子计算最终目标的宝贵工具。鉴于表面代码的二维架构、仅要求本地操作以及对量子噪声的高容忍度，表面代码目前是构建近期纠错量子比特的最有希望的候选者。解码算法是任何纠错方案不可或缺的组成部分，因为它们的任务是准确估计影响量子信息的错误，以便随后对其进行纠正。解码算法的一个关键方面是它们的速度，因为随着时间的推移，量子态会遭受额外的错误。这带来了一个难题，即解码性能的提高是以牺牲复杂性为代价的，反之亦然。在这篇综述中，对表面代码的最新解码算法进行了深入的讨论。这项工作的目标受众既是对该领域有初步了解的读者，也是寻求进一步了解表面代码解码范式的人。我们描述了这些解码方法的核心原理以及有望改善结果的现有变体。此外，还比较了纠错能力和解码复杂度方面的解码性能。还提供了对有关表面代码解码的现有软件工具的回顾。