Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer operators are used to determine appropriate corrections for errors in physical qubits. Decoding algorithms have undergone substantial development, with recent work incorporating machine learning (ML) techniques. Despite promising initial results, the ML-based syndrome decoders are still limited to small scale demonstrations with low latency and are incapable of handling surface codes with boundary conditions and various shapes needed for lattice surgery and braiding. Here, we report the development of an artificial neural network (ANN) based scalable and fast syndrome decoder capable of decoding surface codes of arbitrary shape and size with data qubits suffering from the depolarizing error model. Based on rigorous training over 50 million random quantum error instances, our ANN decoder is shown to work with code distances exceeding 1000 (more than 4 million physical qubits), which is the largest ML-based decoder demonstration to-date. The established ANN decoder demonstrates an execution time in principle independent of code distance, implying that its implementation on dedicated hardware could potentially offer surface code decoding times of O($\mu$sec), commensurate with the experimentally realisable qubit coherence times. With the anticipated scale-up of quantum processors within the next decade, their augmentation with a fast and scalable syndrome decoder such as developed in our work is expected to play a decisive role towards experimental implementation of fault-tolerant quantum information processing.

翻译：表面码纠错为实现可扩展的容错量子计算提供了一条极具前景的途径。当作为稳定子码运行时，表面码计算包含一个综合征解码步骤，其中测量得到的稳定子算子被用于确定对物理量子比特中错误的适当修正。解码算法已经取得了显著发展，近期的工作融入了机器学习技术。尽管初步结果令人鼓舞，基于机器学习的综合征解码器仍局限于低延迟的小规模演示，并且无法处理具有边界条件及晶格手术和编织所需各种形状的表面码。在此，我们报告了一种基于人工神经网络的可扩展且快速的综合征解码器的研发，该解码器能够解码任意形状和大小的表面码，其中数据量子比特受退极化错误模型影响。基于对超过5000万个随机量子错误实例的严格训练，我们的ANN解码器被证明可在代码距离超过1000（超过400万个物理量子比特）时工作，这是迄今为止最大规模的基于机器学习的解码器演示。所建立的ANN解码器展现出原则上与代码距离无关的执行时间，这意味着其在专用硬件上的实现有望提供微秒量级的表面码解码时间，与实验可实现的量子比特相干时间相匹配。随着未来十年量子处理器预期规模的扩大，为其配备如我们工作中所开发的快速可扩展综合征解码器，预计将在实验实现容错量子信息处理方面发挥决定性作用。