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:地表代码错误校正提供了极有希望的实现可缩放的防错量计算的途径。 当以稳定器代码运行时, 表面代码计算包含一个综合解码步骤, 使用测量的稳定器操作员来确定物理夸比错误的适当校正。 解码算法经历了重大发展, 最近的工作包括机器学习( ML) 技术。 尽管初步结果大有希望, 以 ML 为基础的综合解码解码器仍然局限于小规模的演示, 且无法处理符合边界条件和各种形状的地表代码。 这里, 我们报告开发了一个基于可缩放手术和编织所需的人工神经网络( ANN) 的可缩放快速解码操作器, 能够解析任意形状和大小的表面代码的表面代码。 在严格训练超过5 000万个随机量误差的情况下, 我们的ANNU解码显示其代码工作距离超过1000个( 超过400万个物理比特), 这是以最大 ML 为基的解码演示到日期的最大的解码 。 我们的人工神经网络网络网络网络网络网络网络网络(AN- ) 快速解码的自动解码运行功能运行运行将持续进行到十年内的自动运行。