To enable fault tolerance on millions of qubits in real time, scalable decoding is necessary, which motivates this paper. Existing decoding algorithms (decoders), such as clustering, matching, belief propagation (BP), and neural networks, suffer from one or more of inaccuracy, costliness, and incompatibility, upon a broad set of quantum error correction codes, such as surface code, toric code, and bivariate bicycle code. Therefore, there exists a gap between existing decoders and an ideal decoder that is accurate, fast, general, and scalable simultaneously. This paper contributes in three aspects, including decoder, decoder architecture, and decoding simulator. First, we propose Lottery BP, a decoder that introduces randomness during decoding. Lottery BP improves the decoding accuracy over BP by 2~8 orders of magnitude for topological codes. To efficiently decode multi-round measurement errors, we propose syndrome vote as a pre-processing step before Lottery BP, which compresses multiple rounds of syndromes into one. Syndrome vote increases the latency margin of decoding and mitigates the backlog problem. Second, we design a PolyQec architecture that implements Lottery BP as a local decoder and ordered statistics decoding (OSD) as a global decoder, and it is configurable for surface/toric code and X/Z check. Since Lottery BP boosts the local decoding accuracy, PolyQec invokes the costly global OSD decoder less frequently over BP+OSD to enhance the scalability, e.g., 3~5 orders of magnitude less for topological codes. Third, to evaluate decoders fairly, we develop a PyTorch-based decoding simulator, Syndrilla, that modularizes the simulation pipeline and allows to extend new decoders flexibly. We formulate multiple metrics to quantify the performance of decoders and integrate them in Syndrilla. Running on GPUs, Syndrilla is 1~2 orders of magnitude faster than CPUs.

翻译：为实现数百万量子比特的实时容错，规模化解码必不可少，这构成了本文的研究动机。现有解码算法（解码器），如聚类、匹配、置信传播（BP）和神经网络，在表面码、环面码和二变量自行车码等广泛量子纠错码上，存在不准确、成本高昂或不兼容等问题。因此，现有解码器与同时满足精确、快速、通用且可扩展的理想解码器之间存在差距。本文从解码器、解码器架构和解码模拟器三方面做出贡献。首先，我们提出彩票BP解码器，该解码器在解码过程中引入随机性。对于拓扑码，彩票BP将解码精度相比BP提升2~8个数量级。为高效解码多轮测量误差，我们提出将综合征投票作为彩票BP的前处理步骤，将多轮综合征压缩为一轮。综合征投票提高了解码的延迟余量，缓解了积压问题。其次，我们设计了PolyQec架构，将彩票BP作为局部解码器，有序统计解码（OSD）作为全局解码器，且可配置用于表面/环面码及X/Z校验。由于彩票BP提升了局部解码精度，PolyQec相比BP+OSD减少了昂贵全局OSD解码器的调用频率，对于拓扑码而言调用次数降低3~5个数量级，从而增强了可扩展性。第三，为公平评估解码器，我们开发了基于PyTorch的解码模拟器Syndrilla，其模块化模拟流水线，可灵活扩展新解码器。我们制定了多项指标量化解码器性能，并将其集成于Syndrilla中。在GPU上运行时，Syndrilla比CPU快1~2个数量级。