发表机构
University of Strasbourg; CNRS, CESQ and ISIS; QPerfect SAS; Institut Universitaire de France (IUF)（斯特拉斯堡大学; 法国国家科学研究中心，CESQ与ISIS; QPerfect公司; 法国高等研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出POLYMECHANON，一种仅以检测错误模型为输入的图神经网络量子纠错解码器，可解码任意稳定子码，在表面码和qLDPC码上优于现有方法，且支持实时解码和置信度后选择。
AI 中文摘要
我们提出了POLYMECHANON，一种用于量子纠错的图神经网络（GNN）解码器，其唯一输入是给定噪声模型下量子码的检测错误模型（DEM）。我们将DEM表示为检测器、错误机制和逻辑可观测量的三方图，其中每个输入特征都是通过将量子码作为数据而非设计选择来计算的。这样，相同的架构原则上可以解码任何稳定子码，在可以表示为检测错误模型的任何噪声模型下，一旦在DEM上训练即可。我们从四个方向测试了这种方法。首先，在旋转表面码上，该解码器在现象学噪声和电路级噪声下均优于相关的MWPM，逻辑失败率降低高达25%。其次，在一族高码率qLDPC码上，它在较小的码上匹配BP+OSD，在较大的码上超越它，在[![130,4,6]!]上逻辑失败率降低高达16%。第三，其解码时间不依赖于物理错误率，而BP+OSD的解码时间随物理错误率增长：在[![130,4,6]!]上，其在单个GPU上的每发有效成本约为几毫秒，而BP+OSD在单个CPU核心上为几十毫秒，其固定的计算图使其成为中性原子处理器上实时解码的候选方案。最后，一个跨不同码族训练的单一模型在训练期间看到的类图码上优于不相关的MWPM，并在其他码上保持在BP+OSD的10%以内，而它往往无法泛化到未见过的码，尤其是较大的码。其概率输出支持基于置信度的后选择，在表面码上将逻辑错误率降低一个数量级以上，同时保留超过90%的发次。由于只有DEM变化，新码和噪声模型可以在不重新设计解码器的情况下进行解码。
英文摘要
We present POLYMECHANON, a graph neural network (GNN) decoder for quantum error correction whose only input is the detection error model (DEM) of a quantum code under a given noise model. We represent the DEM as a tripartite graph of detectors, error mechanisms and logical observables, where every input feature is computed by using the quantum code as data rather than design choice. In this way, the same architecture decodes in principle any stabiliser code, under any noise model that can be expressed as a detection error model, once trained on the DEM. We test this approach along four directions. Firstly, on the rotated surface code the decoder outperforms correlated MWPM under both phenomenological and circuit-level noise, with up to $25\%$ fewer logical failures. Secondly, on a family of high-rate qLDPC codes it matches BP+OSD on the smaller codes and surpasses it on the larger ones, with up to $16\%$ fewer logical failures on $[\![130,4,6]\!]$. Thirdly, its decoding time does not depend on the physical error rate, whereas that of BP+OSD grows with it: on $[\![130,4,6]\!]$ its effective cost per shot is of the order of a few ms on a single GPU against a few tens of milliseconds for BP+OSD on a single CPU core, and its fixed computational graph makes it a candidate for real-time decoding on neutral-atom processors. Finally, a single model trained across codes of different families outperforms uncorrelated MWPM on the graph-like codes seen during training and stays within $10\%$ of BP+OSD on the others, while it tends to fail to generalize to unseen codes, particularly larger ones. Its probabilistic output enables confidence-based post-selection, lowering the logical error rate by more than an order of magnitude on the surface code while keeping more than $90\%$ of the shots. Since only the DEM changes, new codes and noise models can be decoded without redesigning the decoder.
Comments19 pages, 8 figures, 6 tables
