非阿贝尔拓扑序的融合辅助解码
Fusion-assisted decoding of non-Abelian topological order
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中文总结 AI 辅助
本研究提出利用精炼综合征集（含非阿贝尔任意子融合结果测量）系统提升最大似然解码器性能，并在$D_4$量子双模型下证明存在非零噪声阈值，低于该阈值可单轮测量完整恢复逻辑量子位。
中文摘要 AI 辅助
最大似然（ML）解码器通过测量一组综合征、基于这些综合征和噪声模型经典地计算最优恢复方案，然后执行该恢复方案来进行量子纠错。对于环面码，ML解码器已被充分理解，并可直接推广到具有阿贝尔任意子的其他表面码，在这些码中它们能够达到信息论解码阈值。另一方面，具有非阿贝尔任意子的码变得越来越重要，因为它们能够支持横向或恒定深度的非克利福德门，并在现代量子器件中支持高效的制备协议。然而，它们给解码带来了新的挑战：非阿贝尔任意子通常无法被确定性地湮灭，且逻辑算符无法通过阿贝尔同调来分类。在这项工作中，我们表明精炼的综合征集（包括解析非阿贝尔任意子融合结果的测量）能够系统地提升ML解码器的性能。我们通过为$D_4$量子双模型在电荷噪声下构建显式解码器，并通过映射到经典统计力学模型获得阈值的数值结果来具体展示这一点。我们证明存在一个非零噪声阈值，低于该阈值时，整个逻辑量子位（qudit）可以通过单轮测量被完全恢复。
英文摘要
Maximum likelihood (ML) decoders perform quantum error correction by measuring a set of syndromes, classically computing an optimal recovery based on these syndromes and the noise model, and then performing that recovery. ML decoders are well understood for the toric code and generalize straightforwardly to other surface codes with Abelian anyons, where they can saturate information-theoretic decoding thresholds. On the other hand, codes with non-Abelian anyons have become increasingly relevant because they can support transversal or constant-depth non-Clifford gates and admit efficient preparation protocols in modern quantum devices. However, they present new challenges for decoding: non-Abelian anyons cannot in general be deterministically annihilated, and the logical operators cannot be classified by Abelian homology. In this work, we show that refined syndrome sets, including measurements that resolve non-Abelian anyon fusion outcomes, systematically improve the performance of ML decoders. We demonstrate this concretely by constructing explicit decoders for the $D_4$ quantum double model under charge noise, and obtaining numerical results for thresholds via mappings to classical statistical-mechanics models. We show that there is a nonzero noise threshold below which the entire logical qudit can be recovered with a single round of measurements.
发表机构
- Harvard University（哈佛大学）
- Purdue University（普渡大学）
- New York University（纽约大学）
- State University of New York at Stony Brook（纽约州立大学石溪分校）
- University of Oklahoma（俄克拉荷马大学）
- NIST/University of Maryland（美国国家标准与技术研究院/马里兰大学）
- University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。
