发表机构
California Institute of Technology; Oratomic（加州理工学院; 奥拉原子）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出基于非阿贝尔群的mitten码，构建高速率、低开销的qLDPC处理器，经实验验证其在电路级噪声下具备优异的逻辑错误性能，为容错量子计算提供了实用路径。
AI 中文摘要
尽管量子低密度奇偶校验（qLDPC）码已取得显著进展，但构建兼具高速率、高吞吐量、硬件友好且解码快速的qLDPC处理器仍是一项挑战。我们提出了mitten码，这是一类基于非阿贝尔群的qLDPC处理器码，编码率为20%，校验重为9。其非阿贝尔结构规避了阿贝尔同类码所受的距离界限限制，使mitten码仅用数百个数据量子比特即可达到距离18及以上。mitten码的逻辑算子通过群作用关联，形成了模块化、低开销的逻辑工具包：通过桥接两个可复用的种子手术组件或单个固定提取器即可实现完整的Clifford操作。此外，基于mitten码的qLDPC处理器支持高速率手术，可并行执行多个逻辑测量，并能同时向所有逻辑量子比特注入并行魔法态。在电路级噪声下，采用我们的快速解码器，[⟦300,60,14⟧] mitten码在物理错误率（PER）为0.1%时，无需外推即可达到每轮约10⁻¹¹的块逻辑错误率；而[⟦975,195,≤24⟧]码在PER为0.4%时达到约10⁻⁸的逻辑错误率。在PER为0.1%时对[⟦540,108,18⟧]码进行150亿次手术实验的解码，仅观察到2次逻辑失败，证明该qLDPC处理器可运行约10¹⁰次逻辑操作。我们的解码器支持每个逻辑周期亚毫秒级的平均延迟，足以在中性原子硬件上实现实时解码。mitten码由基于sQetch的端到端设计流程发现，sQetch是一种比现有工具快数个数量级的距离估计器，且能高效映射到近期中性原子和超导硬件上，为容错量子计算开辟了实用路径。
英文摘要
Despite significant progress on quantum low-density parity-check (qLDPC) codes, building qLDPC processors that are high-rate, high-throughput, hardware-friendly, and fast-to-decode remains a challenge. We introduce mitten codes, a family of qLDPC processor codes of encoding rate $20\%$ and check weight $9$, based on non-abelian groups. Their non-abelian structure evades distance bounds constraining abelian counterparts, allowing mitten codes to reach distance $18$ and beyond with just a few hundred data qubits. The logical operators of a mitten code are related by the group action, yielding a modular, low-overhead logical toolkit: full Clifford operations follow from bridging two reusable seed surgery gadgets or from a single fixed extractor. Furthermore, qLDPC processors based on mitten codes support high-rate surgery that executes many logical measurements in parallel, and parallel magic-state injection into all logical qubits at once. Under circuit-level noise, with our fast decoder, the $[\![300,60,14]\!]$ mitten code achieves, without extrapolation, a block logical error rate of ${\sim}10^{-11}$ per round at $0.1\%$ physical error rate (PER), while the $[\![ 975,195,\leq 24 ]\!]$ code reaches ${\sim}10^{-8}$ at $0.4\%$ PER. Decoding $15$ billion surgery experiments on the $[\![540,108,18]\!]$ code at $0.1\%$ PER, we observe only two logical failures, demonstrating a qLDPC processor capable of running ${\sim}10^{10}$ logical operations. Our decoder is compatible with sub-millisecond average latency per logical cycle, sufficient for real-time decoding on neutral atom hardware. Discovered by an end-to-end design pipeline built on sQetch, a distance estimator orders of magnitude faster than existing tools, and mapping efficiently onto near-term neutral atom and superconducting hardware, mitten codes open a practical path toward fault-tolerant quantum computation.
Comments13 pages main text + 75 pages appendix; 13 figures
