发表机构
The University of Chicago; Caltech; Oratomic（芝加哥大学; 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
本文针对规范提升乘积码协同设计逻辑指令集，实现了模块化低开销的容错量子逻辑操作，推进了超高码率量子架构的容错计算研究。
AI 中文摘要
高码率量子低密度奇偶校验（qLDPC）码能用低物理量子比特开销编码大量逻辑量子比特，但在这类密集编码上实现高效容错计算仍是重大挑战。通用的、与码无关的技术（如码手术和门遥传）适用范围广，但难以在复杂高码率码上实现模块化、低开销和完全可验证，这类码的结构未被利用。本文通过为具有循环对称性的广泛\textit{规范}提升乘积（LP）码家族协同设计码及其逻辑指令集，克服了这些障碍。我们证明这类码存在\textit{规范逻辑基}，其中共轭逻辑算子被组织为源自底层经典码的循环轨道行和列，类似于使超图乘积码易于处理的结构。该规范基解锁了完整的逻辑指令集，包括常深度自同构和折叠横向Clifford门、由常数个可复用种子手术器件构建的模块化图码手术或紧凑规范提取器、高度并行的逻辑Pauli乘积测量以及并行魔法态注入。例如，一个$[[1122,148,\text{≤}20]]$（对应$[[4350,1224,\text{≤}20]]$）LP码仅需两个（对应四个）种子手术器件，而任意高权重逻辑测量可使用小于数据码块一半的完整提取器实现。这些结果推进了超高码率量子架构上容错量子计算的前沿。
英文摘要
High-rate quantum low-density parity-check (qLDPC) codes encode many logical qubits with low physical-qubit overhead, but realizing efficient fault-tolerant computation on such dense encodings remains a major challenge. Generic, code-agnostic techniques such as code surgery and gate teleportation apply broadly, but are difficult to make modular, low-overhead, and fully certifiable on complex high-rate codes whose structure is left unexploited. Here we overcome these obstacles by co-designing the code together with its logical instruction set for a broad family of canonical lifted-product (LP) codes with cyclic symmetry. We show that these codes admit a canonical logical basis, in which conjugate logical operators are organized into rows and columns of cyclic orbits inherited directly from the underlying classical codes, analogous to the structure that makes hypergraph-product codes so tractable. This canonical basis enables universal logical processing using magic-state input and a constant number of reusable seed surgery gadgets---only two (resp. four) for a $[[1122,148,\leq 20]]$ (resp. $[[4350,1224,\leq 20]]$) LP code. A fixed extractor smaller than half the data block also enables arbitrarily high-weight logical Pauli-product measurements (PPMs) while preserving the code's cyclic symmetry. These codes also enable rigorously fault-tolerant parallel logic, including PPMs across all logical qubits and magic-state injection from many surface codes into a full LP block. For example, a $[[468,36,20]]$ (resp. $[[952,112,17]]$) code supports simultaneous measurements of arbitrary logically disjoint Pauli products with an ancilla overhead of roughly three (resp. four) times the data block size. These results advance the frontier of fault-tolerant quantum computation on ultra-high-rate quantum architectures.
Comments8 Figures and 8 Tables, 24-page + 65-page appendix
