发表机构
School of Electrical Engineering, Korea University（韩国大学电气工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出直接培育纠缠$|CS\ angle$魔术态的架构，利用Clifford对合和六比特记录保护分支，优化扩展降低操作数，并认证故障阶数三输出通道，在低噪声下优于三T路线。
AI 中文摘要
魔术态培育迄今主要集中于单量子比特的非 Clifford 资源。我们开发了一种针对纠缠态 $|CS\ angle=CS|++\ angle$ 的直接培育架构。两个对易的 Clifford 对合投影到四个由 Pauli 框架更新关联的有效分支上。一个最小的六比特 $[6,2,4]$ 记录保护分支标签免受将有效记录映射到另一有效记录的读出错误。经过验证的 CAT$_7$ 组件、Steane 错误检测、基于 CZZ 的受控检查以及立即的 Steane 到表面码扩展构成了完整的工厂。解码器使用 263 个操作检测比特，而额外的 168 个比特被保留用于后续验证。解码通过精确的低阶解析、预计算的高阶目录以及四陪集 BP+OSD 进行。在所陈述的活跃位置随机 Pauli 模型下，精确枚举未发现通过故障阶数二的可接受闭环逻辑故障机制，而显式的阶数三故障机制存在。有限 $p$ 模拟量化了接受率、残余综合征和解码器工作负载，针对阶数三故障的定向采样估计了主要逻辑错误通道。优化直接 $d=5\ ightarrow13$ 扩展使接受输出的操作数减少约 35--37\%。我们在相同的二进制逻辑错误率下比较两条路线。即使在三条 $T$ 路线获得预先存在的输出补丁的情况下，直接 CS 在两个较低噪声基准点上的操作数仍然更少。排序在 $8\ imes10^{-4}$ 和 $9\ imes10^{-4}$ 之间反转。这些结果表明，纠缠的非 Clifford 态可以通过受保护的分支记录和显式认证的故障阶数三输出通道直接培育。
英文摘要
Magic-state cultivation has so far focused mainly on single-qubit non-Clifford resources. We develop a direct cultivation architecture for the entangled state $|CS\rangle=CS|++\rangle$. Two commuting Clifford involutions project onto four usable branches related by Pauli-frame updates. A minimal six-bit $[6,2,4]$ record protects the branch label against readout errors that map one valid record to another. Verified CAT$_7$ gadgets, Steane error detection, CZZ-based controlled checks, and immediate Steane-to-surface expansion form the complete factory. The decoder uses 263 operational detector bits, while 168 additional bits are withheld for later validation. Decoding proceeds through exact low-order resolution, a precomputed higher-order catalogue, and four-coset BP+OSD. Under the stated active-location stochastic-Pauli model, exact enumeration finds no accepted closed-boundary logical-failure mechanism through fault order two, while explicit order-three failure mechanisms exist. Finite-$p$ simulations quantify acceptance, residual syndromes, and decoder workload, and targeted sampling of order-three faults estimates the leading logical-error channels. Optimizing the direct $d=5\rightarrow13$ expansion reduces accepted-output operation count by approximately 35--37\%. We compare the two routes at the same binary logical-error rate. Direct CS remains cheaper in operation count at the two lower-noise benchmark points even when the three-$T$ route is given pre-existing output patches. The ordering reverses between $8\times10^{-4}$ and $9\times10^{-4}$. These results show that an entangled non-Clifford state can be cultivated directly with a protected branch record and an explicitly certified fault-order-three output channel.
