AI 中文总结
本研究针对3D四面体色码及其变形变体，提出制备|√T⟩魔术态的容错协议，发现该态可降低量子电路综合的时空成本，为通用量子计算拓宽设计空间。
AI 中文摘要
魔术态注入是实现通用容错量子计算的标准途径。克利福德门集合与非克利福德T门的组合是广泛使用的通用门集合，若额外的非克利福德基元能以具有竞争力的资源成本、足够低的逻辑噪声率容错制备，扩展可用非克利福德基元集合可降低编译开销。本研究针对3D四面体色码及其更小的变形变体，引入制备逻辑|√T⟩魔术态的标志容错协议。我们在电路级噪声下的模拟验证了容错性，量化了接受率与逻辑错误率，并通过逻辑过程断层扫描重构了对应电路用于门注入的有效逻辑信道。研究发现，在实际相关的近似 regime 下，相较于克利福德+T门集合，获得√T可将综合哈尔随机单量子比特幺正的平均时空成本降低约20%-30%。这些结果表明，扩展容错非克利福德基元集合可提升计算效率，并拓宽早期容错时代通用量子计算的设计空间。
英文摘要
Magic-state injection is a standard route to realize universal fault-tolerant quantum computation. Whereas the set of Clifford gates in combination with the non-Clifford T gate is a widely used universal gate set, extending the available set of non-Clifford primitives can reduce compilation overhead, provided that the additional primitives can be prepared fault-tolerantly with competitive resource costs and at sufficiently low logical noise rates. In this work, we introduce flag fault-tolerant protocols for preparing logical $|\sqrt{\mathrm{T}} \rangle $ magic states on the 3D tetrahedral color code and its smaller morphed variant. Our simulations under circuit-level noise verify fault tolerance, quantify acceptance and logical error rates, and we reconstruct the effective logical channels of the corresponding circuits for gate injection via logical process tomography. We find that access to $\sqrt{\mathrm{T}}$ reduces the average space-time cost of synthesizing Haar-random single-qubit unitaries by approximately $20$-$30$% relative to the Clifford+T gate set across practically relevant approximation regimes. These results demonstrate how expanding the set of fault-tolerant non-Clifford primitives can improve computational efficiency and broaden the design space for universal quantum computation in the early fault-tolerant era.
Comments18 pages, 10 figures
