多控制Toffoli门与三元Clifford$+P_9$门的高效综合
Efficient Synthesis of Multi-Controlled Toffoli Gates with Ternary Clifford$+P_9$ Gates
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中文总结 AI 辅助
提出一种基于中间qutrit的多控制Toffoli门分解方法，通过树形层次化并行计算将深度从线性降至对数，同时保持$6n+3$的$P_9$计数并减少辅助比特开销，为容错量子算法提供高效构建块。
中文摘要 AI 辅助
暂时占用qutrit能级可以减少量子计算中二进制电路逻辑所需的宽度和深度。我们引入了一种高效的中间qutrit分解方法，用于具有二进制子空间输入和输出的多控制Toffoli门。对于平衡控制宽度$n=2^h-1$，所提出的分解通过树进行层次化评估，允许独立的子树计算并行进行，并将深度从线性降低到对数。平衡低深度构造需要$6n+3$个逻辑$P_9$注入和$\frac{n-3}{4}$个干净的辅助qutrit。它与从最先进工作导出的递归扩展Clifford+$P_9$基线的直接$P_9$计数相匹配，同时使用的干净辅助比特渐近地减少到四分之一，并将线性深度替换为对数深度。对于任意控制宽度，顺序扩展保持了$6n+3$的$P_9$计数，但对于平衡核心$m=2^h-1\leq n$，深度为$O(\log m+n-m)$，在最坏情况下随$n$线性增长。通过减少广泛使用的可逆原语的资源开销，所提出的分解为在容错机制下设计和编译更资源高效的量子算法提供了实用的构建块。
英文摘要
Temporary occupation of qutrit levels can reduce the width and depth required for binary circuit logic in quantum computing. We introduce an efficient intermediate-qutrit decomposition of multi-controlled Toffoli gates with binary-subspace inputs and outputs. For balanced control widths $n=2^h-1$, the proposed decomposition is evaluated hierarchically through a tree, allowing independent subtree computations to proceed in parallel and reducing the depth from linear to logarithmic. The balanced low-depth construction requires $6n+3$ logical $P_9$ injections and $\frac{n-3}{4}$ clean ancillary qutrits. It matches the direct $P_9$ count of a recursively extended Clifford+$P_9$ baseline derived from the state-of-the-art work while using asymptotically one-quarter as many clean ancillas and replacing linear depth with logarithmic depth. For arbitrary control widths, a sequential extension preserves the $6n+3$ $P_9$ count but has depth $O(\log m+n-m)$ for a balanced core $m=2^h-1\leq n$, which is linear in the worst case over $n$. By reducing the resource overhead of a widely used reversible primitive, the proposed decomposition provides a practical building block for the design and compilation of more resource-efficient quantum algorithms in the fault-tolerant regime.
发表机构
- DI-ENS, École Normale Supérieure, Université PSL, CNRS, INRIA（巴黎高等师范学院，巴黎文理研究大学，法国国家科学研究中心，法国国家信息与自动化研究所）
机构由 AI 辅助整理，请以论文原文为准。
