Clifford 层级第三层置换门的表征
量子物理
2025-10-07 v1
摘要
Clifford 层级是量子计算中一个基本结构，其数学性质尚未完全理解。本文对层级第三层的置换门进行表征——这些是置换 基状态的单位算子。我们证明，层级第三层的任何置换门都是 Clifford 置换门的左右乘积下以阶梯形式的 Toffoli 门的乘积。随后，我们给出阶梯形式置换门是否属于层级第三层的必要充分条件。作为推论，我们构造了一个非半-Clifford 置换门族 ，其中每个 属于层级第三层，但其逆向不属于第 层。
关键词
引用
@article{arxiv.2510.04993,
title = {Characterization of permutation gates in the third level of the Clifford hierarchy},
author = {Zhiyang He and Luke Robitaille and Xinyu Tan},
journal= {arXiv preprint arXiv:2510.04993},
year = {2025}
}
备注
Supersedes arXiv:2410.11818, which established only a necessary but not sufficient condition for a permutation gate to lie in the third level of the Clifford hierarchy, and did not include the gates $U_k$ described in the abstract of the present paper