Perfect quantum state transfer plays a crucial role in quantum information processing and quantum computation. There has been extensive study of perfect quantum state transfer on Cayley graphs over abelian groups. In this paper, we consider the existence of perfect quantum state transfer on Cayley graphs over semi-dihedral groups which are non-abelian groups. Using the representations of semi-dihedral groups, we provide some necessary and sufficient conditions for Cayley graphs over semi-dihedral groups admitting perfect quantum state transfer. By those conditions, we present examples of perfect quantum state transfer on Cayley graphs over semi-dihedral groups. In addition, we propose results about whether some new Cayley graphs over non-abelian groups admit perfect quantum state transfer.

完美的量子状态转移在量子信息处理和量子计算中起着至关重要的作用。已经对阿贝尔群上凯莱图上的完美​​量子态转移进行了广泛的研究。在本文中，我们考虑了非交换群半二面体群上凯莱图上完美量子态转移的存在性。使用半二面角群的表示，我们为允许完美量子态转移的半二面角群上的凯莱图提供了一些充分必要条件。通过这些条件，我们展示了半二面角群上凯莱图上完美量子态转移的例子。此外，我们提出了关于非交换群上的一些新凯莱图是否承认完美量子态转移的结果。