Perfect quantum state transfer on Cayley graphs over semi-dihedral groups

• Main Authors: Luo, Gaojun, Cao, Xiwang, Wang, Dandan, Wu, Xia
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2022
• Subjects: Science::Mathematics::Algebra; Perfect Quantum State Transfer; Cayley Graph
• Online Access: https://hdl.handle.net/10356/156041
• Institution: Nanyang Technological University

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.