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

Abstract

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.

Keywords:

• Perfect quantum state transfer
• Cayley graph
• spectrum
• semi-dihedral group

2010 Mathematics Subject Classifications:

• 05C25
• 81P45
• 81Q35

Acknowledgements

We are grateful to the anonymous referees and the editor for useful comments and suggestions that improved the presentation and quality of this paper.

Data availability statements

All data included in this paper are available upon request by contact with the corresponding author.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the NTU Research Grant 04INS000047C230GRT01 and the National Natural Science Foundation of China [grant numbers 11771007, 11971102, 11801070 and 61572027].