2018/09/29 by Wenjing Dai, Dai, Wenjing, Jiabin Yuan +3 · 1 citation
Computer Science · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata
paper · pdf · doi:10.48550/arxiv.1810.00158
openalex publication_date 2018/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The finite dihedral group generated by one rotation and one flip is the simplest case of the non-abelian group. Cayley graphs are diagrammatic counterparts of groups. In this paper, much attention is given to the Cayley graph of the dihedral group. Considering the characteristics of the elements in the dihedral group, we conduct the model of discrete-time quantum walk on the Cayley graph of the dihedral group by special coding mode. This construction makes Fourier transformation can be used to carry out spectral analysis of the dihedral quantum walk, i.e. the non-abelian case. Furthermore, the relation between quantum walk without memory on the Cayley graph of the dihedral group and quantum walk with memory on a cycle is discussed, so that we can explore the potential of quantum walks without and with memory. Here, the numerical simulation is carried out to verify the theoretical analysis results and other properties of the proposed model are further studied.