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Discrete-time Quantum Walk on the Cayley Graph of the Dihedral Group
- Publication Year :
- 2018
-
Abstract
- 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.<br />21 pages, 6 figures
- Subjects :
- Discrete mathematics
Quantum Physics
Cayley graph
FOS: Physical sciences
Statistical and Nonlinear Physics
Dihedral angle
Dihedral group
01 natural sciences
010305 fluids & plasmas
Theoretical Computer Science
Electronic, Optical and Magnetic Materials
Diagrammatic reasoning
symbols.namesake
Fourier transform
Discrete time and continuous time
Modeling and Simulation
0103 physical sciences
Signal Processing
symbols
Quantum walk
Electrical and Electronic Engineering
Quantum Physics (quant-ph)
010306 general physics
Mathematics
Quantum computer
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....bac8e36ae1311ff0217070a9c20356f8