Discrete-time quantum walk on the Cayley graph of the dihedral group
Discrete-time quantum walk on the Cayley graph of the dihedral group
复制标题
二面体群凯莱图上的离散时间量子行走
DOI：
10.1007/s11128-018-2101-9
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发表时间：
2018
影响因子：
2.5
通讯作者：
Dan Li
中科院分区：
文献类型：
--
作者：
Wenjing Dai;Jiabin Yuan;Dan Li
由一次旋转和一次翻转生成的有限二面体群是非阿贝尔群的最简单情况。凯莱图是群的图解对应物。本文重点关注二面群的凯莱图。考虑到二面体群元素的特点，我们通过特殊的编码方式在二面体群的凯莱图上建立了离散时间量子游走模型。这种结构使得傅立叶变换可用于进行二面体量子行走（即非阿贝尔情况）的谱分析。此外，讨论了二面体群凯莱图上的无记忆量子行走与循环上有记忆量子行走之间的关系，以便我们可以探索无记忆和有记忆量子行走的潜力。这里，进行数值模拟以验证理论分析结果，并进一步研究所提出模型的其他特性。
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 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.