论文标题
二面体组的Cayley图上的三州量子步行
Three-state quantum walk on the Cayley Graph of the Dihedral Group
论文作者
论文摘要
通过一个旋转和一种反射产生的有限二面基团是非亚伯群的最简单情况。 cayley图是组的示意图。在本文中，对二面体组的Cayley图给予了很多关注。考虑到二面体组中元素的特征，我们提出了一个带有Grover Coin的二面体组的Caylay图上的三态离散时间量子步行（DTQW）的模型。我们得出了从原点开始的位置概率分布和返回概率的长时间限制的分析表达式。结果表明，定位效应受底层二面群，硬币操作员和初始状态的大小约束。我们还通过概率分布和指定位置的时间平均概率研究了所提出模型的属性。二面体组的Caylay图上三州Grover DTQW的丰富现象可以帮助社区更好地理解和开发新的量子算法。
The finite dihedral group generated by one rotation and one reflection 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 propose a model of three-state discrete-time quantum walk (DTQW) on the Caylay graph of the dihedral group with Grover coin. We derive analytic expressions for the the position probability distribution and the long-time limit of the return probability starting from the origin. It is shown that the localization effect is governed by the size of the underlying dihedral group, coin operator and initial state. We also numerically investigate the properties of the proposed model via the probability distribution and the time-averaged probability at the designated position. The abundant phenomena of three-state Grover DTQW on the Caylay graph of the dihedral group can help the community to better understand and to develop new quantum algorithms.
