论文标题
通过光学偏光元素在图上使用循环矩阵实施离散时间量子步行的设计
Design for implementation of discrete-time quantum walk with circulant matrix on graph by optical polarizing elements
论文作者
论文摘要
在本文中，我们引入了一次量子步行，其在每个顶点的局部散射都用一个单一的循环矩阵表示。即循环量子步行。我们还引入了另一个由循环量子步行引起的量子步行。也就是说，光学量子步行的基础图是$ 2 $的定向图，并通过以某种方式炸毁原始图来获得。我们提出了一个光电路的设计，该设计实现了光学量子步行的固定状态。我们表明，如果感应的光学量子步行不具有$+1 $特征值，则光学量子步行的固定状态将提供原始循环量子步行的速度。从这个结果，我们为设置循环量子步道的设置提供了有用的条件，该量子可以通过该光电路实现。
In this paper, we introduce a quantum walk whose local scattering at each vertex is denoted by a unitary circulant matrix; namely the circulant quantum walk. We also introduce another quantum walk induced by the circulant quantum walk; namely the optical quantum walk, whose underlying graph is a $2$-regular directed graph and obtained by blowing up the original graph in some way. We propose a design of an optical circuit which implements the stationary state of the optical quantum walk. We show that if the induced optical quantum walk does not have $+1$ eigenvalue, then the stationary state of the optical quantum walk gives that of the original circulant quantum walk. From this result, we give a useful condition for the setting of the circulant quantum walks which can be implemented by this optical circuit.
