Implementation of a discrete-time quantum walk with a circulant matrix on a graph by optical polarizing elements
Implementation of a discrete-time quantum walk with a circulant matrix on a graph by optical polarizing elements
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通过光学偏振元件在图上实现带有循环矩阵的离散时间量子行走
DOI：
10.1103/physreva.106.022402
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发表时间：
2022
影响因子：
2.9
通讯作者：
Segawa Etsuo
中科院分区：
文献类型：
--
作者：
Mizutani Yusuke;Horikiri Tomoyuki;Matsuoka Leo;Higuchi Yusuke;Segawa Etsuo
在本文中，我们引入了一种量子行走，其在每个顶点的局部散射由一个酉循环矩阵表示，即循环量子行走。我们还介绍了由循环量子行走引起的另一种量子行走，即光量子行走，它的底层图是一个2-正则有向图，通过某种方式将原图爆破而得到。我们提出了一种实现光量子行走稳态的光路设计。我们证明了如果诱导光量子行走没有本征值，则光量子行走的定态与原循环量子行走的定态相同。从这个结果出发，我们给出了一个可由该光路实现的循环量子行走的条件。
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 haveeigenvalue, 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.