The quantum Perfect State Transfer (PST) is a fundamental tool of quantum communication in a network. It is not easy to achieve in practice. The original idea of PST depends on the fundamentals of the continuous-time quantum walk. A path graph with at most three vertices allows PST based on continuous-time quantum walk. Based on the Markovian quantum walk, we introduce a significantly powerful method for PST in this article. We establish PST between the extreme vertices of a path graph of arbitrary length. Moreover, any pair of symmetric vertices in a path graph allows PST under Markovian quantum walks. We extend our investigations for the cycle graphs. The cycle graphs with more than $4$ vertices do not allow the PST based on the continuous-time quantum walk. In contrast, a cycle graph with $2m$ vertices exhibits PST based on Markovian quantum walk between the vertices $j$ and $j + m$ for $j = 0, 1, \dots (m - 1)$, where $m > 0$ is an integer.

翻译：量子完美态传输（PST）是量子网络通信的一项基本工具，但在实践中难以实现。原始的PST构想依赖于连续时间量子行走的基本原理。基于连续时间量子行走，仅顶点数不超过三个的路径图可实现PST。本文基于马尔可夫量子行走，提出了一种显著更强大的PST实现方法。我们实现了任意长度路径图两端顶点间的PST。此外，在马尔可夫量子行走下，路径图中任意对称顶点对均可实现PST。我们将研究进一步拓展至环图。基于连续时间量子行走，顶点数大于$4$的环图无法实现PST。与之相对，具有$2m$个顶点的环图在马尔可夫量子行走下，可在顶点$j$与$j + m$之间实现PST（其中$j = 0, 1, \dots (m - 1)$，$m > 0$为整数）。