It has been shown classically that combining two chaotic random walks can yield an ordered(periodic) walk. Our aim in this paper is to find a quantum analog for this rather counter-intuitive result. We study chaotic and periodic nature of cyclic quantum walks and focus on a unique situation wherein a periodic quantum walk on a 3-cycle graph is generated via a deterministic combination of two chaotic quantum walks on the same graph. We extend our results to even-numbered cyclic graphs, specifically a 4-cycle graph too. Our results will be relevant in quantum cryptography and quantum chaos control.

翻译：经典地显示,将两个混乱无序的随机行走结合起来,可以产生一个有秩序的(定期)行走。我们在本文中的目的是为这个反直觉的结果找到一个量子类比。我们研究周期性量子行走的混乱性和周期性,并关注一个独特的情况,即三周期图上的定期量子行走是通过同一图上的两次混乱量行走的决定性组合产生的。我们把结果扩大到偶数的周期性图表,特别是四周期图。我们的结果将在量子加密和量子混乱控制中产生。