N叉树上的离散时间量子随机行走

详细信息

Discrete-Time Quantum Random Walks on the N-ary Tree

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, China

Funds: The project was supported by the National Natural Science Foundation of China (Grant No. 11861057).

摘要: 通过离散时间量子随机行走的框架,我们研究了在N叉树上的离散时间量子随机行走, 该框架不需要硬币空间,仅仅只需要选择一个除了酉性再无其它限制的演化算子,并且包含了使用再生结构的轨道枚举和z变换. 作为结果,我们在封闭形式中计算了在根处的振幅的生成函数.
- 量子行走 /
- z变换 /
- 轨道枚举 /
- N叉树
Abstract: We study discrete-time quantum random walks on the $N$-ary tree by a framework for discrete-time quantum random walks, this framework has no need for coin spaces, it just choose the evolution operator with no constraints other than unitarity, and contain path enumeration using regeneration structures and $z$ transform. As a result, we calculate the generating function of the amplitude at the root in closed form.
- quantum random walk /
- z transform /
- path enumeration /
- N-ary tree