单向量子行走：演化和退出时间
Unidirectional quantum walks: evolution and exit times
摘要：
在本文中，我们把注意力集中在一个粒子，遵循单向量子行走，一个替代版本的当今广泛的离散时间量子行走的线。这里，在每个时间步长处的步行者可以保持在原地或者在固定方向上移动，例如，或向上。虽然这两种公式基本上是等效的，本方法导致考虑离散傅立叶变换，这最终导致在有限和方面获得波函数的显式表达式，并允许使用基于快速傅立叶变换的高效算法。这里得到的波函数决定了在任意给定位置找到粒子的概率，但也决定了步行者从固定间隔出发的退出时间概率，这也被分析了。
英文摘要：
In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in place or move in a fixed direction, e.g., rightward or upward. While both formulations are essentially equivalent, the present approach leads to consider Discrete Fourier Transforms, which eventually results in obtaining explicit expressions for the wave functions in terms of finite sums, and allows the use of efficient algorithms based on the Fast Fourier Transform. The wave functions here obtained govern the probability of finding the particle at any given location, but determine as well the exit-time probability of the walker from a fixed interval, which is also analyzed.
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