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Unidirectional quantum walks: Evolution and exit times
Montero Torralbo, Miquel
Universitat de Barcelona
In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the currently 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 us 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.
Partícules (Física nuclear)
Transformacions de Fourier
Ordinadors quàntics
Física matemàtica
Algorismes computacionals
Particles (Nuclear physics)
Fourier transformations
Quantum computers
Mathematical physics
Computer algorithms
(c) American Physical Society, 2013
American Physical Society

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