From Discrete Time Quantum Walk to Continuous Time Quantum Walk in Limit Distribution
Quantum Physics
2013-07-15 v1 Mathematical Physics
math.MP
Probability
Cellular Automata and Lattice Gases
Abstract
The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic behavior, of the one-dimensional discrete time quantum walk is analytically shown. From the limit distribution of the discrete time quantum walk, the discrete time quantum walk can be taken as the quantum dynamical simulator of some physical systems.
Cite
@article{arxiv.1307.3384,
title = {From Discrete Time Quantum Walk to Continuous Time Quantum Walk in Limit Distribution},
author = {Yutaka Shikano},
journal= {arXiv preprint arXiv:1307.3384},
year = {2013}
}
Comments
This is the invited review paper on the special issue on Theoretical and Mathematical Aspects of Discrete Time Quantum Walk from Journal of Computational and Theoretical Nanoscience