Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks
- School of Physical Science and Technology, Soochow University, Suzhou 215006 (China)
- Department of Information Systems Creation, Faculty of Engineering, Kanagawa University, Yokohama, Kanagawa, 221-8686 (Japan)
In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.
- OSTI ID:
- 22617410
- Journal Information:
- Annals of Physics, Vol. 373; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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