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Higher-Dimensional Quantum Walk in Terms of Quantum Bernoulli Noises
As a discrete-time quantum walk model on the one-dimensional integer lattice [Formula: see text] , the quantum walk recently constructed by Wang and Ye [Caishi Wang and Xiaojuan Ye, Quantum walk in terms of quantum Bernoulli noises, Quantum Information Processing 15 (2016), 1897–1908] exhibits quite...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516995/ https://www.ncbi.nlm.nih.gov/pubmed/33286277 http://dx.doi.org/10.3390/e22050504 |
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author | Wang, Ce Wang, Caishi |
author_facet | Wang, Ce Wang, Caishi |
author_sort | Wang, Ce |
collection | PubMed |
description | As a discrete-time quantum walk model on the one-dimensional integer lattice [Formula: see text] , the quantum walk recently constructed by Wang and Ye [Caishi Wang and Xiaojuan Ye, Quantum walk in terms of quantum Bernoulli noises, Quantum Information Processing 15 (2016), 1897–1908] exhibits quite different features. In this paper, we extend this walk to a higher dimensional case. More precisely, for a general positive integer [Formula: see text] , by using quantum Bernoulli noises we introduce a model of discrete-time quantum walk on the d-dimensional integer lattice [Formula: see text] , which we call the d-dimensional QBN walk. The d-dimensional QBN walk shares the same coin space with the quantum walk constructed by Wang and Ye, although it is a higher dimensional extension of the latter. Moreover we prove that, for a range of choices of its initial state, the d-dimensional QBN walk has a limit probability distribution of d-dimensional standard Gauss type, which is in sharp contrast with the case of the usual higher dimensional quantum walks. Some other results are also obtained. |
format | Online Article Text |
id | pubmed-7516995 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75169952020-11-09 Higher-Dimensional Quantum Walk in Terms of Quantum Bernoulli Noises Wang, Ce Wang, Caishi Entropy (Basel) Article As a discrete-time quantum walk model on the one-dimensional integer lattice [Formula: see text] , the quantum walk recently constructed by Wang and Ye [Caishi Wang and Xiaojuan Ye, Quantum walk in terms of quantum Bernoulli noises, Quantum Information Processing 15 (2016), 1897–1908] exhibits quite different features. In this paper, we extend this walk to a higher dimensional case. More precisely, for a general positive integer [Formula: see text] , by using quantum Bernoulli noises we introduce a model of discrete-time quantum walk on the d-dimensional integer lattice [Formula: see text] , which we call the d-dimensional QBN walk. The d-dimensional QBN walk shares the same coin space with the quantum walk constructed by Wang and Ye, although it is a higher dimensional extension of the latter. Moreover we prove that, for a range of choices of its initial state, the d-dimensional QBN walk has a limit probability distribution of d-dimensional standard Gauss type, which is in sharp contrast with the case of the usual higher dimensional quantum walks. Some other results are also obtained. MDPI 2020-04-28 /pmc/articles/PMC7516995/ /pubmed/33286277 http://dx.doi.org/10.3390/e22050504 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Wang, Ce Wang, Caishi Higher-Dimensional Quantum Walk in Terms of Quantum Bernoulli Noises |
title | Higher-Dimensional Quantum Walk in Terms of Quantum Bernoulli Noises |
title_full | Higher-Dimensional Quantum Walk in Terms of Quantum Bernoulli Noises |
title_fullStr | Higher-Dimensional Quantum Walk in Terms of Quantum Bernoulli Noises |
title_full_unstemmed | Higher-Dimensional Quantum Walk in Terms of Quantum Bernoulli Noises |
title_short | Higher-Dimensional Quantum Walk in Terms of Quantum Bernoulli Noises |
title_sort | higher-dimensional quantum walk in terms of quantum bernoulli noises |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516995/ https://www.ncbi.nlm.nih.gov/pubmed/33286277 http://dx.doi.org/10.3390/e22050504 |
work_keys_str_mv | AT wangce higherdimensionalquantumwalkintermsofquantumbernoullinoises AT wangcaishi higherdimensionalquantumwalkintermsofquantumbernoullinoises |