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Duality quantum algorithm efficiently simulates open quantum systems

Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evol...

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Detalles Bibliográficos
Autores principales: Wei, Shi-Jie, Ruan, Dong, Long, Gui-Lu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4964360/
https://www.ncbi.nlm.nih.gov/pubmed/27464855
http://dx.doi.org/10.1038/srep30727
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author Wei, Shi-Jie
Ruan, Dong
Long, Gui-Lu
author_facet Wei, Shi-Jie
Ruan, Dong
Long, Gui-Lu
author_sort Wei, Shi-Jie
collection PubMed
description Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d(3)) in contrast to O(d(4)) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
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spelling pubmed-49643602016-08-08 Duality quantum algorithm efficiently simulates open quantum systems Wei, Shi-Jie Ruan, Dong Long, Gui-Lu Sci Rep Article Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d(3)) in contrast to O(d(4)) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm. Nature Publishing Group 2016-07-28 /pmc/articles/PMC4964360/ /pubmed/27464855 http://dx.doi.org/10.1038/srep30727 Text en Copyright © 2016, The Author(s) http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Wei, Shi-Jie
Ruan, Dong
Long, Gui-Lu
Duality quantum algorithm efficiently simulates open quantum systems
title Duality quantum algorithm efficiently simulates open quantum systems
title_full Duality quantum algorithm efficiently simulates open quantum systems
title_fullStr Duality quantum algorithm efficiently simulates open quantum systems
title_full_unstemmed Duality quantum algorithm efficiently simulates open quantum systems
title_short Duality quantum algorithm efficiently simulates open quantum systems
title_sort duality quantum algorithm efficiently simulates open quantum systems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4964360/
https://www.ncbi.nlm.nih.gov/pubmed/27464855
http://dx.doi.org/10.1038/srep30727
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