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Efficient quantum circuits for dense circulant and circulant like operators

Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering-related fields. They are, in general, non-sparse and non-unitary. In this paper, we present efficient quantum circuits to implement circulant operators using fewer resources an...

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Detalles Bibliográficos
Autores principales: Zhou, S. S., Wang, J. B.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5451789/
https://www.ncbi.nlm.nih.gov/pubmed/28572988
http://dx.doi.org/10.1098/rsos.160906
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author Zhou, S. S.
Wang, J. B.
author_facet Zhou, S. S.
Wang, J. B.
author_sort Zhou, S. S.
collection PubMed
description Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering-related fields. They are, in general, non-sparse and non-unitary. In this paper, we present efficient quantum circuits to implement circulant operators using fewer resources and with lower complexity than existing methods. Moreover, our quantum circuits can be readily extended to the implementation of Toeplitz, Hankel and block circulant matrices. Efficient quantum algorithms to implement the inverses and products of circulant operators are also provided, and an example application in solving the equation of motion for cyclic systems is discussed.
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spelling pubmed-54517892017-06-01 Efficient quantum circuits for dense circulant and circulant like operators Zhou, S. S. Wang, J. B. R Soc Open Sci Physics Circulant matrices are an important family of operators, which have a wide range of applications in science and engineering-related fields. They are, in general, non-sparse and non-unitary. In this paper, we present efficient quantum circuits to implement circulant operators using fewer resources and with lower complexity than existing methods. Moreover, our quantum circuits can be readily extended to the implementation of Toeplitz, Hankel and block circulant matrices. Efficient quantum algorithms to implement the inverses and products of circulant operators are also provided, and an example application in solving the equation of motion for cyclic systems is discussed. The Royal Society Publishing 2017-05-10 /pmc/articles/PMC5451789/ /pubmed/28572988 http://dx.doi.org/10.1098/rsos.160906 Text en © 2017 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Physics
Zhou, S. S.
Wang, J. B.
Efficient quantum circuits for dense circulant and circulant like operators
title Efficient quantum circuits for dense circulant and circulant like operators
title_full Efficient quantum circuits for dense circulant and circulant like operators
title_fullStr Efficient quantum circuits for dense circulant and circulant like operators
title_full_unstemmed Efficient quantum circuits for dense circulant and circulant like operators
title_short Efficient quantum circuits for dense circulant and circulant like operators
title_sort efficient quantum circuits for dense circulant and circulant like operators
topic Physics
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5451789/
https://www.ncbi.nlm.nih.gov/pubmed/28572988
http://dx.doi.org/10.1098/rsos.160906
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