A quantum algorithm based on entanglement measure for classifying Boolean multivariate function into novel hidden classes

Mohammed Zidan; Abdel-Haleem Abdel-Aty; Duc Manh Nguyen; Ahmed S.A. Mohamed; Yazeed Al-Sbou; Hichem Eleuch; Mahmoud Abdel-Aty

Results in Physics (Dec 2019)

A quantum algorithm based on entanglement measure for classifying Boolean multivariate function into novel hidden classes

Mohammed Zidan,
Abdel-Haleem Abdel-Aty,
Duc Manh Nguyen,
Ahmed S.A. Mohamed,
Yazeed Al-Sbou,
Hichem Eleuch,
Mahmoud Abdel-Aty

Affiliations

Mohammed Zidan: University of Science and Technology, Zewail City of Science and Technology, October Gardens 12578, 6th of October City, Giza, Egypt; Center for Photonics and Smart Materials (CPSM), Zewail City of Science and Technology, October Gardens, 6th of October City, Giza 12578, Egypt; Corresponding author.
Abdel-Haleem Abdel-Aty: Department of Physics, College of Sciences, University of Bisha, Bisha 61922, P.O. Box 344, Saudi Arabia; Physics Department, Faculty of Science, Al-Azhar University, 71524 Assiut, Egypt
Duc Manh Nguyen: Coding and Information Theory Lab, University of Ulsan, Ulsan 44610, South Korea
Ahmed S.A. Mohamed: University of Science and Technology, Zewail City of Science and Technology, October Gardens 12578, 6th of October City, Giza, Egypt; Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza 12613, Egypt
Yazeed Al-Sbou: Deanship of Research and Graduate Studies, Applied Science University, P.O. Box 5055, 55222 Manama, Bahrain
Hichem Eleuch: Department of Applied Sciences and Mathematics, College of Arts and Sciences, Abu Dhabi University, Abu Dhabi, United Arab Emirates; Institute for Quantum Science and Engineering, Texas A&M University, College Station, TX 77843, USA
Mahmoud Abdel-Aty: University of Science and Technology, Zewail City of Science and Technology, October Gardens 12578, 6th of October City, Giza, Egypt; Center for Photonics and Smart Materials (CPSM), Zewail City of Science and Technology, October Gardens, 6th of October City, Giza 12578, Egypt; Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

Journal volume & issue: Vol. 15

Abstract

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In this paper, we propose a novel algorithm that solves a generalized version of the Deutsch-Jozsa problem. The proposed algorithm has the potential to classify an oracle UF, that represents an unknown Boolean function on n Boolean variables, to one of 2n different classes instead of only two classes which are constant and balanced classes in the case of Deutsch-Jozsa algorithm. The proposed algorithm is based on the use of entanglement measure to explore 2n-2 additional classes compared to the standard Deutsch-Jozsa algorithm. In addition, the comparison between the proposed quantum algorithm and the classical one is investigated in details. The comparison shows that the proposed algorithm is faster when the number of Boolean variables exceed 14 variables. Keywords: Quantum information, Quantum algorithm, Deutsch-Jozsa algorithm, Quantum entanglement measure

Published in Results in Physics

ISSN: 2211-3797 (Online)
Publisher: Elsevier
Country of publisher: Netherlands
LCC subjects: Science: Physics
Website: http://www.journals.elsevier.com/results-in-physics/

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