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New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm

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Abstract

We present a new method of more speedily calculating a multiplication by using the generalized Bernstein-Vazirani algorithm and many parallel quantum systems. Given the set of real values \(\{a_{1},a_{2},a_{3},\ldots ,a_{N}\}\) and a function \(g:\textbf {R}\rightarrow \{0,1\}\), we shall determine the following values \(\{g(a_{1}),g(a_{2}),g(a_{3}),\ldots , g(a_{N})\}\) simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of \(N\). Next, we consider it as a number in binary representation; M1 = (g(a1),g(a2),g(a3),…,g(a N )). By using \(M\) parallel quantum systems, we have \(M\) numbers in binary representation, simultaneously. The speed of obtaining the \(M\) numbers is shown to outperform the classical case by a factor of \(M\). Finally, we calculate the product; \( M_{1}\times M_{2}\times \cdots \times M_{M}. \) The speed of obtaining the product is shown to outperform the classical case by a factor of N × M.

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Acknowledgements

All authors are grateful to the anonymous referees who provided a great insight into the completion of the final manuscript.

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Authors and Affiliations

  1. Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Korea

    Koji Nagata

  2. Department of Information and Computer Science, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

    Tadao Nakamura

  3. Geurdes Datascience, KvK 64522202, C vd Lijnstraat 164, 2593, NN, Den Haag, Netherlands

    Han Geurdes

  4. Departament de Física, Universitat de les Illes Balears, 07122 Palma de Mallorca, Balearic Islands, Spain

    Josep Batle

  5. Faculty of Science, Department of Physics, King Abdulaziz University Jeddah, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Soliman Abdalla

  6. Faculty of Computers and Information, Computer Sciences Department, Mansoura University, Mansoura, Egypt

    Ahmed Farouk

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  1. Koji Nagata
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  2. Tadao Nakamura
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  3. Han Geurdes
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  4. Josep Batle
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  5. Soliman Abdalla
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  6. Ahmed Farouk
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Correspondence to Koji Nagata.

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Nagata, K., Nakamura, T., Geurdes, H. et al. New Method of Calculating a Multiplication by using the Generalized Bernstein-Vazirani Algorithm. Int J Theor Phys 57, 1605–1611 (2018). https://doi.org/10.1007/s10773-018-3687-5

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  • DOI: https://doi.org/10.1007/s10773-018-3687-5

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