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

  • Koji Nagata
  • Tadao Nakamura
  • Han Geurdes
  • Josep Batle
  • Soliman Abdalla
  • Ahmed Farouk
Article
  • 7 Downloads

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.

Keywords

Quantum computation Quantum algorithms 

Notes

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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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Koji Nagata
    • 1
  • Tadao Nakamura
    • 2
  • Han Geurdes
    • 3
  • Josep Batle
    • 4
  • Soliman Abdalla
    • 5
  • Ahmed Farouk
    • 6
  1. 1.Department of PhysicsKorea Advanced Institute of Science and TechnologyDaejeonKorea
  2. 2.Department of Information and Computer ScienceKeio UniversityYokohamaJapan
  3. 3.Geurdes DatascienceDen HaagNetherlands
  4. 4.Departament de FísicaUniversitat de les Illes BalearsBalearic IslandsSpain
  5. 5.Faculty of Science, Department of PhysicsKing Abdulaziz University JeddahJeddahSaudi Arabia
  6. 6.Faculty of Computers and Information, Computer Sciences DepartmentMansoura UniversityMansouraEgypt

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