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Quantum Algorithm for Determining a Complex Number String

  • Koji NagataEmail author
  • Han Geurdes
  • Santanu Kumar Patro
  • Shahrokh Heidari
  • Ahmed Farouk
  • Tadao Nakamura
Article

Abstract

Here, we discuss the generalized Bernstein-Vazirani algorithm for determining a complex number string. The generalized algorithm presented here has the following structure. Given the set of complex values {a1, a2, a3,…, aN} and a special function \( g:\mathbf{C}\to \mathbf{C} \), we determine N real parts of values of the function l(a1), l(a2), l(a3),…, l(aN) and N imaginary parts of values of the function h(a1), h(a2), h(a3),…, h(aN) simultaneously. That is, we determine the N complex values g(aj) = l(aj) + ih(aj) simultaneously. We mention the two computing can be done in parallel computation method simultaneously. The speed of determining the string of complex values is shown to outperform the best classical case by a factor of N. Additionally, we propose a method for calculating many different matrices A, B, C,... into g(A), g(B), g(C),... simultaneously. The speed of solving the problem is shown to outperform the classical case by a factor of the number of the elements of them. We hope our discussions will give a first step to the quantum simulation problem.

Keywords

Quantum algorithms Quantum computation 

Notes

Acknowledgments

We thank Professor Do Ngoc Diep and Professor Germano Resconi for valuable comments.

Compliance with Ethical Standards

Conflict of interests

On behalf of all authors, the corresponding author states that there is no conflict of interest.

References

  1. 1.
    Bernstein, E., Vazirani, U.: In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing (STOC ’93), pp. 11–20 (1993)Google Scholar
  2. 2.
    Bernstein, E., Vazirani, U.: SIAM J. Comput. 26–5, 1411–1473 (1997)CrossRefGoogle Scholar
  3. 3.
    Du, J., Shi, M., Zhou, X., Fan, Y., Ye, B.J., Han, R., Wu, J.: Phys. Rev. A 64, 042306 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    Brainis, E., Lamoureux, L.-P., Cerf, N.J., Emplit, P.H., Haelterman, M., Massar, S.: Phys. Rev. Lett. 90, 157902 (2003)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Cross, A.W., Smith, G., Smolin, J.A.: Phys. Rev. A 92, 012327 (2015)ADSCrossRefGoogle Scholar
  6. 6.
    Li, H., Yang, L.: Quantum Inf. Process. 14, 1787 (2015)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Nagata, K., Nakamura, T., Farouk, A.: Int. J. Theor. Phys. 56, 2887 (2017)CrossRefGoogle Scholar
  8. 8.
    Fallek, S.D., Herold, C.D., McMahon, B.J., Maller, K.M., Brown, K.R., Amini, J.M.: New J. Phys. 18, 083030 (2016)ADSCrossRefGoogle Scholar
  9. 9.
    Krishna, R., Makwana, V., Suresh, A.P. arXiv:1609.03185 [quant-ph] (2016)
  10. 10.
    Nagata, K., Nakamura, T.: Int. J. Theor. Phys. 58, 247 (2019)CrossRefGoogle Scholar
  11. 11.
    Nagata, K., Geurdes, H., Patro, S.K., Heidari, S., Farouk, A., Nakamura, T.: Quantum Stud. Math. Found.  https://doi.org/10.1007/s40509-019-00196-4 (2019)

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsKorea Advanced Institute of Science and TechnologyDaejeonKorea
  2. 2.Geurdes DatascienceDen HaagNetherlands
  3. 3.Department of MathematicsBerhampur UniversityBerhampurIndia
  4. 4.Young Researchers and Elite Club, Kermanshah BranchIslamic Azad UniversityKermanshahIran
  5. 5.Department of Physics and Computer Science, Faculty of ScienceWilfrid Laurier UniversityWaterlooCanada
  6. 6.Center for Quantum Computing and Artificial Intelligent, Faculty of ScienceSohag UniversitySohagEgypt
  7. 7.Department of Information and Computer ScienceKeio UniversityKohoku-kuJapan

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