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International Journal of Theoretical Physics

, Volume 57, Issue 4, pp 973–980 | Cite as

Creating Very True Quantum Algorithms for Quantum Energy Based Computing

  • Koji NagataEmail author
  • Tadao Nakamura
  • Han Geurdes
  • Josep Batle
  • Soliman Abdalla
  • Ahmed Farouk
  • Do Ngoc Diep
Article

Abstract

An interpretation of quantum mechanics is discussed. It is assumed that quantum is energy. An algorithm by means of the energy interpretation is discussed. An algorithm, based on the energy interpretation, for fast determining a homogeneous linear function f(x) := s.x = s 1 x 1 + s 2 x 2 + ⋯ + s N x N is proposed. Here x = (x 1, … , x N ), x j R and the coefficients s = (s 1, … , s N ), s j N. Given the interpolation values \((f(1), f(2),...,f(N))=\vec {y}\), the unknown coefficients \(s = (s_{1}(\vec {y}),\dots , s_{N}(\vec {y}))\) of the linear function shall be determined, simultaneously. The speed of determining the values is shown to outperform the classical case by a factor of N. Our method is based on the generalized Bernstein-Vazirani algorithm to qudit systems. Next, by using M parallel quantum systems, M homogeneous linear functions are determined, simultaneously. The speed of obtaining the set of M homogeneous linear functions is shown to outperform the classical case by a factor of N × M.

Keywords

Quantum computation Quantum algorithms 

Notes

Acknowledgements

We thank Prof. Germano Resconi and Prof. Shahrokh Heidari for valuable comments.

References

  1. 1.
    De Broglie-Bohm theory - Wikipedia, the free encyclopediaGoogle Scholar
  2. 2.
    Schon, C., Beige, A.: Phys. Rev. A 64, 023806 (2001)ADSCrossRefGoogle Scholar
  3. 3.
    Deutsch, D.: Proc. Roy. Soc. London Ser. A 400, 97 (1985)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Deutsch, D., Jozsa, R.: Proc. Roy. Soc. London Ser. A 439, 553 (1992)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Proc. Roy. Soc. London Ser. A 454, 339 (1998)ADSCrossRefGoogle Scholar
  6. 6.
    Jones, J.A., Mosca, M.: J. Chem. Phys. 109, 1648 (1998)ADSCrossRefGoogle Scholar
  7. 7.
    Gulde, S., Riebe, M., Lancaster, G.P.T., Becher, C., Eschner, J., Häffner, H., Schmidt-Kaler, F., Chuang, I.L., Blatt, R.: Nature (London) 421, 48 (2003)ADSCrossRefGoogle Scholar
  8. 8.
    de Oliveira, A.N., Walborn, S.P., Monken, C.H.: J. Opt. B: Quantum Semiclass. Opt. 7, 288–292 (2005)ADSCrossRefGoogle Scholar
  9. 9.
    Mohseni, M., Lundeen, J.S., Resch, K.J., Steinberg, A.M.: Phys. Rev. Lett. 91, 187903 (2003)ADSCrossRefGoogle Scholar
  10. 10.
    Tame, M.S., Prevedel, R., Paternostro, M., Böhi, P., Kim, M.S., Zeilinger, A.: Phys. Rev. Lett. 98, 140501 (2007)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    Bernstein, E., Vazirani, U.: . In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing (STOC ’93), pp 11–20 (1993).  https://doi.org/10.1145/167088.167097
  12. 12.
    Bernstein, E., Vazirani, U.: SIAM J. Comput. 26-5, 1411–1473 (1997)CrossRefGoogle Scholar
  13. 13.
    Simon, D.R.: Foundations of computer science. In: 35th Annual Symposium on Proceedings. retrieved 2011-06-06, pp 116–123 (1994)Google Scholar
  14. 14.
    Du, J., Shi, M., Zhou, X., Fan, Y., Ye, B.J., Han, R., Wu, J.: Phys. Rev. A 64, 042306 (2001)ADSCrossRefGoogle Scholar
  15. 15.
    Brainis, E., Lamoureux, L.-P., Cerf, N.J., Emplit, P.h., Haelterman, M., Massar, S.: Phys. Rev. Lett. 90, 157902 (2003)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Cross, A.W., Smith, G., Smolin, J.A.: Phys. Rev. A 92, 012327 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    Li, H., Yang, L.: Quantum Inf. Process. 14, 1787 (2015)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Adcock, M.R.A., Hoyer, P., Sanders, B.C.: Quantum Inf. Process. 15, 1361 (2016)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    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
  20. 20.
    Diep, D.N., Giang, D.H., Van Minh, N.: Int. J Theor. Phys. 56, 1948 (2017).  https://doi.org/10.1007/s10773-017-3340-8 CrossRefGoogle Scholar
  21. 21.
    Jin, W.: Quantum Inf. Process. 15, 65 (2016)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Nagata, K., Resconi, G., Nakamura, T., Batle, J., Abdalla, S., Farouk, A., Geurdes, H.: Asian J. Math. Phys. 1(1), 1–4 (2017)Google Scholar
  23. 23.
    Nagata, K., Nakamura, T.: Open Access Library J 2, e1798 (2015).  https://doi.org/10.4236/oalib.1101798 Google Scholar
  24. 24.
    Nagata, K., Nakamura, T.: Int. J. Theor. Phys. 56, 2086 (2017).  https://doi.org/10.1007/s10773-017-3352-4 CrossRefGoogle Scholar
  25. 25.
    Nagata, K., Nakamura, T., Farouk, A.: Int. J. Theor. Phys. 56, 2887 (2017).  https://doi.org/10.1007/s10773-017-3456-x CrossRefGoogle Scholar
  26. 26.
    Diep, D.N., Giang, D.H.: Int. J. Theor. Phys. 56, 2797 (2017).  https://doi.org/10.1007/s10773-017-3444-1 CrossRefGoogle Scholar
  27. 27.
    Nagata, K., Resconi, G., Nakamura, T., Batle, J., Abdalla, S., Farouk, A.: MOJ Ecology Environ. Sci. 2(1), 00010 (2017)Google Scholar
  28. 28.
    Krishna, R., Makwana, V., Suresh, A.P.: arXiv:1609.03185[quant-ph] (2016)

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  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 BalearsPalma de MallorcaSpain
  5. 5.Department of Physics, Faculty of ScienceKing Abdulaziz University JeddahJeddahSaudi Arabia
  6. 6.Computer Sciences Department, Faculty of Computers and InformationMansoura UniversityMansouraEgypt
  7. 7.TIMASThang Long University, Nghiem Xuan Yem, Dai Kim, Hoang MaiHanoiVietnam

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