Skip to main content
SpringerLink
Log in

Necessary and Sufficient Condition for Quantum Computing

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

A necessary and sufficient condition for quantum computing performed with, for example, the Deutsch-Jozsa algorithm or the Bernstein-Vazirani algorithm, has theoretically been investigated. Assume a 2N qubit-quantum computing which starts with the state \(|\overbrace {0,0,...,0,1}^{N}\rangle |\overbrace {1,1,...,1}^{N}\rangle \) as follows: Uf|0,0,...,0,1〉|1,1,...,1〉 = |0,0,...,0,1〉 \( |\overline {f(0,0,...,0,1)}\rangle . \) Surprisingly the relation f(x) = f(−x) is the necessary and sufficient condition of holding this fundamental relation if local unitary operations can be used.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Rennie, R. (ed.): Oxford dictionary of physics, 7th. Oxford University Press, Oxford (2015)

  2. Deutsch, D.: Soc, Proc. Roy. London Ser. A 400, 97 (1985)

    Article  ADS  Google Scholar 

  3. Deutsch, D., Jozsa, R.: Proc. Roy. Soc. London Ser. A 439, 553 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  4. Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Proc. Roy. Soc. London Ser. A 454, 339 (1998)

    Article  ADS  Google Scholar 

  5. Jones, J.A., Mosca, M.: J. Chem. Phys. 109, 1648 (1998)

    Article  ADS  Google Scholar 

  6. Gulde, S., Riebe, M., Lancaster, G.P.T., Becher, C., Eschner, J., Häffner, H., Schmidt-Kaler, F., Chuang, I.L., Blatt, R.: Nat. (London) 421, 48 (2003)

    Article  ADS  Google Scholar 

  7. de Oliveira, A.N., Walborn, S.P., Monken, C.H.: J. Opt. B: Quantum Semiclass. Opt. 7, 288–292 (2005)

  8. Kim, Y.-H.: Rev, Phys. A 67(R), 040301 (2003)

    Article  Google Scholar 

  9. Mohseni, M., Lundeen, J.S., Resch, K.J., Steinberg, A.M.: Phys. Rev. Lett. 91, 187903 (2003)

    Article  ADS  Google Scholar 

  10. Tame, M.S., Prevedel, R., Paternostro, M., Böhi, P., Kim, M.S., Zeilinger, A.: Phys. Rev. Lett. 98, 140501 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  11. Bernstein, E., Vazirani, U.: . In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing (STOC ’93), pp 11–20 (1993)

  12. Bernstein, E., Vazirani, U.: SIAM J. Comput. 26-5, 1411–1473 (1997)

    Article  Google Scholar 

  13. Nagata, K., Resconi, G., Nakamura, T., Batle, J., Abdalla, S., Farouk, A.: MOJ Ecol Environ Sci 2(1), 00010 (2017)

    Google Scholar 

  14. Simon, D.R.: Foundations of computer science. In: Proceedings 35th Annual Symposium on: 116-123, retrieved 2011-06-06 (1994)

  15. Shor, P.W.: . In: Proceedings of the 35th IEEE Symposium on Foundations of computer science, p 124 (1994)

  16. Grover, L.K.: . In: Proceedings of the twenty-eighth annual ACM symposium on theory of computing, p 212 (1996)

  17. Du, J., Shi, M., Zhou, X., Fan, Y., Ye, B.J., Han, R., Wu, J.: Phys. Rev. A 64, 042306 (2001)

    Article  ADS  Google Scholar 

  18. Brainis, E., Lamoureux, L.-P., Cerf, N.J., Emplit, P.h., Haelterman, M., Massar, S.: Phys. Rev. Lett. 90, 157902 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  19. Cross, A.W., Smith, G., Smolin, J.A.: Phys. Rev. A 92, 012327 (2015)

    Article  ADS  Google Scholar 

  20. Li, H., Yang, L.: Quantum Inf. Process. 14, 1787 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  21. Adcock, M.R.A., Hoyer, P., Sanders, B.C.: Quantum Inf. Process. 15, 1361 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  22. Fallek, S.D., Herold, C.D., McMahon, B.J., Maller, K.M., Brown, K.R., Amini, J.M.: New J. Phys. 18, 083030 (2016)

    Article  ADS  Google Scholar 

  23. Diep, D.N., Giang, D.H., Van Minh, N.: Int. J. Theor. Phys. 56, 1948 (2017)

    Article  Google Scholar 

  24. Jin, W.: Quantum Inf. Process. 15, 65 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  25. 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 

  26. Nagata, K., Nakamura, T., Geurdes, H., Batle, J., Abdalla, S., Farouk, A., Diep, D.N.: Int. J. Theor. Phys. 57, 973 (2018)

    Article  Google Scholar 

  27. Nagata, K., Nakamura, T., Geurdes, H., Batle, J., Abdalla, S., Farouk, A.: Int. J. Theor. Phys. 57, 1605 (2018)

    Article  Google Scholar 

  28. Nagata, K., Nakamura, T.: J Sci Eng Res 5(3), 326–328 (2018)

    Google Scholar 

  29. Nagata, K., Nakamura, T., Batle, J., Farouk, A.: Int. J. Theor. Phys. 57, 3098 (2018)

    Article  Google Scholar 

  30. Nagata, K., Nakamura, T.: Open Access Library J. 2, e1798 (2015)

    Google Scholar 

  31. Nagata, K., Nakamura, T.: Int. J. Theor. Phys. 56, 2086 (2017)

    Article  Google Scholar 

  32. Nagata, K., Nakamura, T., Farouk, A.: Int. J. Theor. Phys. 56, 2887 (2017)

    Article  Google Scholar 

  33. Diep, D.N., Giang, D.H.: Int. J. Theor. Phys. 56, 2797 (2017)

    Article  Google Scholar 

  34. Diep, D.N., Giang, D.H., Phu, P.H.: Int. J. Theor. Phys. 57, 841 (2018)

    Article  Google Scholar 

  35. Resconi, G., Nagata, K.: Intern. J. Gen. Eng. Technol. 7(1), 1–20 (2018)

    Google Scholar 

  36. Nagata, K., Nakamura, T., Geurdes, H., Batle, J., Farouk, A., Diep, D.N., Patro, S.K.: Int. J. Theor. Phys. 57, 2546 (2018)

    Article  Google Scholar 

  37. Nagata, K., Nakamura, T.: Quantum algorithm for the root-finding problem, Quantum Stud.: Math. Found. https://doi.org/10.1007/s40509-018-0171-0 (2018)

  38. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  39. Devitt, S.J., Munro, W.J., Nemoto, K.: Rep. Prog. Phys. 76, 076001 (2013)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank Professor Han Geurdes, Professor Shahrokh Heidari, Professor Hamed Daei Kasmaei, and Professor Mark Behzad Doost for valuable comments.

Author information

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. Department of Physics and Computer Science, Faculty of Science, Wilfrid Laurier University, Waterloo, Canada

    Ahmed Farouk

  4. TIMAS, Thang Long University, Nghiem Xuan Yem road, Hoang Mai district, Hanoi, Vietnam

    Do Ngoc Diep

  5. Institute of Mathematics, VAST, 18 Hoang Quoc Viet road, Cau Giay district, Hanoi, Vietnam

    Do Ngoc Diep

Authors
  1. Koji Nagata
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tadao Nakamura
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ahmed Farouk
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Do Ngoc Diep
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Koji Nagata.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nagata, K., Nakamura, T., Farouk, A. et al. Necessary and Sufficient Condition for Quantum Computing. Int J Theor Phys 58, 136–142 (2019). https://doi.org/10.1007/s10773-018-3917-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-018-3917-x

Keywords

Search

Navigation