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.
Similar content being viewed by others
References
Rennie, R. (ed.): Oxford dictionary of physics, 7th. Oxford University Press, Oxford (2015)
Deutsch, D.: Soc, Proc. Roy. London Ser. A 400, 97 (1985)
Deutsch, D., Jozsa, R.: Proc. Roy. Soc. London Ser. A 439, 553 (1992)
Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Proc. Roy. Soc. London Ser. A 454, 339 (1998)
Jones, J.A., Mosca, M.: J. Chem. Phys. 109, 1648 (1998)
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)
de Oliveira, A.N., Walborn, S.P., Monken, C.H.: J. Opt. B: Quantum Semiclass. Opt. 7, 288–292 (2005)
Kim, Y.-H.: Rev, Phys. A 67(R), 040301 (2003)
Mohseni, M., Lundeen, J.S., Resch, K.J., Steinberg, A.M.: Phys. Rev. Lett. 91, 187903 (2003)
Tame, M.S., Prevedel, R., Paternostro, M., Böhi, P., Kim, M.S., Zeilinger, A.: Phys. Rev. Lett. 98, 140501 (2007)
Bernstein, E., Vazirani, U.: . In: Proceedings of the Twenty-Fifth Annual ACM Symposium on Theory of Computing (STOC ’93), pp 11–20 (1993)
Bernstein, E., Vazirani, U.: SIAM J. Comput. 26-5, 1411–1473 (1997)
Nagata, K., Resconi, G., Nakamura, T., Batle, J., Abdalla, S., Farouk, A.: MOJ Ecol Environ Sci 2(1), 00010 (2017)
Simon, D.R.: Foundations of computer science. In: Proceedings 35th Annual Symposium on: 116-123, retrieved 2011-06-06 (1994)
Shor, P.W.: . In: Proceedings of the 35th IEEE Symposium on Foundations of computer science, p 124 (1994)
Grover, L.K.: . In: Proceedings of the twenty-eighth annual ACM symposium on theory of computing, p 212 (1996)
Du, J., Shi, M., Zhou, X., Fan, Y., Ye, B.J., Han, R., Wu, J.: Phys. Rev. A 64, 042306 (2001)
Brainis, E., Lamoureux, L.-P., Cerf, N.J., Emplit, P.h., Haelterman, M., Massar, S.: Phys. Rev. Lett. 90, 157902 (2003)
Cross, A.W., Smith, G., Smolin, J.A.: Phys. Rev. A 92, 012327 (2015)
Li, H., Yang, L.: Quantum Inf. Process. 14, 1787 (2015)
Adcock, M.R.A., Hoyer, P., Sanders, B.C.: Quantum Inf. Process. 15, 1361 (2016)
Fallek, S.D., Herold, C.D., McMahon, B.J., Maller, K.M., Brown, K.R., Amini, J.M.: New J. Phys. 18, 083030 (2016)
Diep, D.N., Giang, D.H., Van Minh, N.: Int. J. Theor. Phys. 56, 1948 (2017)
Jin, W.: Quantum Inf. Process. 15, 65 (2016)
Nagata, K., Resconi, G., Nakamura, T., Batle, J., Abdalla, S., Farouk, A., Geurdes, H.: Asian J. Math. Phys. 1(1), 1–4 (2017)
Nagata, K., Nakamura, T., Geurdes, H., Batle, J., Abdalla, S., Farouk, A., Diep, D.N.: Int. J. Theor. Phys. 57, 973 (2018)
Nagata, K., Nakamura, T., Geurdes, H., Batle, J., Abdalla, S., Farouk, A.: Int. J. Theor. Phys. 57, 1605 (2018)
Nagata, K., Nakamura, T.: J Sci Eng Res 5(3), 326–328 (2018)
Nagata, K., Nakamura, T., Batle, J., Farouk, A.: Int. J. Theor. Phys. 57, 3098 (2018)
Nagata, K., Nakamura, T.: Open Access Library J. 2, e1798 (2015)
Nagata, K., Nakamura, T.: Int. J. Theor. Phys. 56, 2086 (2017)
Nagata, K., Nakamura, T., Farouk, A.: Int. J. Theor. Phys. 56, 2887 (2017)
Diep, D.N., Giang, D.H.: Int. J. Theor. Phys. 56, 2797 (2017)
Diep, D.N., Giang, D.H., Phu, P.H.: Int. J. Theor. Phys. 57, 841 (2018)
Resconi, G., Nagata, K.: Intern. J. Gen. Eng. Technol. 7(1), 1–20 (2018)
Nagata, K., Nakamura, T., Geurdes, H., Batle, J., Farouk, A., Diep, D.N., Patro, S.K.: Int. J. Theor. Phys. 57, 2546 (2018)
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)
Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2000)
Devitt, S.J., Munro, W.J., Nemoto, K.: Rep. Prog. Phys. 76, 076001 (2013)
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
Corresponding author
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-018-3917-x