Skip to main content
SpringerLink
Log in

Two notes on Grover’s search: Programming and discriminating

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

In this work we address two questions concerning Grover’s algorithm. In the first part we give an answer to the question on how to employ Grover’s algorithm for actual search over database. We introduce a quantum model of an unordered phone book (quantum database) with programmable queries to search in the phone book either for a number or for a name. In the second part we investigate how successful the algorithm can be if the number of elements of the database is not known precisely. This question reduces to analysis of the distinguishability of states occurring during Grover’s algorithm. We found that using an unambiguous discrimination scheme even a seemingly good guess that is close to the optimal one, can result in a rather small success rate.

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. L.K. Grover, Phys. Rev. Lett. 79, 325 (1997).

    Article  ADS  Google Scholar 

  2. A. Ambainis, SIAM J. Comput. 37, 210 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  3. C.H. Bennett, E. Bernstein, C. Brassard, U. Vazirani, SIAM J. Comput. 26, 1510 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  4. M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).

  5. N. Brunner, S. Pironio, A. Acin, N. Gisin, A.A. Méthot, V. Scarani, Phys. Rev. Lett. 100, 210503 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  6. M.M. Wolf, D. Perez-Garcia, Phys. Rev. Lett. 102, 190504 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  7. A. Chefles, A. Kitagawa, M. Takeoka, M. Sasaki, J. Twamley, J. Phys. A 40, 10183 (2007).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. X. Wu, R. Duan, Phys. Rev. A 78, 012303 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  9. C. Zalka, Phys. Rev. A 60, 2746 (1999).

    Article  ADS  Google Scholar 

  10. M. Sedlák, Acta Phys. Slovaca 59, 653 (2009).

    Article  ADS  Google Scholar 

  11. A. Chefles, S.M. Barnett, Phys. Lett. A 250, 223 (1998).

    Article  ADS  Google Scholar 

  12. A.S. Holevo, J. Multivar. Anal. 3, 337 (1973).

    Article  MATH  MathSciNet  Google Scholar 

  13. S.M. Barnett, S. Croke, J. Phys. A 42, 062001 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  14. M. Ban, K. Kurokawa, R. Momose, O. Hirota, Int. J. Theor. Phys. 36, 1269 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  15. C. Cafaro, S. Mancini, Physica A 391, 1610 (2012).

    Article  ADS  MathSciNet  Google Scholar 

  16. N. Shenvi, K.R. Brown, K.B. Whaley, Phys. Rev. A 68, 052313 (2003).

    Article  ADS  Google Scholar 

  17. O. Regev, L. Schiff, Impossibility of a Quantum Speed-Up with a Faulty Oracle, in Proceedings of the 35th International Colloquium on Automata, Languages and Programming, Vol. 1 (2008) p. 773.

Download references

Author information

Authors and Affiliations

  1. Institute of Physics, Slovak Academy of Sciences, Dúbravská cesta 9, 845 11, Bratislava, Slovakia

    Daniel Reitzner & Mário Ziman

  2. Department of Physics, Hunter College of CUNY, 695 Park Avenue, 10021, New York, New York, USA

    Daniel Reitzner

  3. Faculty of Informatics, Masaryk University, Botanická 68a, 60210, Brno, Czech Republic

    Mário Ziman

Authors
  1. Daniel Reitzner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mário Ziman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Reitzner.

Additional information

Contribution to the Focus Point on “Quantum information and complexity” edited by S. Mancini, G. Marmo, S. Pascazio.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Reitzner, D., Ziman, M. Two notes on Grover’s search: Programming and discriminating. Eur. Phys. J. Plus 129, 128 (2014). https://doi.org/10.1140/epjp/i2014-14128-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/i2014-14128-9

Keywords

Search

Navigation