Grover’s Algorithm and Its Generalization

  • Renato Portugal
Chapter
Part of the Quantum Science and Technology book series (QST)

Abstract

Grover’s algorithm is a search algorithm originally designed to look for an element in an unsorted database with no repeated elements. If the database elements are stored in a random order, the only available method to find a specific element is an exhaustive search. Usually, this is not the best way to use databases, especially if it is queried several times. It is better to sort the elements, which is an expensive task, but performed only once. In the context of quantum computing, storing data in superposition or in an entangled state for a long period of time is not an easy task. Because of that, Grover’s algorithm is introduced following an alternative route, which shows its wide applicability.

References

  1. 4.
    Aharonov, D.: Quantum computation – a review. In: Stauffer, D. (ed.) Annual Review of Computational Physics, vol. VI, pp. 1–77. World Scientific, , Singapore (1998)Google Scholar
  2. 10.
    Ambainis, A., Kempe, J., Rivosh, A.: Coins make quantum walks faster. In: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA, pp. 1099–1108 (2005)Google Scholar
  3. 16.
    Bennett, C.H., Bernstein, E., Brassard, G., Vazirani, U.V.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26(5), 1510–1523 (1997)MathSciNetMATHCrossRefGoogle Scholar
  4. 17.
    Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. Forstschritte Der Physik 4, 820–831 (1998)Google Scholar
  5. 18.
    Brassard, G., Høyer, P., Mosca, M., Tapp, A.: Quantum amplitude amplification and estimation. Quant. Comput. Quant. Inform. Sci., AMS Contemp. Math. Ser. 305, 53–74, (2002), quant-ph/0005055Google Scholar
  6. 32.
    Grover, L.K.: Quantum computers can search arbitrarily large databases by a single query. Phys. Rev. Lett. 79(23), 4709–4712 (1997)ADSCrossRefGoogle Scholar
  7. 33.
    Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79(2), 325–328 (1997)ADSCrossRefGoogle Scholar
  8. 34.
    Grover, L.K.: Quantum computers can search rapidly by using almost any transformation. Phys. Rev. Lett. 80(19), 4329–4332 (1998)ADSCrossRefGoogle Scholar
  9. 41.
    Kaye, P., Laflamme, R., Mosca, M.: An Introduction to Quantum Computing. Oxford University Press, Oxford (2007)MATHGoogle Scholar
  10. 61.
    Mosca, M.: Counting by quantum eigenvalue estimation. Theor. Comput. Sci. 264(1), 139–153 (2001)MathSciNetMATHCrossRefGoogle Scholar
  11. 64.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, New York (2000)MATHGoogle Scholar
  12. 83.
    Zalka, C.: Grover’s Quantum Searching Algorithm is Optimal. (1997), quant-ph/9711070Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Renato Portugal
    • 1
  1. 1.Department of Computer ScienceNational Laboratory of Scientific Computing (LNCC)PetrópolisBrazil

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