Advertisement

Quantum counting

  • Gilles Brassard
  • Peter HØyer
  • Alain Tapp
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1443)

Abstract

We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching algorithm over classical brute force can still be obtained for a large family of search problems for which good classical heuristics exist. Finally, as our main result, we combine ideas from Grover's and Shor's quantum algorithms to perform approximate counting, which can be seen as an amplitude estimation process.

Keywords

Boolean Function Success Probability Quantum Algorithm Search Problem Quantum Search Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Barenco, Adriano, “Quantum physics and computers”, Contemporary Physics, Vol. 38, 1996, pp. 357–389.Google Scholar
  2. 2.
    Bennett, Charles H., Ethan Bernstein, Gilles Brassard and Umesh Vazirani, “Strengths and weaknesses of quantum computing”, SIAM Journal on Computing, Vol. 26, no. 5, October 1997, pp. 1510–1523.zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Boyer, Michel, Gilles Brassard, Peter HØyer and Alain Tapp, “Tight bounds on quantum searching”, Proceedings of Fourth Workshop on Physics and Computation — PhysComp '96, November 1996, pp. 36–43. Final version to appear in Fortschritte Der Physik.Google Scholar
  4. 4.
    Brassard, Gilles, “A quantum jump in computer science”, in Computer Science Today, Jan van Leeuwen (editor), Lecture Notes in Computer Science, Vol. 1000, Springer-Verlag, 1995, pp. 1–14.Google Scholar
  5. 5.
    Brassard, Gilles, “New horizons in quantum information processing”, Proceedings of this ICALP Conference, 1998.Google Scholar
  6. 6.
    Brassard, Gilles and Peter HØyer, “An exact quantum polynomial-time algorithm for Simon's problem”, Proceedings of Fifth Israeli Symposium on Theory of Computing and Systems — ISTCS '97, June 1997, IEEE Computer Society Press, pp. 12–23.Google Scholar
  7. 7.
    Chi, Dong-Pyo and Jinsoo Kim, “Quantum database searching by a single query”, Lecture at First NASA International Conference on Quantum Computing and Quantum Communications, Palm Springs, February 1998.Google Scholar
  8. 8.
    Cleve, Richard, Artur Ekert, Chiara Macchiavello and Michele Mosca, “Quantum algorithms revisited”, Proceedings of the Royal Society, London, Vol. A354, 1998, pp. 339–354.MathSciNetGoogle Scholar
  9. 9.
    Grover, Lov K., “Quantum mechanics helps in searching for a needle in a haystack”, Physical Review Letters, Vol. 79, no. 2, 14 July 1997, pp. 325–328.CrossRefGoogle Scholar
  10. 10.
    Mosca, Michele, “Quantum computer algorithms and interferometry”, Lecture at BRICS Workshop on Algorithms in Quantum Information Processing, Aarhus, January 1998.Google Scholar
  11. 11.
    Shor, Peter W., “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer”, SIAM Journal on Computing, Vol. 26, no. 5, October 1997, pp. 1484–1509.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Gilles Brassard
    • 1
  • Peter HØyer
    • 2
  • Alain Tapp
    • 1
  1. 1.Université de MontréalCanada
  2. 2.Odense UniversityDenmark

Personalised recommendations