Quantum counting

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


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.


Boolean Function Success Probability Quantum Algorithm Search Problem Quantum Search Algorithm 
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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

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