Quantum Search on Bounded-Error Inputs

  • Peter Høyer
  • Michele Mosca
  • Ronald de Wolf
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2719)


Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(\( \sqrt n \)) repetitions of the base algorithms and with high probability finds the index of a 1-bit among these n bits (if there is such an index). This shows that it is not necessary to first significantly reduce the error probability in the base algorithms to O(1/poly(n)) (which would require O(\( \sqrt n \log n \) log n) repetitions in total). Our technique is a recursive interleaving of amplitude amplification and error-reduction, and may be of more general interest. Essentially, it shows that quantum amplitude amplification can be made to work also with a bounded-error verifier. As a corollary we obtain optimal quantum upper bounds of O(\( \sqrt N \)) queries for all constant-depth AND-OR trees on N variables, improving upon earlier upper bounds of O(\( \sqrt N \) polylog(N)).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Peter Høyer
    • 1
  • Michele Mosca
    • 2
  • Ronald de Wolf
    • 3
  1. 1.Dept. of Computer ScienceUniv. of CalgaryCanada
  2. 2.Dept. of Combinatorics & OptimizationUniv. of WaterlooCanada
  3. 3.CWIAmsterdamThe Netherlands

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