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Improved Algorithms for Quantum Identification of Boolean Oracles

  • Andris Ambainis
  • Kazuo Iwama
  • Akinori Kawachi
  • Rudy Raymond
  • Shigeru Yamashita
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4059)

Abstract

The oracle identification problem (OIP) was introduced by Ambainis et al. [3]. It is given as a set S of M oracles and a blackbox oracle f. Our task is to figure out which oracle in S is equal to the blackbox f by making queries to f. OIP includes several problems such as the Grover Search as special cases. In this paper, we improve the algorithms in [3] by providing a mostly optimal upper bound of query complexity for this problem: (i) For any oracle set S such that \(|S| \le 2^{N^d}\) (d < 1), we design an algorithm whose query complexity is \(O(\sqrt{N\log{M}/\log{N}})\), matching the lower bound proved in [3]. (ii) Our algorithm also works for the range between \(2^{N^d}\) and 2 N/logN (where the bound becomes O(N)), but the gap between the upper and lower bounds worsens gradually. (iii) Our algorithm is robust, namely, it exhibits the same performance (up to a constant factor) against the noisy oracles as also shown in the literatures [2, 11, 18] for special cases of OIP.

Keywords

Success Probability Query Complexity Improve Algorithm Main Loop Quantum Search 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Andris Ambainis
    • 1
  • Kazuo Iwama
    • 2
  • Akinori Kawachi
    • 3
  • Rudy Raymond
    • 2
  • Shigeru Yamashita
    • 4
  1. 1.Department of Combinatorics and OptimizationUniversity of Waterloo 
  2. 2.Graduate School of InformaticsKyoto University 
  3. 3.Tokyo Institute of TechnologyGraduate School of Information Science and Engineering 
  4. 4.Nara Institute of Science and TechnologyGraduate School of Information Science 

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