Improved algorithms for quantum identification of boolean oracles

  • Authors:

  • Andris Ambainis;Kazuo Iwama;Akinori Kawachi;Rudy Raymond;Shigeru Yamashita

  • Affiliations:

  • Department of Combinatorics and Optimization, University of Waterloo;Graduate School of Informatics, Kyoto University;Tokyo Institute of Technology, Graduate School of Information Science and Engineering;Graduate School of Informatics, Kyoto University;Nara Institute of Science and Technology, Graduate School of Information Science

  • Venue:
  • SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
  • Year:
  • 2006

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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 ii) Our algorithm also works for the range between $2^{N^d}$ and 2N/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