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, Canada;Graduate School of Informatics, Kyoto University, Japan;Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Japan;IBM Tokyo Research Laboratory, Japan;Graduate School of Information Science, Nara Institute of Science and Technology, Japan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2007

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Abstract

The oracle identification problem (OIP) was introduced by Ambainis et al. [A. Ambainis, K. Iwama, A. Kawachi, H. Masuda, R.H. Putra, S. Yamashita, Quantum identification of boolean oracles, in: Proc. of STACS'04, in: LNCS, vol. 2996, 2004, pp. 105-116]. 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 [A. Ambainis, K. Iwama, A. Kawachi, H. Masuda, R.H. Putra, S. Yamashita, Quantum identification of boolean oracles, in: Proc. of STACS'04, in: LNCS, vol. 2996, 2004, pp. 105-116] by providing a mostly optimal upper bound of query complexity for this problem: (i) For any oracle set S such that |S|@?2^N^^^d(d