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A new quantum claw-finding algorithm for three functions

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Abstract

Fork functionsf 1, ...f k, ak-tuple (x 1, ...x k) such thatf 1(x 1)=...=f k(x k) is called a claw off 1, ...,f k. In this paper, we construct a new quantum claw-finding algorithm for three functions that is efficient when the numberM of intermediate solutions is small. The known quantum claw-finding algorithm for three functions requiresO(N 7/8 logN) queries to find a claw, but our algorithm requiresO(N 3/4 logN) queries ifM ≤ √N andO(N 7/12 M 1/3 logN) queries otherwise. Thus, our algorithm is more efficient ifM≤N 7/8.

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Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, 606-8501, Kyoto, Japan

    Kazuo Iwama & Akinori Kawachi

  2. Quantum Computation and Information Project, ERATO, JST, 406, Iseya-cho, Kamigyo-ku, 602-0873, Kyoto, Japan

    Kazuo Iwama & Akinori Kawachi

Authors
  1. Kazuo Iwama
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  2. Akinori Kawachi
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Correspondence to Kazuo Iwama.

Additional information

Kazuo Iwama, Ph.D.: Professor of Informatics, Kyoto University, Kyoto 606-8501, Japan. Received BE, ME, and Ph.D. degrees in Electrical Engineering from Kyoto University in 1978, 1980 and 1985, respectively. His research interests include algorithms, complexity theory and quantum computation. Editorial board of Information Processing Letters and Parallel Computing. Council Member of European Association for Theoretical Computer Science (EATCS).

Akinori Kawachi: Received B.Eng. and M.Info. from Kyoto University in 2000 and 2002, respectively. His research interests are quantum computation and distributed computation.

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Iwama, K., Kawachi, A. A new quantum claw-finding algorithm for three functions. New Gener Comput 21, 319–327 (2003). https://doi.org/10.1007/BF03037306

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  • DOI: https://doi.org/10.1007/BF03037306

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