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Efficient Quantum Algorithm for the Parity Problem of a Certain Function

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Abstract

Based on a particular mathematical structure of a certain function f(x) under our attention, we present a novel quantum algorithm. The algorithm allows one to determine the property of a certain function. In our study, it is f(x) = f(−x). Therefore, there would be a question here, “How fast can we succeed in this?” All we need to do is only the evaluation of a single quantum state \(|\overbrace {0,0,\ldots ,0,1}^{N}\rangle \) (N ≥ 2). Only using that with a little amount of information, we can derive the global property f(x) = f(−x). Our quantum algorithm overcomes a classical counterpart by a factor of the order of 2N.

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Acknowledgments

We thank Professor Han Geurdes for valuable discussions.

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Authors and Affiliations

  1. Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Korea

    Koji Nagata

  2. Department of Information and Computer Science, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

    Tadao Nakamura

  3. Departament de Física, Universitat de les Illes Balears, 07122, Palma de Mallorca, Balearic Islands, Spain

    Josep Batle

  4. Department of Physics and Computer Science, Faculty of Science, Wilfrid Laurier University, Waterloo, Canada

    Ahmed Farouk

Authors
  1. Koji Nagata
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  2. Tadao Nakamura
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  3. Josep Batle
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  4. Ahmed Farouk
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Correspondence to Koji Nagata.

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Nagata, K., Nakamura, T., Batle, J. et al. Efficient Quantum Algorithm for the Parity Problem of a Certain Function. Int J Theor Phys 57, 3098–3103 (2018). https://doi.org/10.1007/s10773-018-3827-y

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  • DOI: https://doi.org/10.1007/s10773-018-3827-y

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