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Quantum algorithm for the root-finding problem

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Abstract

A quantum algorithm of finding the roots of a polynomial function \(f(x)=x^m +a_{m-1}x^{m-1}+\cdots +a_1x+ a_0\) is discussed by using the generalized Bernstein–Vazirani algorithm. Our algorithm is presented in the modulo 2. Here all the roots are in the integers Z. The speed of solving the problem is shown to outperform the best classical case by a factor of m.

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Authors and Affiliations

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

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  1. Koji Nagata
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  2. Tadao Nakamura
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Correspondence to Koji Nagata.

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Nagata, K., Nakamura, T. Quantum algorithm for the root-finding problem. Quantum Stud.: Math. Found. 6, 135–139 (2019). https://doi.org/10.1007/s40509-018-0171-0

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  • DOI: https://doi.org/10.1007/s40509-018-0171-0

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