Efficient Quantum Algorithms of Finding the Roots of a Polynomial Function

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Abstract

Two quantum algorithms of finding the roots of a polynomial function f(x) = xm + am− 1xm− 1 + ... + a1x + a0 are discussed by using the Bernstein-Vazirani algorithm. One algorithm is presented in the modulo 2. The other algorithm is presented in the modulo d. 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 in both cases.

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Acknowledgements

We thank Professor Germano Resconi and Professor Shahrokh Heidari for valuable comments.

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Correspondence to Koji Nagata.

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Nagata, K., Nakamura, T., Geurdes, H. et al. Efficient Quantum Algorithms of Finding the Roots of a Polynomial Function. Int J Theor Phys 57, 2546–2555 (2018). https://doi.org/10.1007/s10773-018-3776-5

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Keywords

  • Quantum computation
  • Quantum algorithms