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International Journal of Theoretical Physics

, Volume 57, Issue 8, pp 2546–2555 | Cite as

Efficient Quantum Algorithms of Finding the Roots of a Polynomial Function

  • Koji NagataEmail author
  • Tadao Nakamura
  • Han Geurdes
  • Josep Batle
  • Ahmed Farouk
  • Do Ngoc Diep
  • Santanu Kumar Patro
Article

Abstract

Two quantum algorithms of finding the roots of a polynomial function f(x) = x m + 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.

Keywords

Quantum computation Quantum algorithms 

Notes

Acknowledgements

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

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsKorea Advanced Institute of Science and TechnologyDaejeonKorea
  2. 2.Department of Information and Computer ScienceKeio UniversityKohoku-ku, YokohamaJapan
  3. 3.Geurdes DatascienceDen HaagNetherlands
  4. 4.Departament de FísicaUniversitat de les Illes BalearsPalma de MallorcaSpain
  5. 5.Department of Physics and Computer Science, Faculty of ScienceWilfrid Laurier UniversityWaterlooCanada
  6. 6.TIMASThang Long UniversityHoang Mai districtVietnam
  7. 7.Institute of MathematicsVASTCau Giay districtVietnam
  8. 8.Department of MathematicsBerhampur UniversityBerhampurIndia

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