Efficient Quantum Algorithms of Finding the Roots of a Polynomial Function

被引：0
|
作者：
Koji Nagata
Tadao Nakamura
Han Geurdes
Josep Batle
Ahmed Farouk
Do Ngoc Diep
Santanu Kumar Patro
机构：
[1] Korea Advanced Institute of Science and Technology,Department of Physics
[2] Keio University,Department of Information and Computer Science
[3] Geurdes Datascience,Departament de Física
[4] Universitat de les Illes Balears,Department of Physics and Computer Science, Faculty of Science
[5] Wilfrid Laurier University,TIMAS
[6] Thang Long University,Institute of Mathematics
[7] VAST,Department of Mathematics
[8] Berhampur University,undefined
来源：
International Journal of Theoretical Physics | 2018年 / 57卷
关键词：
Quantum computation; Quantum algorithms;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
引用
收藏
页码：2546 / 2555
页数：9
相关论文
共 50 条
  • [1] Efficient Quantum Algorithms of Finding the Roots of a Polynomial Function
    Nagata, Koji
    Nakamura, Tadao
    Geurdes, Han
    Batle, Josep
    Farouk, Ahmed
    Do Ngoc Diep
    Patro, Santanu Kumar
    INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2018, 57 (08) : 2546 - 2555
  • [2] Polynomial-time quantum algorithms for finding the linear structures of Boolean function
    Wu, WanQing
    Zhang, HuanGuo
    Wang, HouZhen
    Mao, ShaoWu
    QUANTUM INFORMATION PROCESSING, 2015, 14 (04) : 1215 - 1226
  • [3] Polynomial-time quantum algorithms for finding the linear structures of Boolean function
    WanQing Wu
    HuanGuo Zhang
    HouZhen Wang
    ShaoWu Mao
    Quantum Information Processing, 2015, 14 : 1215 - 1226
  • [4] Quantum Phase Estimation Algorithm for Finding Polynomial Roots
    Tansuwannont, Theerapat
    Limkumnerd, Surachate
    Suwanna, Sujin
    Kalasuwan, Pruet
    OPEN PHYSICS, 2019, 17 (01): : 839 - 849
  • [5] Parallel algorithms for finding polynomial Roots on OTIS-torus
    Keny T. Lucas
    Prasanta K. Jana
    The Journal of Supercomputing, 2010, 54 : 139 - 153
  • [6] Parallel algorithms for finding polynomial Roots on OTIS-torus
    Lucas, Keny T.
    Jana, Prasanta K.
    JOURNAL OF SUPERCOMPUTING, 2010, 54 (02): : 139 - 153
  • [7] Efficient algorithms for computing the nearest polynomial with constrained roots
    Hitz, Markus A.
    Kaltofen, Erich
    Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, : 236 - 243
  • [8] ON HIGHLY EFFICIENT SIMULTANEOUS SCHEMES FOR FINDING ALL POLYNOMIAL ROOTS
    Shams, Mudassir
    Rafiq, Naila
    Kausar, Nasreen
    Agarwal, Praveen
    Mir, Nazir Ahmad
    Li, Yong-Min
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2022, 30 (10)
  • [9] A METHOD FOR FINDING ROOTS OF A POLYNOMIAL
    SOUKUP, J
    NUMERISCHE MATHEMATIK, 1969, 13 (04) : 349 - &
  • [10] A COMBINATORIAL CONSTRUCTION OF HIGH ORDER ALGORITHMS FOR FINDING POLYNOMIAL ROOTS OF KNOWN MULTIPLICITY
    Jin, Yi
    Kalantari, Bahman
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (06) : 1897 - 1906
12345