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

页码：2546 / 2555

页数：9

共 50 条

[31] A GLOBALLY CONVERGENT METHOD FOR SIMULTANEOUSLY FINDING POLYNOMIAL ROOTS
PASQUINI, L
TRIGIANTE, D
MATHEMATICS OF COMPUTATION, 1985, 44 (169) : 135 - 149
[32] Mixed parallel iteration method for finding roots of a polynomial
Weidianzixue yu Jisuanji, 4 (52-56):
[33] A POLYALGORITHM FOR FINDING ROOTS AND ERROR BOUNDS FOR POLYNOMIAL EQUATIONS
EIDSON, HD
MCDONALD, AE
WILKSINS.BM
YOUNG, DM
SIAM REVIEW, 1969, 11 (01) : 111 - &
[34] FINDING POLYNOMIAL ROOTS BY DYNAMICAL SYSTEMS - A CASE STUDY
Shemyakov, Sergey
Chernov, Roman
Rumiantsau, Dzmitry
Schleicher, Dierk
Schmitt, Simon
Shemyakov, Anton
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2020, 40 (12) : 6945 - 6965
[35] Quantum algorithms for subset finding
Childs, AM
Eisenberg, JM
QUANTUM INFORMATION & COMPUTATION, 2005, 5 (07) : 593 - 604
[36] An Algorithms for Finding the Cube Roots in Finite Fields
Faisal
Rojali
Bin Mohamad, Mohd Sham
5TH INTERNATIONAL CONFERENCE ON COMPUTER SCIENCE AND COMPUTATIONAL INTELLIGENCE 2020, 2021, 179 : 838 - 844
[37] On efficient algorithms for finding efficient salvo policies
van Ee, Martijn
NAVAL RESEARCH LOGISTICS, 2020, 67 (02) : 147 - 158
[38] ALGORITHMS FOR LOCALIZING ROOTS OF A POLYNOMIAL AND PISOT VIJAYARAGHAVAN NUMBERS
DUFFIN, RJ
PACIFIC JOURNAL OF MATHEMATICS, 1978, 74 (01) : 47 - 56
[39] EFFICIENT POLYNOMIAL ALGORITHMS FOR DISTRIBUTIVE LATTICES
BORDAT, JP
DISCRETE APPLIED MATHEMATICS, 1991, 32 (01) : 31 - 50
[40] POLYNOMIAL ALGORITHMS FOR FINDING CYCLES AND PATHS IN BIPARTITE TOURNAMENTS
MANOUSSAKIS, Y
TUZA, Z
SIAM JOURNAL ON DISCRETE MATHEMATICS, 1990, 3 (04) : 537 - 543

← 1 2 3 4 5 →