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Title: Quantum Phase Estimation Algorithm for Finding Polynomial Roots
Authors: Theerapat Tansuwannont
Surachate Limkumnerd
Sujin Suwanna
Pruet Kalasuwan
Chulalongkorn University
University of Waterloo
Mahidol University
Prince of Songkla University
Ministry of Education
Keywords: Physics and Astronomy
Issue Date: 1-Jan-2020
Citation: Open Physics. Vol.17, No.1 (2020), 839-849
Abstract: © 2019 T. Tansuwannont et al., published by De Gruyter. Quantum algorithm is an algorithm for solving mathematical problems using quantum systems encoded as information, which is found to outperform classical algorithms in some specific cases. The objective of this study is to develop a quantum algorithm for finding the roots of nth degree polynomials where n is any positive integer. In classical algorithm, the resources required for solving this problem increase drastically when n increases and it would be impossible to practically solve the problem when n is large. It was found that any polynomial can be rearranged into a corresponding companion matrix, whose eigenvalues are roots of the polynomial. This leads to a possibility to perform a quantum algorithm where the number of computational resources increase as a polynomial of n. In this study, we construct a quantum circuit representing the companion matrix and use eigenvalue estimation technique to find roots of polynomial.
ISSN: 23915471
Appears in Collections:Scopus 2020

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