Publication: Quantum Phase Estimation Algorithm for Finding Polynomial Roots
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Issued Date
2020-01-01
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ISSN
23915471
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2-s2.0-85078459624
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Mahidol University
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SCOPUS
Bibliographic Citation
Open Physics. Vol.17, No.1 (2020), 839-849
Suggested Citation
Theerapat Tansuwannont, Surachate Limkumnerd, Sujin Suwanna, Pruet Kalasuwan Quantum Phase Estimation Algorithm for Finding Polynomial Roots. Open Physics. Vol.17, No.1 (2020), 839-849. doi:10.1515/phys-2019-0087 Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/53911
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Title
Quantum Phase Estimation Algorithm for Finding Polynomial Roots
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.