  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.
