Quantum computation of first-principles molecular dynamics: quest for smaller computational complexity

In this paper, we present a quantum algorithm that enables us to perform first-principles molecular dynamics. In this algorithm, the optimum of wavefunctions and atomic structures is given by a root of a system of polynomial equations derived from the first principles of quantum mechanics. The computational steps consist of symbolic and quantum parts. First, the symbolic computation prepares a set of matrices whose eigenvalues are the roots of the given equation. Second, the quantum computation evaluates the eigenvectors and eigenvalues. In a preceding work, the authors presented another algorithm directed to the same end, and its deficiency is the complexity of the symbolic computations, which would be enormous in the worst cases. In this study, we try to reduce the cost of symbolic computation, utilizing the latest achievements of classical algorithms. Finally, we show how to transform this classical algorithm into a quantum one.