Can quantum natural gradient improve variational quantum algorithms?

Natural gradients have been used to improve convergence of the classical variational Monte Carlo methods to simulate molecular Hamiltonians. Recently a quantum genralization of the natural gradient approach was proposed based on the quantum Fisher information. We employ quantum circuits to compute the components of the Fisher information matrix and study the contribution of diagonal and off-diagnoal terms on the convergence of variation quantum eigensolver by considering two different classes of quantum chemistry Hamiltonians.