Variational quantum algorithm for molecular geometry optimization

Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already few-atom systems. In this work, we introduce a variational quantum algorithm finding most stable structure molecule by explicitly considering parametric dependence electronic Hamiltonian on nuclear coordinates. The is obtained minimizing more general cost depends both circuit and parameters, which are simultaneously optimized at each step. applied to find geometries ${\mathrm{H}}_{2},$ ${\mathrm{H}}_{3}{}^{+},$ ${\mathrm{BeH}}_{2},$ ${\mathrm{H}}_{2}\mathrm{O}$ molecules. circuits used prepare ground state were designed using an adaptive where excitation gates in form Givens rotations selected according norm their gradient. All simulations performed PennyLane library differentiable programming. geometrical parameters simulated show excellent agreement with counterparts computed classical chemistry methods.