Blueprint for a digital-analog variational quantum eigensolver using Rydberg atom arrays

We address the task of estimating the ground-state energy of Hamiltonians coming from chemistry. We study numerically the behavior of a digital-analog variational quantum eigensolver for the H2, LiH, and BeH2 molecules, and we observe that one can estimate the energy to a few percent points of error leveraging on learning the atom register positions with respect to selected features of the molecular Hamiltonian and then an iterative pulse-shaping optimization, where each step performs a derandomization energy estimation.