Variational quantum algorithms (VQAs) have seen significant application to ab initio simulation of quantum chemistry systems. In this work, we propose a novel VQA to calculate the ground state of interacting molecules in condensed phase systems based on the classical method of electronic coarse graining. The electronic coarse grained approach uses coupled quantum Drude oscillators to represent interacting molecular moieties. It can model two- and many-body polarisation and dispersion interactions to all orders without a priori knowledge about the dominant interaction scales. We present simulated results of using this VQA to find ground states for small systems of interacting Drude oscillators that include effective three-body interaction terms. This work opens up the possibility of using quantum computers for quantum chemistry calculations at time and length scales beyond those captured by ab initio methods.