  Variational quantum algorithms (VQAs) are increasingly being applied in
simulations of strongly-bound (covalently bonded) systems using full molecular
orbital basis representations. The application of quantum computers to the
weakly-bound intermolecular and non-covalently bonded regime however has
remained largely unexplored. In this work, we develop a coarse-grained
representation of the electronic response that is ideally suited for
determining the ground state of weakly interacting molecules using a VQA. We
require qubit numbers that grow linearly with the number of molecules and
derive scaling behaviour for the number of circuits and measurements required,
which compare favourably to traditional variational quantum eigensolver
methods. We demonstrate our method on IBM superconducting quantum processors
and show its capability to resolve the dispersion energy as a function of
separation for a pair of non-polar molecules - thereby establishing a means by
which quantum computers can model Van der Waals interactions directly from
zero-point quantum fluctuations. Within this coarse-grained approximation, we
conclude that current-generation quantum hardware is capable of probing
energies in this weakly bound but nevertheless chemically ubiquitous and
biologically important regime. Finally, we perform experiments on simulated and
real quantum computers for systems of three, four and five oscillators as well
as oscillators with anharmonic onsite binding potentials; the consequences of
the latter are unexamined in large systems using classical computational
methods but can be incorporated here with low computational overhead.
