  In the near future, material and drug design may be aided by quantum computer
assisted simulations. These have the potential to target chemical systems
intractable by the most powerful classical computers. However, the resources
offered by contemporary quantum computers are still limited, restricting the
chemical simulations to very simple molecules. In order to rapidly scale up to
more interesting molecular systems, we propose the embedding of the quantum
electronic structure calculation into a classically computed environment
obtained at the Hartree-Fock (HF) or Density Functional Theory (DFT) level of
theory. We achieve this by constructing an effective Hamiltonian that
incorporates a mean field potential describing the action of the inactive
electrons on a selected Active Space (AS). The ground state of the AS
Hamiltonian is determined by means of the Variational Quantum Eigensolver (VQE)
algorithm. With the proposed iterative DFT embedding scheme we are able to
obtain energy correction terms for a single pyridine molecule that outperform
the Complete Active Space Self Consistent Field (CASSCF) results regardless of
the chosen AS.
