A simple embedding scheme for quantum computer simulations of molecules

Current era noisy intermediate-scale quantum computers are limited in what they can accurately simulate. One of the most successful applications to date has been the variational quantum eigensolver, which uses the quantum computer to create a trial wavefunction and then employs a simple circuit to measure the expectation value of different pieces of the Hamiltonian. A classical computer is employed to accumulate all of the results and determine the energy; it also is employed to optimize the trial wavefunction, if desired. In this work, we focus on the question of whether one can easily improve the accuracy of this calculation via an embedding strategy. We take a classical Hartree-Fock (or similar) approximation for a large system and correct its energy using the correlation energy derived from the smaller quantum computer calculation. We illustrate this concept with calculations performed on some simple molecules.