Postponing the orthogonality catastrophe: efficient state preparation for electronic structure simulations on quantum devices

Many proposals for efficiently simulating eigenstates of physical systems on quantum computers require that one can easily initialize wavefunctions with non-vanishing overlap on eigenstates of interest. Though there is now a large body of work exploring the costs of simulating electronic structure systems on a quantum computer,
the challenge of preparing states with sufficient ground state support has so far been largely ignored. In this work we demonstrate that the adaptive sampling configuration interaction technique can be used to investigate the overlap issue. Using this technique, we find that easy-to-prepare single Slater determinants such as the Hartree-Fock state often have surprisingly robust support on the ground state for many applications of interest. For the most difficult systems, we introduce a method for preparation of multi-determinant states on quantum computers. We investigate several prominent applications of quantum simulations including organic molecules, transition metal complexes, the uniform electron gas, Hubbard models, and the quantum impurity models arising from embedding formalisms such as dynamical mean-field theory.