  Despite significant work on resource estimation for quantum simulation of
electronic systems, the challenge of preparing states with sufficient ground
state support has so far been largely neglected. In this work we investigate
this issue in several systems of interest, including organic molecules,
transition metal complexes, the uniform electron gas, Hubbard models, and
quantum impurity models arising from embedding formalisms such as dynamical
mean-field theory. Our approach uses a state-of-the-art classical technique for
high-fidelity ground state approximation. 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, single-determinant reference states may be
insufficient, but low-complexity reference states may suffice. For this we
introduce a method for preparation of multi-determinant states on quantum
computers.
