  In this work, we test a recently developed method to enhance classical
auxiliary-field quantum Monte Carlo (AFQMC) calculations with quantum computers
against examples from chemistry and material science, representatives of
classes of industry-relevant systems. As molecular test cases, we calculate the
energy curve of H4 and relative energies of ozone and singlet molecular oxygen
with respect to triplet molecular oxygen, which are industrially relevant in
organic oxidation reactions. We find that trial wave functions beyond single
Slater determinants improve the performance of AFQMC and allow to generate
energies close to chemical accuracy compared to full configuration interaction
(FCI) or experimental results. As a representative for material science we
study a quasi-1D Fermi-Hubbard model derived from CuBr2, a compound displaying
electronic structure properties analogous to cuprates. We find that trial wave
functions with both, significantly larger fidelities and lower energies over a
Hartree-Fock solution, do not necessarily lead to better AFQMC results.
