  We propose to use wavefunction overlaps obtained from a quantum computer as
inputs for the classical split-amplitude techniques, tailored and externally
corrected coupled cluster, to achieve balanced treatment of static and dynamic
correlation effects in molecular electronic structure simulations. By combining
insights from statistical properties of matchgate shadows, which are used to
measure quantum trial state overlaps, with classical correlation diagnostics,
we are able to provide quantum resource estimates well into the classically no
longer exactly solvable regime. We find that rather imperfect wavefunctions and
remarkably low shot counts are sufficient to cure qualitative failures of plain
coupled cluster singles doubles and to obtain chemically precise dynamic
correlation energy corrections. We provide insights into which wavefunction
preparation schemes have a chance of yielding quantum advantage, and we test
our proposed method using overlaps measured on Google's Sycamore device.
