  Simulating complex molecules and materials is an anticipated application of
quantum devices. With strong quantum advantage demonstrated in artificial
tasks, we examine how such advantage translates into modeling physical problems
of correlated electronic structure. We simulate static and dynamical electronic
structure on a superconducting quantum processor derived from Google's Sycamore
architecture for two representative correlated electron problems: the
nitrogenase iron-sulfur molecular clusters, and $\alpha$-ruthenium trichloride,
a proximate spin-liquid material. To do so, we simplify the electronic
structure into low-energy spin models that fit on the device. With extensive
error mitigation and assistance from classically simulated data, we achieve
quantitatively meaningful results deploying about 1/5 of the gate resources
used in artificial quantum advantage experiments on a similar architecture.
This increases to over 1/2 of the gate resources when choosing a model that
suits the hardware. Our work serves to convert artificial measures of quantum
advantage into a physically relevant setting.
