The ability of superconducting quantum processors to control and make quantum non-demolition (QND) measurements of individual microwave photons is a powerful resource for quantum simulation, especially for simulation of condensed matter models and lattice gauge theories containing bosons.   I will illustrate these capabilities with recent experiments on a programmable quantum simulator that uses efficient boson sampling of microwave photons to predict the Franck-Condon vibrational spectra of various small molecules.  I will also explore possible future directions for simulation of quantum many-body problems such as the fractional quantum Hall effect, and Z2 lattice gauge theories.