  There has been a growing interest in realizing quantum simulators for
physical systems where perturbative methods are ineffective. The scalability
and flexibility of circuit quantum electrodynamics (cQED) make it a promising
platform to implement various types of simulators, including lattice models of
strongly-coupled field theories. Here, we use a multimode superconducting
parametric cavity as a hardware-efficient analog quantum simulator, realizing a
lattice in synthetic dimensions with complex hopping interactions. The coupling
graph, \textit{i.e.} the realized model, can be programmed \textit{in situ}.
The complex-valued hopping interaction further allows us to simulate, for
instance, gauge potentials and topological models. As a demonstration, we
simulate a plaquette of the bosonic Creutz ladder. We characterize the lattice
with scattering measurements, reconstructing the experimental Hamiltonian and
observing emerging topological features. This platform can be easily extended
to larger lattices and different models involving other interactions.
