Quantum Simulation of the Bosonic Creutz Ladder with a Parametric Cavity

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