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Résumé : 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. Lattices sites are linked by applying pump tones at special frequencies, realizing both hopping and pairing interactions, both of which can have complex amplitudes. The coupling graph, i.e., the realized model, can be programmed in situ. The realization of complex-valued interactions further allows us to simulate, for instance, gauge potentials and topological models. As a demonstration, we simulate small realizations of a number of paradigmatic topological models including the bosonic Creutz ladder, the bosonic Kitaev chain, and the SSH model. We characterize the lattices with scattering measurements, reconstructing the experimental Hamiltonian and observing important precursors of topological features including chiral transport and Ahranov-Bohm caging. This platform can be easily extended to larger lattices and different models involving other interactions.
