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We propose a superconducting circuit platform for simulating spin-1 models.To this purpose we consider a chain of N ultrastrongly coupled qubit-resonatorsystems interacting through a grounded SQUID. The anharmonic spectrum of thequbit-resonator system and the selection rules imposed by the global paritysymmetry allow us to activate well controlled two-body quantum gates viaAC-pulses applied to the SQUID. We show that our proposal has the samesimulation time for any number of spin-1 interacting particles. This scheme maybe implemented within the state-of-the-art circuit QED in the ultrastrongcoupling regime.

Spin-1 models in the ultrastrong coupling regime of circuit QED