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We propose possible approaches for the quantum simulation of itinerantspin-carrying particles in a superconducting qubit-resonator array. Thestandard Jaynes-Cummings-Hubbard setup considered in several recent studies canreadily be used as a quantum simulator for a number of relevant phenomena,including the interaction with external magnetic fields and spin-orbitcoupling. A more complex setup where multiple qubits and multiple resonatormodes are utilized in the simulation gives a higher level of complexity,including the simulation of particles with high spin values and allowing moredirect control on processes related to spin-orbit coupling. This proposal couldbe implemented in state-of-the-art superconducting circuits in the near future.

Simulating systems of itinerant spin-carrying particles using arrays of superconducting qubits and resonators