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