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

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 it allows 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.