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

We propose potential setups for the quantum simulation of itinerant spin-carrying particles in a superconducting qubit-resonator array. The standard Jaynes-Cummings-Hubbard setup studied by several authors is readily amenable to being used as a quantum simulator for some spin-related phenomena. A more complex setup where multiple qubits and multiple resonator modes are utilized in the simulation gives a higher level of complexity, allowing for example the simulation of external magnetic fields and spin-orbit coupling. This proposal could be implemented in state-of-the-art superconducting circuits in the near future.