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. These proposals include the use of multiple polariton branches, multiple resonator modes and multiple qubits coupled to each resonator. We argue that a combination of using multiple qubits and multiple resonator modes is a promising route in this context, allowing the simulation of external magnetic fields and various forms of spin-dependent inter-site hopping, including spin-orbit coupling. This proposal could be implemented in state-ofthe-art superconducting circuits in the near future.