We propose the implementation of a digital quantum simulation of spin chains coupled to bosonic field modes in superconducting circuits. Gates with high fidelities allows one to simulate a variety of Ising magnetic pairing interactions with transverse field, Tavis-Cummings interaction between spins and a bosonic mode, and a spin model with three-body terms. We analyze the feasibility of the implementation in realistic circuit quantum electrodynamics setups, where the interactions are either realized via capacitive couplings or mediated by microwave resonators.
Heras, U. L., García-Álvarez, L., Mezzacapo, A., Solano, E., & Lamata, L. (2016). Quantum Simulation of Spin Chains Coupled to Bosonic Modes with Superconducting Circuits (pp. 93–103). https://doi.org/10.1007/978-4-431-55342-7_8