  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.

Quantum Physics