  We show how a quantum Ising spin chain in a time-dependent transverse
magnetic field can be simulated and experimentally probed in the framework of
circuit QED with current technology. The proposed setup provides a new platform
for observing the nonequilibrium dynamics of interacting many-body systems. We
calculate its spectrum to offer a guideline for its initial experimental
characterization. We demonstrate that quench dynamics and the propagation of
localized excitations can be observed with the proposed setup and discuss
further possible applications and modifications of this circuit QED quantum
simulator.
