  We propose the implementation of a digital quantum simulator for prototypical
spin models in a circuit quantum electrodynamics architecture. We consider the
feasibility of the quantum simulation of Heisenberg and frustrated Ising models
in transmon qubits coupled to coplanar waveguide microwave resonators.
Furthermore, we analyze the time evolution of these models and compare the
ideal spin dynamics with a realistic version of the proposed quantum simulator.
Finally, we discuss the key steps for developing the toolbox of digital quantum
simulators in superconducting circuits.
