  We present a scalable architecture for the exploration of interacting
topological phases of photons in arrays of microwave cavities, using
established techniques from cavity and circuit quantum electrodynamics. A
time-reversal symmetry breaking (non-reciprocal) flux is induced by coupling
the microwave cavities to ferrites, allowing for the production of a variety of
topological band structures including the $\alpha=1/4$ Hofstadter model.
Effective photon-photon interactions are included by coupling the cavities to
superconducting qubits, and are sufficient to produce a $\nu=1/2$ bosonic
Laughlin puddle. We demonstrate by exact diagonalization that this architecture
is robust to experimentally achievable levels of disorder. These advances
provide an exciting opportunity to employ the quantum circuit toolkit for the
exploration of strongly interacting topological materials.
