  We propose a nanophotonic platform for topological quantum optics. Our system
is composed of a two-dimensional lattice of non-linear quantum emitters with
optical transitions embedded in a photonic crystal slab. The emitters interact
through the guided modes of the photonic crystal, and a uniform magnetic field
gives rise to large topological band gaps and an almost completely flat
topological band. Topological edge states arise on the boundaries of the system
that are protected by the large gap against missing lattice sites and to the
inhomogeneous broadening of emitters. These results pave the way for exploring
topological many-body states in quantum optical systems.
