Artificial Photonic Materials in Circuit QED

After two decades of development, superconducting circuits have emerged as a rich platform for quantum computation and simulation. Here I will describe some of the techniques that have emerged for building synthetic photonic materials from these quantum circuits with a focus on lattices of 2D waveguide resonators. I will highlight some of the unique capabilities of these systems, including the ability to realize lattices that exist in an effective curved space with negative, hyperbolic, curvature, as well as the ability to realize lattices with gapped flat bands.