Generation of photonic tensor network states with Circuit QED

We propose a circuit QED platform and protocol to deterministically generate microwave photonic tensor network states. We first show that using a microwave cavity as ancilla and a transmon qubit as emitter is a favorable platform to produce photonic matrix-product states. The ancilla cavity combines a large controllable Hilbert space with a long coherence time, which we predict translates into a high number of entangled photons and states with a high bond dimension. Going beyond this paradigm, we then consider a natural generalization of this platform, in which several cavity–qubit pairs are coupled to form a chain. The photonic states thus produced feature a two-dimensional entanglement structure and are readily interpreted as radial plaquette projected entangled pair states, which include many paradigmatic states, such as the broad class of isometric tensor network states, graph states, string-net states.