Generation of photonic tensor network states with Circuit QED

We propose a circuit QED platform and protocol to generate microwave photonic tensor network states deterministically. We first show that using a microwave cavity as ancilla and a transmon qubit as emitter is a good 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 can be interpreted as $\textit{radial plaquette}$ projected entangled pair states [Wei, Malz, and Cirac, Phys. Rev. Lett. 128, 010607 (2022)], which include many paradigmatic states, such as the broad class of isometric tensor network states, graph states, and string-net states.