  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.
