  We present protocols for the generation of high-dimensional entangled states
of anharmonic oscillators by means of coherent manipulation of light-matter
systems in the ultrastrong coupling regime. Our protocols consider a pair of
ultrastrong coupled qubit-cavity systems, each coupled to an ancilla qubit, and
combine classical pulses plus the selection rules imposed by the parity
symmetry. We study the robustness of the entangling protocols under dissipative
effects. This proposal may have applications within state-of-art circuit
quantum electrodynamics.
