  We devise an all-optical scheme for the generation of entangled multimode
photonic states encoded in temporal modes of light. The scheme employs a
nonlinear down-conversion process in an optical loop to generate one- and
higher-dimensional tensor network states of light. We illustrate the principle
with the generation of two different classes of entangled tensor network states
and report on a variational algorithm to simulate the ground-state physics of
many-body systems. We demonstrate that state-of-the-art optical devices are
capable of determining the ground-state properties of the spin-1/2 Heisenberg
model. Finally, implementations of the scheme are demonstrated to be robust
against realistic losses and mode mismatch.
