  We show how one can deterministically generate photonic matrix product states
with high bond and physical dimensions with an atomic array if one has access
to a Rydberg-blockade mechanism. We develop both a quantum gate and an optimal
control approach to universally control the system and analyze the photon
retrieval efficiency of atomic arrays. Comprehensive modeling of the system
shows that our scheme is capable of generating a large number of entangled
photons. We further develop a multi-port photon emission approach that can
efficiently distribute entangled photons into free space in several directions,
which can become a useful tool in future quantum networks.
