  We exploit the duality between quantum channels and sequentially generated
states to construct families of highly entangled states that undergo phase
transitions. These highly entangled states can be sequentially generated by
collecting the emitted radiation from an open quantum system. In the dual
perspective, the open system is regarded as a quantum-state-generating machine.
A nontrivial class of such machines are quantum push-down automata, which can
be used to create highly entangled states including the ground state of the
spin-2 Motzkin spin chain parametrically faster than adiabatic evolution. We
construct generalizations of the Motzkin state that can be efficiently
sequentially generated.
