  We propose and study a specific adiabatic path to prepare those tensor
network states that are unique ground states of few-body parent Hamiltonians in
finite lattices, which include normal tensor network states, as well as other
relevant nonnormal states. This path guarantees a gap for finite systems and
allows for efficient numerical simulation. In one dimension, we numerically
investigate the preparation of a family of states with varying correlation
lengths and the one-dimensional Affleck-Kennedy-Lieb-Tasaki (AKLT) state and
show that adiabatic preparation can be much faster than standard methods based
on sequential preparation. We also apply the method to the two-dimensional AKLT
state on the hexagonal lattice, for which no method based on sequential
preparation is known, and show that it can be prepared very efficiently for
relatively large lattices.
