  We consider a family of tensor network states defined on regular lattices
that come with a natural definition of an adiabatic path to prepare them. This
family comprises relevant classes of states, such as injective Matrix Product
and Projected Entangled-Pair States, and some corresponding to classical spin
models. We show how uniform lower bounds to the gap of the parent Hamiltonian
along the adiabatic trajectory can be efficiently computed using semi-definite
programming. This allows one to check whether the adiabatic preparation can be
performed efficiently with a scalable effort. We also derive a set of
observables whose expectation values can be easily determined and that form a
complete set, in the sense that they uniquely characterize the state. We
identify a subset of those observables which can be efficiently computed if one
has access to the quantum state and local measurements, and analyze how they
can be used in verification procedures.
