  We give a sufficient criterion that guarantees that a many-body quantum
system can be controlled by properly manipulating the (local) Hamiltonian of
one of its subsystems. The method can be applied to a wide range of systems: it
does not depend on the details of the couplings but only on their associated
topology. As a special case, we prove that Heisenberg and
Affleck-Kennedy-Lieb-Tasaki chains can be controlled by operating on one of the
spins at their ends. In principle, arbitrary quantum algorithms can be
performed on such chains by acting on a single qubit.
