  We consider a network of n spin 1/2 systems which are pairwise interacting
via Ising interaction and are controlled by the same electro-magnetic control
field. Such a system presents symmetries since the Hamiltonian is unchanged if
we permute two spins. This prevents full (operator) controllability in that not
every unitary evolution can be obtained. We prove however that controllability
is verified if we restrict ourselves to unitary evolutions which preserve the
above permutation invariance. For low dimensional cases, n=2 and n=3, we
provide an analysis of the Lie group of available evolutions and give explicit
control laws to transfer between any two permutation invariant states. This
class of states includes highly entangled states such as GHZ states and W
states, which are of interest in quantum information.
