  We discuss some systematic methods for implementing state manipulations in
systems formally similar to chains of a few spins with nearest-neighbor
interactions, arranged such that there are strong and weak scales of coupling
links. States are permuted by means of bias potentials applied to a few
selected sites. This generic structure is then related to an atoms-in-a-cavity
model that has been proposed in the literature as a way of achieving a
decoherence free subspace. A new method using adiabatically varying laser
detuning to implement a CNOT gate in this model is proposed.
