  We show that trapped ions can be used to simulate a highly symmetrical
Hamiltonian with eingenstates naturally protected against local sources of
decoherence. This Hamiltonian involves long range coupling between particles
and provides a more efficient protection than nearest neighbor models discussed
in previous works. Our results open the perspective of experimentally realizing
in controlled atomic systems, complex entangled states with decoherence times
up to nine orders of magnitude longer than isolated quantum systems.
