Reversible universal quantum computation within translation invariant   systems
  We show how to perform reversible universal quantum computation on a translationally invariant pure state, using only global operations based on next-neighbor interactions. We do not need not to break the translational symmetry of the state at any time during the computation. Since the proposed scheme fulfills the locality condition of a quantum cellular automata, we present a reversible quantum cellular automaton capable of universal quantum computation. 
K. G. H. Vollbrecht and J. I. Cirac