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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 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.
Vollbrecht et al. (Wed,) studied this question.