Geometric manipulation of trapped ions for quantum computation

We propose an experimentally feasible scheme to achieve quantum computation based solely on geometric manipulations of a quantum system. The desired g eometric operations are obtained by driving the quantum system to undergo a ppropriate adiabatic cyclic evolutions. Our implementation of the all-geome tric quantum computation is based on Laser manipulation of a set of trapped ions. An all-geometric approach, apart from its fundamental interest, offe rs a possible method for robust quantum computation.