We show that the notion of generalized Berry phase i.e., non-abelian
holonomy, can be used for enabling quantum computation. The computational space
is realized by a n-fold degenerate eigenspace of a family of Hamiltonians
parametrized by a manifold M. The point of M represents classical
configuration of control fields and, for multi-partite systems, couplings
between subsystem. Adiabatic loops in the control M induce non trivial
unitary transformations on the computational space. For a generic system it is
shown that this mechanism allows for universal quantum computation by composing
a generic pair of loops in M.Comment: Presentation improved, accepted by Phys. Lett. A, 5 pages LaTeX, no
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