  In the holonomic approach to quantum computation information is encoded in a
degenerate eigenspace of a parametric family of Hamiltonians and manipulated by
the associated holonomic gates. These are realized in terms of the non-abelian
Berry connection and are obtained by driving the control parameters along
adiabatic loops. We show how it is possible, for a specific model, to
explicitly determine the loops generating any desired logical gate, thus
producing a universal set of unitary transformations. In a multi-partite system
unitary transformations can be implemented efficiently by sequences of local
holonomic gates. Moreover a conceptual scheme for obtaining the required
Hamiltonian family, based on frequently repeated pulses, is discussed, together
with a possible process whereby the initial state can be prepared and the final
one can be measured.
