  We show how to realize, by means of non-abelian quantum holonomies, a set of
universal quantum gates acting on decoherence-free subspaces and subsystems. In
this manner we bring together the quantum coherence stabilization virtues of
decoherence-free subspaces and the fault-tolerance of all-geometric holonomic
control. We discuss the implementation of this scheme in the context of quantum
information processing using trapped ions and quantum dots.
