  We develop a non-adiabatic generalization of holonomic quantum computation in
which high-speed universal quantum gates can be realized by using non-Abelian
geometric phases. We show how a set of non-adiabatic holonomic one- and
two-qubit gates can be implemented by utilizing optical transitions in a
generic three-level $\Lambda$ configuration. Our scheme opens up for universal
holonomic quantum computation on qubits characterized by short coherence times.
