Non-adiabatic holonomic quantum computation
  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. 
Erik Sj\"oqvist, D.M. Tong, L. Mauritz Andersson, Bj\"orn Hessmo,   Markus Johansson, Kuldip Singh
quant-ph