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 Λ configuration. Our scheme opens up for universal holonomic quantum computation on qubits characterized by short coherence times.
@article{arxiv.1107.5127,
title = {Non-adiabatic holonomic quantum computation},
author = {Erik Sjöqvist and D. M. Tong and L. Mauritz Andersson and Björn Hessmo and Markus Johansson and Kuldip Singh},
journal= {arXiv preprint arXiv:1107.5127},
year = {2012}
}