Time-optimal holonomic quantum computation

A three-level system can be used in a Λ-type configuration in order to construct auniversal set of non-adiabatic quantum gates through the use of non-Abelian non-adiabatic geometrical phases. Such construction allows for high-speed operation times which diminish the effects of decoherence. This might be, however, accompanied by a breakdown of the validity of the rotating wave approximation (RWA) due to the comparable timescale between the counter-rotating terms and the pulse length, which greatly affects the dynamics. Here we investigate the trade-off between dissipative effects and the RWA validity, obtaining the optimal regime for the operation of the holonomic quantum gates