Minimum time generation of SU(2) transformations with asymmetric bounds on the controls

Abstract

We study how to generate in minimum time special unitary transformations for a two-level quantum system under the assumptions that: (i) the system is subject to a constant drift, (ii) its dynamics can be affected by three independent, bounded controls, (iii) the bounds on the controls are asymmetric, that is, the constraint on the control in the direction of the drift is independent of that on the controls in the orthogonal plane. Using techniques recently developed for the analysis of SU(2) transformations, we fully characterize the reachable sets of the system, and the optimal control strategies for any possible target transformation.