  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.
