Geometric control theory and Riemannian techniques are used to describe
the reachable set at time t of left invariant single-input control systems
on semi-simple compact Lie groups and to
estimate the minimal time needed to reach any point from identity.
This method provides an effective way to give an upper and a lower bound
for the minimal time needed to transfer a controlled quantum system
with a drift from a given initial position to a given final position.
The bounds include diameters of the flag manifolds; the latter are
also explicitly computed in the paper.