  Numerical and experimental realizations of quantum control are closely
connected to the properties of the mapping from the control to the unitary
propagator. For bilinear quantum control problems, no general results are
available to fully determine when this mapping is singular or not. In this
paper we give suffcient conditions, in terms of elements of the evolution
semigroup, for a trajectory to be non-singular. We identify two lists of
"way-points" that, when reached, ensure the non-singularity of the control
trajectory. It is found that under appropriate hypotheses one of those lists
does not depend on the values of the coupling operator matrix.
