Critical points of the optimal quantum control landscape: A propagator approach

Numerical and experimental realizations of quantum control are closely connected to the properties of the mapping from the control to the unitary propagator (Rabitz et al. in Science 303(5666):1998-2001, 2004). 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 sufficient 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.