Quantum control landscapes

In this talk we will consider the problem of studying the landscapes of control problems for quantum systems, namely, the problem of the presence or absence of traps - local, but not global extrema of objective functionals. The absence of traps was proved for two-level quantum systems. Also, the absence of traps was proved for the problem of controlling tunneling of a quantum particle through a potential barrier. For some quantum systems of dimension more than two, the trapping behavior was shown - namely, the presence of critical points for the objective functional, which are not global maxima, at which the Hessian of the objective functional is negatively semidefinite. In the general case, the problem remains open.