There has been great interest in recent years in quantum control landscapes. Given an objective J(u) as a functional of the control field u(t) the dynamical control landscape is defined by the properties of the Hessian H of the objective J at the critical controls u(t) where grad J=0. Particularly important features of a control landscape are traps defined as local maxima of J(u) and second order traps where the gradient grad J=0 and the Hessian H is negative semidefinite but J(u) is not a global maximum. The presence of traps may significantly hinder the search for globally optimal controls using local search algorithms motivating the importance of the analysis of traps. We will discuss recent new results in the analysis of quantum control landscapes.

Reference: A.N. Pechen and D.J. Tannor, Are there traps in quantum control landscapes? Phys. Rev. Lett., 106, 120402 (2011).