Higher order traps in quantum control landscapes

Mathematical analysis of quantum control landscapes, which includes proving either absence or existence of traps for quantum control objective functionals, is an important topic in the quantum control theory. Traps are points of local but not global extrema of the objective functional. Traps of n-th order are singular controls defined by the Taylor expansion of the objective functional up to the n-th order. Their existence in quantum landscape can reduce the performance of local search optimal control protocols. In this talk, we discuss the presence of n-th order traps for the control problem of some closed multilevel systems.