  We examine the relevance of Level Set Methods (LSM)in coherent control
quantum systems where the objective is to retain or attain a particular
expectation value of a given measurable. The differences with the usual
applications of LSM, where continuous closed interfaces are involved, and the
quantum case, where we may have a discrete number of points to deal with, are
noted. The question of optimization in this new context is also clarified.
Simple examples with symmetric and asymmetric multidimensional potentials are
briefly considered.
