We propose in this paper a gradient-type dynamical system to solve the problem of maximizing quantum observables for finite dimensional closed quantum ensembles governed by the controlled Liouville-von Neumann equation. The asymptotic behavior is analyzed: we show that under the regularity assumption on the controls the dynamical system almost always converges to a solution of the maximization problem; we also detail the difficulties related to the occurrence of singular controls.
@article{arxiv.1109.6364,
title = {Gradient flow for controlling quantum ensemble},
author = {Ruixing Long and Herschel Rabitz},
journal= {arXiv preprint arXiv:1109.6364},
year = {2011}
}