Optimal Control Algorithms for Quantum Systems and their Limitations
Some of the limitations of popular optimal control algorithms such as Lyapunov control, the Krotov method and other iterative algorithms based on functional gradients are considered. Lyapunov control, while elegant and generally effective for ideal systems, struggles for many realistic systems. Iterative techniques such as the Krotov method tend to be more effective, but the inclusion of an energy penalty term implies that the resulting solutions are not critical points of the objective functional alone, and do not maximize it. These problems can be avoided by using functional gradients without penalty terms, but even these techniques fail for some problems.