Limitations of Quantum Optimal Control

Abstract: The use of local, typically gradient based, optimisation
algorithms has proven to be particularly effective in achieving control
objectives for quantum mechanical systems. Some authors have sought a
theoretical justification for this empirical observation of the
numerical techniques' behavior. A set of papers, falling under the
banner of "optimal control landscapes" claim to offer such a
justification, in the form of proofs that such optimisation always
achieves the control objective (ignoring numerical limitations). I will
present a number of problems inherent in said "landscape" analysis.