Newton Methods for the Optimal Control of Closed Quantum Spin Systems

An efficient and robust computational framework for solving closed quantum spin optimal-control and exact-controllability problems with control constraints is presented. Closed spin systems are of fundamental importance in modern quantum technologies such as nuclear magnetic resonance (NMR) spectroscopy, quantum imaging, and quantum computing. These systems are modeled by the Liouville--von Neumann master (LvNM) equation describing the time evolution of the density operator representing the state of the system. A unifying setting is provided to discuss optimal-control and exact-controllability results. Different controllability results for the LvNM model are given, and necessary optimality conditions for the LvNM control problems are analyzed. Existence and regularity of optimal controls are proved. The computational framework is based on matrix-free reduced-Hessian semismooth Krylov--Newton schemes for solving optimal-control problems of the LvNM equation in a real vector space rotating-frame representat...

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