In this talk, ensemble control-theoretic approaches for optimal pulse design in quantum control will be introduced. A new method that integrates Lie algebras with polynomial approximation for analyzing controllability of spin ensemble systems will be presented. In addition, robust computational methods for optimal pulse synthesis will also be presented, which include a unified computational method based on multidimensional pseudospectral approximations and an optimization-free iterative algorithm based on the singular value decomposition. Commonly used pulses in various fields of quantum control developed by these computational methods will be illustrated, and, moreover, experimental realizations of these optimal pulses will be shown to demonstrate the robustness and applicability of these newly developed methods.
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