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A theoretical and computational framework is presented to obtain accurate controls for fast quantum state transitions that are needed in a host of applications such as nanoelectronic devices and quantum computing. This method is based on a reduced Hessian Krylov-Newton scheme applied to a norm-preserving discrete model of a dipole quantum control problem. The use of second-order numerical methods for solving the control problem is justified, proving the existence of optimal solutions and analyzing first- and second-order optimality conditions. Criteria for the discretization of the nonconvex optimization problem and for the formulation of the Hessian are given to ensure accurate gradients and a symmetric Hessian. Robustness of the Newton approach is obtained using a globalization strategy with a robust linesearch procedure. Results of numerical experiments demonstrate that the Newton approach presented in this paper is able to provide fast and accurate controls for high-energy state transitions.

A Globalized Newton Method for the Accurate Solution of a Dipole Quantum Control Problem