Towards a minimum L2-norm exact control of the Pauli equation

A computational framework for the exact-control of the magnetic state and the spin of an electron is presented. The evolution of this quantum system is governed by the Pauli equation, that is a system of Schrodinger equations coupled by the action of magnetic fields. The magnetic fields are used as controls in order to steer the quantum system from an initial state to a desired target state at a given final time. This control framework is based on a minimum norm optimization formulation of exact-controllability quantum problems, that allows the application of efficient Krylov-Newton optimization techniques. In order to provide this framework with an adequate initialization, a continuation procedure is discussed. Results of numerical experiments demonstrate the effectiveness of the proposed framework.