Maximization of the Overlap between Density Matrices for a Two-Level Open Quantum System Driven by Coherent and Incoherent Controls

The article considers a two-level open quantum system evolving under the action of coherent and incoherent controls using the general control method proposed in Phys. Rev. A. 73, 062102 (2006). Coherent control determines the Hamiltonian aspects of the dynamics whereas incoherent control determines the dissipative aspects. The goal is to find controls which steer the initial density matrix into a state which maximizes overlap with a predefined target density matrix. The controlled dynamics is represented as evolution in the Bloch ball and is analyzed analytically using Pontryagin maximum principle and numerically using optimization either in the functional space of controls (with the conditional and projected gradient methods) or through reduction to a finite-dimensional control space.