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The article considers a two-level open quantum system whose dynamics isdriven by a combination of coherent and incoherent controls. Coherent controlenters into the Hamiltonian part of the dynamics whereas incoherent controlenters into the dissipative part. The goal is to find controls which move thesystem from an initial density matrix to a given target density matrix as fastas possible. To achieve this goal, we reformulate the optimal control problemin terms of controlled evolution in the Bloch ball and then apply Pontryaginmaximum principle and gradient projection method to numerically find minimaltime and optimal coherent and incoherent controls. General method is providedand several examples of initial and target states are explicitly considered.

Minimal Time Generation of Density Matrices for a Two-Level Quantum System Driven by Coherent and Incoherent Controls