Optimization of state transfer and exact dynamics for the open two-level quantum system

We consider the state-to-state transfer control problem for the open two-level quantum system (qubit) with evolution governed by the master equation with coherent and incoherent controls. General form of the GKSL master equation in the absence of controls was derived in particular in the weak coupling limit and in the stochastic limit of quantum theory. We introduce the specific model of the such master equation, include coherent and incoherent controls, and for the state-to-state transfer problem study the complexity of the GRAPE optimization method. Moreover we derive exact expressions for the dynamics of the system and for the gradient of the objective functional necessary for optimization.