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This work considers two-qubit open quantum systems driven by coherent andincoherent controls. Incoherent control induces time-dependent decoherencerates via time-dependent spectral density of the environment which is used as aresource for controlling the system. The system evolves according to theGorini-Kossakowski-Sudarshan-Lindblad master equation with time-dependentcoefficients. For two types of interaction with coherent control, three typesof objectives are considered: 1) maximizing the Hilbert-Schmidt overlap betweenthe final and target density matrices; 2) minimizing the Hilbert-Schmidtdistance between these matrices; 3) steering the overlap to a given value. Forthe first problem, we develop the Krotov type methods directly in terms ofdensity matrices with or without regularization for piecewise continuousconstrained controls and find the cases where the methods produce (eitherexactly or with some precision) zero controls which satisfy the Pontryaginmaximum principle and produce the overlap's values close to their upperestimates. For the problems 2) and 3), we find cases when the dual annealingmethod steers the objectives close to zero and produces a non-zero control.

Krotov Type Optimization of Coherent and Incoherent Controls for Open Two-Qubit Systems