Numerical estimation of reachable and controllability sets for a two-level open quantum system driven by coherent and incoherent controls
Oleg Vasilevich Morzhin, Alexander N. Pechen · AIP conference proceedings · 2021
The article considers a two-level open quantum system, whose evolution is governed by the Gorini–Kossakowski– Lindblad–Sudarshan master equation with Hamiltonian and dissipation superoperator depending, correspondingly, on piecewise constant coherent and incoherent controls with constrained magnitudes. Additional constraints on controls’ variations are also considered. The problem is analyzed using Bloch parametrization of system’s density matrix. We adapt the section method for obtaining outer parallelepipedal and pointwise estimations of reachable and controllability sets in the Bloch ball via solving a number of problems for optimizing coherent and incoherent controls with respect to some objective criteria. The differential evolution and dual annealing optimization methods are used. The numerical results show how the reachable sets’ estimations depend on distances between the system’s initial states and the Bloch ball’s center point, final times, constraints on controls’ magnitudes and variations.