On machine learning for time-minimal control for an open two-level quantum system with coherent and incoherent controls

For the case of the 2nd order density matrix, we consider the Gorini–Kossakowski–Sudarshan–Lindblad equation depending simultaneously on coherent control (included in the Hamiltonian) and incoherent control (included in the dissipator), and a class of time-minimal control problems for this equation, where different constraints on controls are used. For a set of initial density matrices, which represent pure states, and a given target density matrix, which represents some mixed quantum state, the solutions of the corresponding time-minimal control problems were numerically found that it was used for formulating multidimensional regression problem for obtaining suboptimal final times and controls for arbitrary initial density matrices also representing pure states. Some algorithm, which combines the $k$-nearest neighbours method and training some neural network. The numerical experiments' results are given for different cardinalities of the training sets. The talk is based on the article [O.V. Morzhin, A.N. Pechen, “Machine learning for finding suboptimal final times and coherent and incoherent controls for an open two-level quantum system”, Lobachevskii J. Math., 41:12, 2353–2369 (2020)].