Abstract:
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)].