Achieving the laboratory control of quantum dynamics phenomena using nonlinear functional maps

This paper introduces a new algorithm for achieving closed-loop laboratory control of quantum dynamics phenomena. The procedure makes use of nonlinear functional maps to exploit laboratory control data for revealing the relationship between control fields and their effect on the observables of interest. Control is achieved by (1) constructing the maps by performing laboratory experiments during an initial learning phase and then (2) searching the maps for fields that drive the system to the desired target during a separate, offline optimization stage. Once the map is learned, additional laboratory experiments are not necessarily required if the control target is changed. Maps also help to determine the control mechanism and assess the robustness of the outcome to fluctuations in the field since they explicitly measure the nonlinear response of the observable to field variations. To demonstrate the operation of the proposed map based control algorithm, two illustrations involving simulated population transfer experiments are performed.