On a greedy algorithm for the Hamiltonian identification

Gabriele Ciaramella
MOX, Dipartimento di Matematica, Politecnico di Milano
Tuesday 19th October 2021
Live: Aula Saleri, MOX - Dipartimento di Matematica - Politecnico di Milano
Online: https://mox.polimi.it/elenco-seminari/?id_evento=2085&t=763721
The identification of Hamiltonian operators plays a fundamental role in fields like quantum physics, quantum chemistry and nuclear magnetic resonance. The term Hamiltonian identification often refers to two distinct problems. On the one hand, it can indicate the inverse problem associated with the identification of a Hamiltonian operator obtained by a numerical fitting of simulated experimental data. On the other hand, it can refer to both the problem of designing experimental parameters (input control functions) allowing a tailored production of laboratory data and the subsequent inverse identification problem. In this talk, a novel computational greedy-type approach for design of control functions will be presented and analyzed. This strategy is based on an offline/online decomposition of the reconstruction process. In the offline phase, a family of control functions is built iteratively in a greedy manner to maximize the distinguishability of the system. This phase exploits only the theoretical quantum model, without any use of laboratory information. The computed control functions are experimentally implemented in the online phase to produce laboratory data, which are in turn used to define and solve an identification inverse problem. The convergence analysis reveals the strong dependence of the performance of the greedy strategy on the observability and controllability of the system and allows us to introduce a new and more robust optimized greedy strategy whose efficiency is demonstrated by numerical experiments. Contatto: paola.antonietti@polimi.it