Tommaso Grigoletto

My research interests are in the field of control and systems theory.
Topics of interest include (but are not limited to):

Quantum information theory and quantum probability theory;

Quantum control and simulation of quantum systems;

Quantum random walks and open quantum systems;

Linear, non-linear and complex systems;

Probability theory and hidden Markov models.

Model reduction for probabilistic systems

Finding simpler descriptions for dynamical models is a fundamental task in many scientific fields, including quantum physics. The main focus of this research area is to find reduced order models of quantum systems of interest while preserving the physical constraints given by quantum mechanics. When looking for reduced order models one could look for smaller description that reproduce the behavior of the original model exactly or smaller models that reproduce the behavior with a given accuracy. Both these directions are being investigated in our group.
The possible application of these model reduction techniques is manifold. Just to name a few: (1) finding better and more efficient ways of simulating quantum models on both classical and quantum computers; (2) obtain a better understanding of complex systems while focusing on simpler to study models; (3) constructing reduced-order state observers that allow for more efficient implementation of quantum controllers.
Furthermore, this research area is tightly connected to relevant areas of interest for control system theory, such as hidden Markov models, positive systems, and complex networks.