Tommaso Grigoletto: Research

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.

Switching control for quantum systems

Publications - Complete list from arXiv

• September 9th 2025
  Exact Model Reduction for Continuous-Time Open Quantum Dynamics
  Poster presentation at IQIS 2025, Bologna Italy [poster];
• March 13th 2025
  Exact Model Reduction for Quantum Dynamics
  Invited talk at Quantum Nano Seminar - Dartmouth College [slides];
• January 20th 2025
  Applications of quantum conditional expectations
  Two-hour lecture included in the Ph.D. course ``Quantum Probability Information and Dynamics'' held by Francesco Ticozzi, University of Padua [slides];
• January 10th 2025
  Quantum conditional expectation and the Takesaki Theorem
  Two-hour lecture included in the Ph.D. course ``Quantum Probability Information and Dynamics'' held by Francesco Ticozzi, University of Padua [slides];
• December 2024
  Exact Model Reduction for Discrete-Time Conditional Quantum Dynamics
  Invited session at IEEE Conference on Decision and Control, Milan [slides];
• March 21st 2024
  Exact model reduction for quantum systems
  Ph.D. Thesis defense, University of Padua [slides];
• September 22nd 2023
  Exact model reduction for Quantum Systems: an algebraic approach
  Invited talk at Inria Paris, Quantic group [slides];
• June 27th 2023
  Exact model reduction for Quantum Systems: an algebraic approach
  Seminar talk for the quantum lunch at the department of information engineering, University of Padua [slides];
• December 2022
  Minimal resources for exact simulation of quantum walks
  IEEE Conference on Decision and Control, Cancun;
• April 2022
  Algebraic reduction of Hidden Markov Models
  Seminar talk at the department of information engineering, University of Padua;

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  University of Padua

  I belong to the Automatica group at the Department of Information Engeeniring of the University of Padua and part of the Quantum Dynamics, Information and Control group lead by Prof. Francesco Ticozzi.

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  Dartmouth College

  I have been a visiting scholar at the Physics and Astronomy Department of Dartmouth College under the supervision of Prof. Lorenza Viola, working closely with her research group.
  

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  Université Paul Sabatier

  I have been collaborating with Professor Clément Pellegrini from Laboratoire de Statistique et Probabilités Université Paul Sabatier

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  Inria Paris

  I have been collaborating with Professor Alain Sarlette from the Quantic group at Inria Paris.