We are interested in the control, optimization and estimation issues emerging from quantum information processing tasks, and their connections with information, control and dynamical systems theories.

The research on open quantum system dynamics is conducted in strict collaboration with the group of Prof. Lorenza Viola, at the Physics and Astronomy Department at Dartmouth College (NH, USA).

RECENT RESEARCH PROJECTS:

(1) Symmetrization, Consensus and Quantum Dynamics:

We extended the gossip algorithm, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. In doing so, we reinterpret the classical algorithm and the average consensus task as a symmetrization problem with respect to the action of the permutation group. This allows us to extend in a natural way the gossip consensus algorithm to the quantum setting and many others, and prove its convergence properties to symmetric states independently of the particular application.

1. Selected Relevant Publications:
   
   A New Perspective on Gossip Iterations: from Symmetrization to Quantum Consensus.  L. Mazzarella, A. Sarlette, F. Ticozzi, 52st IEEE Conference on Decision and Control proceedings, 2013.
   

2. [preprint]
    
   Consensus for Quantum Networks: From Symmetry to Gossip Iteration. L. Mazzarella, A. Sarlette, F. Ticozzi.
   [preprint]
   
   Symmetrizing quantum dynamics beyond gossip-type algorithms. 
   F. Ticozzi. Automatica,74:38-46, 2016.
   

3. [http://arxiv.org/abs/1509.01621] [online]
   

(2) Entanglement Generation in Quantum Networks:

We seek a solution to the problem of determining whether a target pure state can be asymptotically prepared using dissipative Markovian dynamics under fixed locality constraints. Connections with the formalism of frustration-free parent Hamiltonians are analyzed, as well as control design protocols and feedback implementations.

1. Selected Relevant Publications:
   
   Steady-state entanglement by engineered quasi-local Markovian dissipation
   

2. F. Ticozzi and L. Viola, Quantum Information and Computation, 14(3-4), 0265-0294, 2013.
   [preprint] 
               
   

3. Stabilizing entangled states with quasi-local dynamical semigroups.
   

4. F. Ticozzi and L. Viola,Philosophical Transaction of the Royal Society A, 370(1978), 5259-5269, 2012. [preprint] [online]
   

5. 
   

(3) Engineering Quantum Evolutions:

We investigate the dynamical properties of quantum Markovian dynamics, and control methods for enforcing a desired asymptotic  (or finite-time) behavior. In particular we focus on Feedback State Preparation and Noiseless Subsystem Engineering. Applications to physically relevant systems are sought.

1. Selected Relevant Publications:
   
   Stabilization of Stochastic Quantum Dynamics via Open and Closed Loop Control  F. Ticozzi, K. Nishio and C. Altafini, submitted, 2011 [preprint]
       
   Hamiltonian Control of Quantum Dynamical Semigroups: Stabilization and Convergence Speed
   F. Ticozzi, R. Lucchese, P. Cappellaro, and L. Viola, IEEE Transaction on Automatic Control, to appear, 2011. [preprint]
   

2.   
   

3. Discrete-Time Controllability for Feedback Quantum Dynamics
   

4. F. Albertini and F. Ticozzi, Automatica 47 (2011) 2451–2456. [preprint] [online]
   

5.   
   Stabilizing generic quantum states with Markovian dynamical semigroups
   F. Ticozzi, S. G. Schirmer, X. Wang. IEEE Transaction of Automatic Control 55(12):2901-2905, 2010. [preprint] [online]
   

6.   
   

7. Quantum Information Encoding, Protection, and Correction from Trace-Norm Isometries.
   

8. F. Ticozzi and L. Viola. Physical Review A,  81(3):032313, 2010. [preprint] [online]
   

9.     
   

10. Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition.
    S. Bolognani and F. Ticozzi. IEEE Transaction on Automatic Control,  55(12):2721-2734, 2010. [preprint] [online]
    

11.      
    

12. Analysis and synthesis of attractive quantum Markovian dynamics  F. Ticozzi and L. Viola. Automatica 45: 2002–2009 , 2009. [preprint] [online]
    

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14. Quantum Markovian Subsystems: Invariance, Attractivity and Control. F. Ticozzi and L. Viola. IEEE Transaction on Automatic Control, 53(9):2048-2063, 2008. [preprint][online]
    

(4) Channel Estimation and Optimal Encodings for 
     Quantum Cryptography and Communication

Part of the QFuture Project, in collaboration with N. Dalla Pozza, N. Laurenti, M. Zorzi. See also: QFuture Website

 

    On Quantum Channel Estimation with Minimal Resources

    M. Zorzi, F. Ticozzi and A. Ferrante, submitted, 2011 [preprint]

   
    Engineering a Long Distance Free- Space Quantum Channel  
    R. Corvaja, I. Capraro, A. Dall’Arche, N. Dalla Pozza, F. Gerlin,
    A.Tomaello, M. Zorzi, A. Assalini, A. Ferrante, G. Pierobon, F. Ticozzi,
    G. Vallone, P. Villoresi Invited paper at Isabel 2011, to appear, 2011.

  

(5) New Mathematical Approaches to Encoding and
     Protection of Quantum Information

1. 
   Relevant Publications:
   

2. 
   

3. Quantum Information Encoding, Protection, and Correction from Trace-Norm Isometries.
   

4. F. Ticozzi and L. Viola. Physical Review A,  81(3):032313, 2010. [preprint] [online]
   

5.     
   

6. On Time-reversal and space-time harmonic processes for Markovian quantum channels.
   

7. F. Ticozzi and M. Pavon. Quantum Information Processing, 9(5):551-574, 2010.
   [preprint] [online]
   

8. 
   
   

FUNDING:

Active Grants:

University of Padova research grant “New challenges in reciprocal processes, Schroedinger bridges, optimal transport and their respective geometries with applications to control engineering problems for classical and quantum systems”

Former Grants:

> The group is member of the QFUTURE  and QUINTET strategic research project of the University of Padua and the Dept. of Information Engineering, respectively.

> University of Padova research grant CPDA080209/08: “Schroedinger Bridges for Quantum Channels: A New Approach to Information Encoding and Control Design”

> 2008 GNAMPA project:

“Teoria del Controllo per Sistemi Quantistici”

(Control Theory for Quantum Systems, link to the project website, in Italian).

PHD STUDENTS

Giacomo Baggio (2015 - 2018)

Luca Mazzarella (2012-2014)

Mattia Zorzi (2011- 2013)

PRESENT AND PAST VISITORS:

Alain Sarlette (2012)

Claudio Altafini (2009-2010)

Lorenza Viola (2008-2012)

Domenico D’Alessandro (2008)

PAST PROJECTS:

> Feedback Control and Entropy Production for Markovian Dynamics

> Linear-Algebraic Techniques for Dynamical Decoupling

> Robustness in Quantum Adiabatic Control

> Model-based feedback Design for Quantum Control

(with G. Raccanelli)

FORMER THESIS STUDENTS:

Luca Zuccato

Master Thesis, research project on alternating projections methods for stabilization of quantum systems.

Pierre Scaramuzza

Master Thesis, research project on switching strategies for stabilization of quantum systems.

 

Giuseppe Ilario Cirillo

Master Thesis, research project on convergence features of discrete-time quantum Markov processes and Perron-Frobenius Theory

  

Giacomo Baggio

Bachelor Thesis, research project on discrete-time feedback for state stabilization.

  

Riccardo Lucchese

Bachelor Thesis, research project on speed of convergence of quantum dynamical semigroups.

Francesco Guarato

Master Thesis, research project on Lyapunov analysis of discrete-time feedback control of quantum systems.

Enrico Avventi

Master Thesis, research project on Hamiltonian compensation of quantum jumps.

Quantum Information and Control Group