Thesis proposals


PhD thesis proposals

Projects for PhD theses (PhD in Mathematical Engineering, Physics, Mathematics) can be conducted in the Research Topics of our team.

Laurea Magistrale

  1. Stochastic differential equations in the theory of open quantum systems.
    Different types of stochastic differential equations are used in quantum optics, in the theory of open quantum systems and in the theory of quantum measurements in continuous time. In the literature such equations appear under various key words: quantum continuous measurements, quantum jumps, stochastic Schroedinger equation, unravelling of the master equation, quantum trajectories, quantum filtering... Various topics are possible for a thesis, which can be oriented on the mathematical or on the physical side, according to the interests of the student.
  2. Entropic inequalities in quantum information.
    Quantum information theory has analogies with the classical theory, founded by Shannon. Various quantities of entropic type are used to quantify the information which is transmitted through quantum systems (channels); various inequalities involving such entropic quantities give bounds on the maximum amount of information which can be transmitted. Also the uncertainty rules for incompatible measurements on quantum systems can be formulated by means of entropic inequalities. A possible thesis would be to study concrete examples in order to compute explicitly the involved quantities and to clarify the meaning of the theoretical inequalities.
  3. Teoria delle grandi deviazioni e applicazioni all'analisi statistica delle reti.
    Il risultato di vari fenomeni casuali in prima approssimazione si può considerare deterministico. La teoria delle grandi deviazioni nasce con lo scopo di studiare la differenza o deviazione da quest'approssimazione. Si pensi, per esempio alla Legge dei Grandi Numeri; la teoria permette di dimostrare che la probabilità che la media empirica si allontani dal valore teorico è esponenzialmente piccola. Scopo della tesi è lo studio dei risultati principali della teoria e la loro applicazione alla valutazione della probabilità di perdita di pacchetti nelle reti di trasmissione dati per mezzo di pochi parametri legati alla qualità delle performances della rete.
    Prerequisiti: conoscenze di Probabilità e Statistica della Laurea triennale in Ingegneria Matematica, Analisi funzionale e reale.
  4. Quantum annealing of open systems.
    Advances in experimental control of quantum systems opened the way to new technologies based on purely quantum phenomena in which the behaviour of equilibrium plays an important role. Equilibrium is typically lost through interaction with external reservoirs involving dissipation generating dynamics that are intriguing both from a theoretical and a computational point of view. Moreover, one can think of using dissipation cleverly so as to exploit it as a resource because it might be easier to reach a steady-state of an open system rather than preparing the ground state of a closed one. Quantum annealing occurs when the temperatures of an external reservoir coupled to the system slowly converges to zero. The aim of the project is the exploration of the techniques to study convergence of the evolution of an open quantum system towards a steady state and the application to quantum computations based on annealing algorithms.
    Part of the work will be done in an internship at NTT Data (
  5. Quantum vs Classical Annealing
    The main advantage of a quantum computer is it can execute many tasks faster when compared to a classical computer. Many classical algorithms can be implemented on quantum computers (e.g. D-Wave systems) as annealing algorithms that have already been involved in several areas requiring optimization, simulation, and machine learning. The aim of the thesis is a comparative study of some quantum and classical annealing algorithm in order to understand advantanges of quantum computing in terms of speed of convergence and side drawbacks.
    Part of the work will be done in an internship at NTT Data (