1

Theoretical and practical introduction to quantum machine learning

20

First & Second

Content:

° Basic notions of machine learning

° Different learning paradigms

(unsupervised, supervised,

reinforced), different models (types of neural networks)

° Different training methods

(stochastic gradient descent and its variants)

° Basic notions of quantum

computation relevant to understand efficiency claims.

° Quantum-enhanced machine

learning vs machine learning

applied to quantum: the many

different ways to merge machine

learning and quantum information science.

° Some case studies of problems

arising in quantum information

theory which can be tackled with

machine learning.

2

Introduction to agent-based models

20

First & Second

The course will provide basic concepts about agent-based models with an emphasis on their origin and their applications. The contributions from statistical physics to the understanding and solution of ABMs will also be discussed by considering toy-models such as the Ising model on a lattice. Applications in physics, social sciences and economy will also be considered.

3

Quantum tools for future scientific research

20

First & Second

The goal of the course is to present the current available methodologies and concepts developed in quantum information theory and their

potential applications to different

research areas, such as condensed

matter physics and high energy

physics. This will pass through the acquisition of knowledge on tensor network methods as a key

methodological tool.

4

Neural networks

20

First & Second

The course on neural networks

introduces the principles and

applications of artificial neural

networks, which are computational models inspired by the structure and function of biological neurons.

It covers the fundamental concepts of feedforward and recurrent neural networks, including architectures, learning algorithms, and optimization techniques. Students will learn how to design, train, and evaluate neural networks for a variety of tasks, such as classification, regression, and sequence modeling. The course covers the basics of neural network models, including perceptrons, multilayer perceptrons, and recurrent neural networks. It also delves into deep learning, including convolutional neural networks and autoencoders. The course emphasizes the practical aspects of neural networks, including the

design and implementation of

networks, the analysis of their

behavior and performance, and

their application to real-world

problems. Students will learn how

to apply neural networks to a

variety of domains, such as image

and speech recognition, natural

language processing, and robotics. Overall, this course provides students with a solid understanding of neural networks and their applications. By the end of the course, students will have gained practical experience in designing, training, and evaluating neural networks to solve complex

problems.

5

Physics for computation

20

First & Second

This course focuses on the study of physics concepts and their

application to computational

systems. Topics include quantum

mechanics, statistical mechanics,

thermodynamics, and information theory. The course aims to provide students with a deep understanding of the fundamental physical principles that underpin modern computing, and their applications in various fields such as quantum computing, information processing, and cryptography. In this way, students will be able to use physics-based tools and techniques to analyze and design

computational systems. Upon

completion of the course, students will have gained the knowledge and skills necessary to work in fields such as quantum computing, information processing, and cryptography.

6

Engineering of machine learning

20

First & Second

The course on the engineering of

machine learning focuses on the

practical aspects of building, deploying, and maintaining

machine learning systems. It covers the entire machine learning pipeline, from data preparation and feature engineering to model selection and evaluation, to deployment and monitoring. Students will learn how to design and implement machine learning

systems that are scalable, efficient,

and maintainable. The course

covers the basics of software

engineering for machine learning,

including version control, testing,

debugging, and documentation. It

also delves into the challenges of

productionizing machine learning,

such as model serving, infrastructure management, and

data privacy. The course emphasizes the importance of

collaboration and communication

in machine learning engineering,

including best practices for working in teams, sharing code and data, and communicating results to stakeholders. Students will learn how to work with common machine learning frameworks and tools, such as TensorFlow, PyTorch, and Scikit-learn. Overall, this course provides students with a solid understanding of the engineering of machine learning systems and their applications. By the end of the course, students will have gained practical experience in

building, deploying, and maintaining machine learning

systems that meet real-world

requirements.

7

Long range correlations in statistical physics

20

First & Second

Contents

Part 1: Long-range correlations in

continuous stochastic processes

° Introduction to stochastic processes. Langevin equation as a

motion equation in presence of noise

° Langevin equation and Fokker-Planck equation

° Eigenfunctions methodology

° Memory properties in stochastic

processes. Doob theorem

° Ergodicity of log range correlated processes

° Extreme value theory

Part 2: Long-range correlations in

discrete stochastic processes

° Markov chains

° Hidden Markov Models

° ARCH e GARCH stochastic

processes

° FbM, ARIMA, FARIMA,

FI-GARCH stochastic processes

Part 3: Long-range interactions in

statistical mechanics

° Mean field theories

° Hamiltonian systems with long

range interactions

° Quantum systems with long-range interactions

° Out-of-equilibrium long-range

correlations

8

Networks and Big Data

20

First & Second

In this course, we will first provide an overview of “big data” and network theory. We will then focus on real (big) datasets in economics, finance, and other social sciences, and show how network tools, methods, and models might be useful to reveal the emergent properties of investigated systems. We will learn the basic structural and

dynamical properties of networks

and how to apply these concepts to real systems. We will investigate, starting from real

(big) data, the structure and properties of several social networks including financial networks, trading networks, crime networks, and phone-call networks. We will also explore the dynamics of processes occurring on networks, such as

market contagion, and macroscopic phenomena related to these processes, including information cascades and herding. Students will be expected

to think critically about concepts, models, and empirical evidences presented in class. They will be also expected to apply concepts and analysis tools to real-world

networks.

9

Text analysis through network analysis approach

20

First & Second

This course offers a comprehensive introduction to advanced text analysis techniques, with a particular focus on topic modeling. We explore the fundamental concepts, state-of-the-art models, and inherent limitations of topic modeling. Then, we introduce the network theory examining how network-based tools, methods, and models can be employed to reveal the emergent properties of complex

systems. Specifically, we introduce the Statistically Validated Networks (SVN) method and demonstrate its application across various domains, including textual analysis. Indeed, special attention

will be given to the construction

and analysis of word co occurrence networks—graph-based representations of text corpora. The core component of the course focus on i) exploring network-based approaches to constructing topic models directly, and ii) designing and applying coherence measures for evaluating topic models. Throughout the course, students are expected to engage critically with the theoretical concepts, models, and empirical findings discussed in class. They will also apply analytical techniques to real-world textual data, gaining practical experience with cutting-edge methods in computational text analysis and network science.

10

Open quantum systems & dynamics

20

First & Second

Contents:

° Python and Quantum Physics:

° Operators and Superoperators

° Quantum Dynamical Maps

° Positive and Complete Positive

Maps, Operator-sum representation

° Markovian Semigroup

° Open Quantum System Dynamics

° Stochastic Master Equation

(Monte Carlo Method)

° Collision models

11

Photonic quantum technologies

20

First & Second

The course is designed to provide

in-depth knowledge and advanced research skills in the intersection of photonics and quantum technologies. Students will first explore the technology currently adopted for single-photon generation, manipulation and detection via bulk and integrated photonics. The second part of the course will address the use of photonics devices for quantum information processing. The course will present the students with forefront methods of experimental quantum information processing in photonic platforms that will inform the development of their research project.