Università di Pavia - Offerta formativa

THEORETICAL AND QUANTUM PHYSICS FOR AI

Anno immatricolazione

2021/2022

Anno offerta

2022/2023

Normativa

DM270

SSD

FIS/02 (FISICA TEORICA, MODELLI E METODI MATEMATICI)

Dipartimento

DIPARTIMENTO DI MATEMATICA 'FELICE CASORATI'

Corso di studio

ARTIFICIAL INTELLIGENCE

Curriculum

PERCORSO COMUNE

Anno di corso

2°

Periodo didattico

Annualità Singola (03/10/2022 - 19/06/2023)

Crediti

12

Ore

112 ore di attività frontale

Lingua insegnamento

INGLESE

Tipo esame

SCRITTO E ORALE CONGIUNTI

Docente

Prerequisiti

Basic concepts of calculus and linear algebra: multivariable functions, derivatives, integrals, Taylor series, vectors, eigenvalues and eigenvectors of a linear operator Basic concepts of physics: scalar and vectorial quantities, fundamental concepts of Newtonian mechanics, principle of energy conservation.

Obiettivi formativi

Module #1: Statistical Physics

This module presents, at a basic level, the theoretical approach of physics to systems with a large number of degrees of freedom, also concerning its interdisciplinary applications. The successful student will be able to

• Perform Fermi estimates and use scaling arguments for physical and non-physical phenomena

• Decide, within simple models with many degrees of freedom, if the law of large numbers and the central limit theorem hold

• Compute physical quantities from thermodynamic potentials

• Derive the thermodynamic properties of many-body systems from their microscopic description

Module #2: Quantum Physics

The objective of this module is providing the student with the basic knowledge of quantum physics. At the end of the module, the student is expected

• to be familiar with the main concepts of quantum physics, such as observable, quantum state, measurement, distinguishability, quantum superposition, quantum entanglement.

• To be familiar with the basic concepts of quantum information theory, and their relevance for quantum communication and quantum computation.

• To be able to understand and describe the behavior of simple quantum systems (e.g., a two-qubits state), including their evolution.

This module presents, at a basic level, the theoretical approach of physics to systems with a large number of degrees of freedom, also concerning its interdisciplinary applications. The successful student will be able to

• Perform Fermi estimates and use scaling arguments for physical and non-physical phenomena

• Decide, within simple models with many degrees of freedom, if the law of large numbers and the central limit theorem hold

• Compute physical quantities from thermodynamic potentials

• Derive the thermodynamic properties of many-body systems from their microscopic description

Module #2: Quantum Physics

The objective of this module is providing the student with the basic knowledge of quantum physics. At the end of the module, the student is expected

• to be familiar with the main concepts of quantum physics, such as observable, quantum state, measurement, distinguishability, quantum superposition, quantum entanglement.

• To be familiar with the basic concepts of quantum information theory, and their relevance for quantum communication and quantum computation.

• To be able to understand and describe the behavior of simple quantum systems (e.g., a two-qubits state), including their evolution.

Programma e contenuti

Module #1: Statistical Physics

Scaling, dimensional analysis, Fermi estimates; elementary Lagrangian and Hamiltonian mechanics; thermodynamics; probabilistic models in physics; maximum entropy principle; statistical mechanics (microcanonical and canonical ensembles, the ideal gas, the Ising model)

Module #2: Quantum Physics

This module deals with the basic knowledge of quantum systems and quantum information theory. Topics include: definition of states and observables; measurement of a quantum system; evolution of a quantum system; entanglement; description of pure and mixed states; main concepts connected with the application of quantum physics in communications and computations.

Scaling, dimensional analysis, Fermi estimates; elementary Lagrangian and Hamiltonian mechanics; thermodynamics; probabilistic models in physics; maximum entropy principle; statistical mechanics (microcanonical and canonical ensembles, the ideal gas, the Ising model)

Module #2: Quantum Physics

This module deals with the basic knowledge of quantum systems and quantum information theory. Topics include: definition of states and observables; measurement of a quantum system; evolution of a quantum system; entanglement; description of pure and mixed states; main concepts connected with the application of quantum physics in communications and computations.

Metodi didattici

Module #1: Statistical Physics

This module will consist of lectures, pair/group activities in class, and dedicated training sessions, where students will work on assignments individually.

Lectures will be given in a style encouraging student engagement and interaction.

Module #2: Quantum Physics

In this module lectures will be implemented by using Power-Point slides and notes given at the blackboard. The module also includes a training session (some 16 hours) in which the teacher will show how to solve problems and exercises connected with the lectures’ topics. Attendance and interaction with the teacher during the entire course are strongly recommended.

This module will consist of lectures, pair/group activities in class, and dedicated training sessions, where students will work on assignments individually.

Lectures will be given in a style encouraging student engagement and interaction.

Module #2: Quantum Physics

In this module lectures will be implemented by using Power-Point slides and notes given at the blackboard. The module also includes a training session (some 16 hours) in which the teacher will show how to solve problems and exercises connected with the lectures’ topics. Attendance and interaction with the teacher during the entire course are strongly recommended.

Testi di riferimento

Module #1: Statistical Physics

• M. Kardar “Statistical physics of particles”, Cambridge University Press, 2007 (ISBN 9780521873420)

• H.C. Van Ness “Understanding thermodynamics”, Dover Publications Inc., New York, 1983 (ISBN 9780486632773)

• A.M. Glazer, J.S. Wark “Statistical mechanics - A survival guide”, Oxford University Press, 2001 (ISBN 9780198508168)

(Kardar’s textbook alone is enough, although minimalistic: the other two are supplementary)

Module #2: Quantum Physics –

B. Schumacher and M. Westmoreland – Quantum Processes Systems, and Information 2010 Cambirdge University Press (ISBN 978-0-521-87534-9)

• M. Kardar “Statistical physics of particles”, Cambridge University Press, 2007 (ISBN 9780521873420)

• H.C. Van Ness “Understanding thermodynamics”, Dover Publications Inc., New York, 1983 (ISBN 9780486632773)

• A.M. Glazer, J.S. Wark “Statistical mechanics - A survival guide”, Oxford University Press, 2001 (ISBN 9780198508168)

(Kardar’s textbook alone is enough, although minimalistic: the other two are supplementary)

Module #2: Quantum Physics –

B. Schumacher and M. Westmoreland – Quantum Processes Systems, and Information 2010 Cambirdge University Press (ISBN 978-0-521-87534-9)

Modalità verifica apprendimento

The exam consists in a test with multiple choice questions to establish the student knowledge of the concepts presented in the course and the capability to solve simple exercises. The duration of the test is 120 minutes. The written exam can be integrated with an oral exam at the discretion of the teacher.

Altre informazioni

Obiettivi Agenda 2030 per lo sviluppo sostenibile