Presentazione

Organizzazione della Didattica

DM270
PHYSICS ORD. 2017

Quantum information

6

Physics of matter

 

Frontali Esercizi Laboratorio Studio Individuale
ORE: 48 0 0 85

Periodo

AnnoPeriodo
II anno1 semestre

Frequenza

Facoltativa

Erogazione

Convenzionale

Lingua

Inglese

Calendario Attività Didattiche

InizioFine
01/10/201818/01/2019

Tipologia

TipologiaAmbitoSSDCFU
caratterizzanteMicrofisico e della struttura della materiaFIS/036


Responsabile Insegnamento

ResponsabileSSDStruttura
Prof. MONTANGERO SIMONEFIS/03

Altri Docenti

Non previsti

Attività di Supporto alla Didattica

Non previste

Bollettino

Quantum mechanics and elements of programming.

The course aims to introduce the students to tensor network methods, one of the most versatile simulation approach exploited in quantum science. It will provide a hands-on introduction to these methods and will present a panoramic overview of some of tensor network methods most successful and promising applications. Indeed, they are routinely used to characterize low-dimensional equilibrium and out-of-equilibrium quantum processes to guide and support the development of quantum science and quantum technologies. Recently, it has also been put forward their possible exploitation in computer science applications such as classification and deep learning algorithms.

The course will be composed of lessons in class and programming labs.

Basics in computational physics 1. Large matrix diagonalization 2. Numerical integration, optimizations, and solutions of PDE 3. Elements of Gnuplot, modern FORTRAN, python 4. Elements of object-oriented programming 5. Schrödinger equation (exact diagonalization, Split operator method, Suzuki-trotter decomposition, ...) Basics of quantum information: 1. Density matrices and Liouville operators 2. Many-body Hamiltonians and states (Tensor products, Liouville representation, ...) 3. Entanglement measures 4. Entanglement in many-body quantum systems Theory: 1. Numerical Renormalization Group 2. Density Matrix Renormalization group 3. Introduction to tensor networks 4. Tensor network properties 5. Symmetric tensor networks 6. Algorithms for tensor networks optimization 7. Exact solutions of benchmarking models Applications: 1. Critical systems 2. Topological order and its characterization 3. Adiabatic quantum computation 4. Quantum annealing of classical hard problems 5. Kibble-Zurek mechanism 6. Optimal control of many-body quantum systems 7. Open quantum systems (quantum trajectories, MPDO, LPTN, ...) 8. Tensor networks for classical problems: regressions, classifications, and deep learning.

The exam will be a final project composed of programming, data acquisition, and analysis, which will be discussed orally.

The student will be evaluated in terms of: - The knowledge of the course content; - The programming skill and the quality of the written code; - The data analysis and presentation; - The physical analysis and global understanding of the treated problem.

S. Montangero, Introduction to Tensor Network Methods. Berlino: Springer International Publishing, 2018

The course will be based on lecture notes and other electronic and hard copy didactical material (Ph.D. thesis, documentation etc.)