
Course unit
QUANTUM INFORMATION
SCP7081801, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2018/19
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Educational activities in elective or integrative disciplines 
FIS/03 
Material Physics 
6.0 
Course unit organization
Period 
First semester 
Year 
2nd Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Lecture 
6.0 
48 
102.0 
No turn 
Examination board
Board 
From 
To 
Members of the board 
1 Commissione Information Theory and Computation 
01/10/2019 
30/11/2020 
MONTANGERO
SIMONE
(Presidente)
SALASNICH
LUCA
(Membro Effettivo)
DELL'ANNA
LUCA
(Supplente)

Prerequisites:

Quantum mechanics and elements of programming. 
Target skills and knowledge:

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 handson 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 lowdimensional equilibrium and outofequilibrium 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. 
Examination methods:

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

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. 
Course unit contents:

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 objectoriented programming
5. SchrÃ¶dinger equation (exact diagonalization, Split operator method, Suzukitrotter
decomposition, ...)
Basics of quantum information:
1. Density matrices and Liouville operators
2. Manybody Hamiltonians and states (Tensor products, Liouville representation, ...)
3. Entanglement measures
4. Entanglement in manybody 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. KibbleZurek mechanism
6. Optimal control of manybody quantum systems
7. Open quantum systems (quantum trajectories, MPDO, LPTN, ...)
8. Tensor networks for classical problems: regressions, classifications, and deep learning. 
Planned learning activities and teaching methods:

The course will be composed of lessons in class and programming labs. 
Additional notes about suggested reading:

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

Montangero, Simone, Introduction to tensor network methodsnumerical simulations of lowdimensional manybody quantum systemsSimone Montangero. Cham: Springer, 2018.

Innovative teaching methods: Teaching and learning strategies
 Lecturing
 Laboratory
 Problem based learning
 Case study
 Interactive lecturing
 Working in group
 Questioning
 Problem solving
Innovative teaching methods: Software or applications used
 Moodle (files, quizzes, workshops, ...)
 Latex

