First cycle
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Second cycle
degree courses
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degree courses
School of Science
Course unit
SCP7081801, A.A. 2019/20

Information concerning the students who enrolled in A.Y. 2018/19

Information on the course unit
Degree course Second cycle degree in
SC2382, Degree course structure A.Y. 2017/18, A.Y. 2019/20
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Degree course track PHYSICS OF MATTER [002PD]
Number of ECTS credits allocated 6.0
Type of assessment Mark
Course unit English denomination QUANTUM INFORMATION
Website of the academic structure
Department of reference Department of Physics and Astronomy
E-Learning website
Mandatory attendance No
Language of instruction English
Single Course unit The Course unit can be attended under the option Single Course unit attendance
Optional Course unit The Course unit can be chosen as Optional Course unit

Teacher in charge SIMONE MONTANGERO FIS/03

Course unit code Course unit name Teacher in charge Degree course code

ECTS: details
Type Scientific-Disciplinary 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 of
Individual study
Lecture 6.0 48 102.0 No turn

Start of activities 30/09/2019
End of activities 18/01/2020
Show course schedule 2019/20 Reg.2017 course timetable

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 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.
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 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

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

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.
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 low-dimensional many-body quantum systemsSimone Montangero. Cham: Springer, 2018. Cerca nel catalogo

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