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Insegnamento
INFORMATION THEORY AND COMPUTATION
SCP8082709, A.A. 2019/20
Informazioni valide per gli studenti immatricolati nell'A.A. 2018/19
Dettaglio crediti formativi
Tipologia |
Ambito Disciplinare |
Settore Scientifico-Disciplinare |
Crediti |
AFFINE/INTEGRATIVA |
Attività formative affini o integrative |
FIS/03 |
6.0 |
Organizzazione dell'insegnamento
Periodo di erogazione |
Primo semestre |
Anno di corso |
II Anno |
Modalità di erogazione |
frontale |
Tipo ore |
Crediti |
Ore di didattica assistita |
Ore Studio Individuale |
LEZIONE |
6.0 |
48 |
102.0 |
Inizio attività didattiche |
30/09/2019 |
Fine attività didattiche |
18/01/2020 |
Visualizza il calendario delle lezioni |
Lezioni 2019/20 Ord.2018
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Commissioni d'esame
Nessuna commissione d'esame definita
Prerequisiti:
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Quantum mechanics and elements of programming. |
Conoscenze e abilita' da acquisire:
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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. |
Modalita' di esame:
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The exam will be a final project composed of programming, data acquisition, and analysis, which will be discussed orally. |
Criteri di valutazione:
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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. |
Contenuti:
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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. |
Attivita' di apprendimento previste e metodologie di insegnamento:
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The course will be composed of lessons in class and programming labs. |
Eventuali indicazioni sui materiali di studio:
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The course will be based on lecture notes and other electronic and hard copy didactical material (Ph.D. thesis, documentation etc.) |
Testi di riferimento: |
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Montangero, Simone, Introduction to tensor network methodsnumerical simulations of low-dimensional many-body quantum systemsSimone Montangero. Cham: Springer, 2018.
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Didattica innovativa: Strategie di insegnamento e apprendimento previste
- Lecturing
- Laboratory
- Problem based learning
- Case study
- Interactive lecturing
- Working in group
- Questioning
- Problem solving
Didattica innovativa: Software o applicazioni utilizzati
- Moodle (files, quiz, workshop, ...)
- Latex
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