INFORMATION THEORY AND COMPUTATION

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.