This course provides an introduction to simulation methods for quantum systems. Starting from the one-body problem, a special emphasis is on quantum many-body problems, where we cover both approximate methods (Hartree-Fock, density functional theory) and exact methods (exact diagonalization, matrix product states, and quantum Monte Carlo methods).

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This course offers an introduction to quantum field theories, in particular QCD, formulated on a space-time lattice. The lattice provides a non-perturbative, gauge-invariant regularization scheme for the Euclidean path integral. The course introduces both the theoretical background and the computational tools, like Monte Carlo simulations, used for the quantitative study of quarks and gluons.

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