Quantum Simulation

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The first part of the course will discuss various state of the art methods for the numerical description of many-body quantum systems. In particular, I will explain successful applications and inherent limitations due to the exponential complexity of the many-body problem.

In the second part of the course, I will show how using highly controllable quantum system such as ultracold atoms will provide a way to overcome the limitations of classical simulation methods. I will discuss several theoretical and experimental achievements and outline the road for future developments.

Classical simulation of quantum systemsEdit

Exact diagonalizationEdit

Quantum Monte-CarloEdit

Density-Matrix Renormalization GroupEdit

Quantum simulation with ultracold atomsEdit

Analog quantum simulationEdit

Digital quantum simulationEdit