Building a quantum computer is a very rewarding task. Such computers would help us to perform certain computations which are not possible with present or future classical computers. Neutral atoms confined in optical lattices and manipulated by lasers provide us with one of the most promising avenues to implement a quantum computer or to perform quantum simulations. Whereas to perform a useful quantum computation (e.g. for factorization) one needs approximately 100.000 qubits, interesting quantum simulations require a much smaller number of qubits and are within reach of planned experimental setups.

The main goal of this project is to theoretically study new routes towards simulating quantum systems which overcome the numerical methods that exist so far. This goal is relevant for other branches of physics, like condensed matter physics, since it would allow us to understand physical properties of certain materials that so far have eluded a theoretical description or numerical simulations. We will, on the one hand, study how to use atoms in optical lattices and other quantum optical systems to build quantum simulators. On the other hand, we will develop numerical algorithms to simulate many-body quantum systems using (classical) computers. We will also apply those algorithms to the study of various quantum optical experimental setups. Apart from that, we will analyze quantum many-body system from the perspective of Quantum Information Theory. In particular, we will study their entanglement properties in order to obtain a new perspective on interesting phenomena (e.g., quantum phase transitions) exhibited by those systems. We will also develop theoretical tools to identify, classify and quantify entanglement in current experiments.