The numerical simulation of strongly correlated quantum systems is a major challenge in different branches of modern physics as condensed matter, quantum information, cold atoms and lattice gauge theories. Indeed, numerical simulations lie at the hearth of our theoretical understanding of many different phenomena and of the support, design and verification of experimental setups ranging from single optical tables to large particle physics facilities. On top of that, the ability to control the dynamics of correlated many-body quantum systems paves the way for the design of novel experiments, the optimal engineering of quantum technologies, and the exploration of the fundamental limits of such protocols.
We illustrate some recent developments in numerical tensor network methods to simulate strongly correlated quantum systems, present an efficient algorithm to optimally control their dynamics and some fundamental bounds to the resources needed to achieve such control.
Finally, we report on novel theoretical and experimental applications of these methods, in particular we present some time-optimal protocols to drive cold atoms in optical lattices and in atom chips.