The purpose of this project is to study quantum systems which allow only a partial control by a constrained set of quantum operations. Typical examples are many particle quantum systems like cold atoms in optical lattices or other multi-atom ensembles, which can be manipulated collectively but not individually (e.g. because the spatial resolution of the used devices is not good enough to address single particles). Such restrictions are currently one of the biggest obstacles against working quantum computers. Instead of improving the corresponding experimental methods (i.e. searching for better implementations) this project aims at a systematic study of the tasks which can be performed with currently available techniques. To this end we want to develop theoretical models which can on the one hand reflect the limitations of current experimental setups, but are on the other hand powerful enough to allow non-trivial practical applications. This point of view is new and complementary to most other research in quantum information science, where complete control over a small number of particles is assumed. Based on these models we plan in a second step to produce strategies for the generation ofdevices which are -- at least for a very special task -- more powerful than classical computers, and at the same time easily implementable. Possible applications of this procedure are simulations of other quantum systems, like models for ferromagnetic materials with long range quantum correlations or lattice approximations of quantum field theories, which can not be treated efficiently on classical computers (i.e. the computation time grows exponentially with the system size). The advantage of our approach over other research which directly tries to implement universal quantum computers is a much greater success probability (at least short- or mid-term).