  We propose the use of Rydberg interactions and ensembles of cold atoms in
mixed state for the implementation of a protocol for deterministic quantum
computation with one quantum bit (DQC1) that can be readily operated in high
dimensional Hilbert spaces. We propose an experimental test for the scalability
of the protocol and to study the physics of discord. Furthermore we develop a
scheme to add control to non-trivial unitaries that will enable the study of
many-body physics with ensembles in mixed states.
