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

A cold-atoms based processor for deterministic quantum computation with one qubit in intractably large Hilbert spaces