In this thesis, I describe a proposal for experiments with dense ensembles of ultracold Rubidium atoms optically excited to highlying electronic states known as Rydberg states. The proposed experiment is designed to implement a model of quantum computation known as deterministic quantum computation with one qubit (DQC1). My proposal is novel among other proposals for Rydberg atoms because it employs mixed states and could provide insights into the source of the enhancements of quantum technology over classical technology. I demonstrate that ultracold atoms and Rydberg interactions offer new perspectives for exploring the DQC1 model. This is mainly due to the large strength, long range and controllability of Rydberg interactions.
My specific contributions include: a proposal that solves one of the main issues with implementing quantum logic gates between ensembles of atoms; numerical simulations of the proposed cold atom implementation of a DQC1 protocol; and the design and laboratory implementation of a high-performance optical system for imaging ultracold atoms. These contributions bring the experimental exploration of the DQC1 model closer to realisation
