This thesis proposes a novel method to implement universal quantum gates for photonic qubits using the strong dipole-dipole interactions present in a cold gas of Rydberg atoms and the control offered by microwave fields. By means of electromagnetically induced transparency (EIT) we store the information encoded in photonic qubits as Rydberg excitations, and then couple these to neighbouring states using microwaves. Microwaves alter the range of the dipole-dipole interactions between the excitations, and a suitable geometrical arrangement of the excitations in the cloud leads to a controlled π phase shift in the system's wavefunction, the basis of the universal gates proposed. After processing, the excitations in the medium are later retrieved as photons.
A theoretical description of the implementation of a 2-qubit universal gate is presented and a numerical analysis shows the feasibility of its implementation in a cold cloud of Rubidium atoms. A scheme is also proposed to construct more general gates with applications in quantum information processing. These schemes have been made possible by the analysis of recent experiments performed in
the group. This analysis is repeated here, along with the characterization of parts of the detection system required to obtain them
