Precise single-qubit control of the reflection phase of a photon mediated by a strongly-coupled ancilla-cavity system

We propose to use the interaction between a single qubit atom and a surrounding ensemble of three level atoms to control the phase of light reflected by an optical cavity. Our scheme employs an ensemble dark resonance that is perturbed by the qubit atom to yield a single-atom single photon gate. We show here that off-resonant excitation towards Rydberg states with strong dipolar interactions offers experimentally-viable regimes of operations with low errors (in the 10(-3) range) as required for fault-tolerant optical-photon, gate-based quantum computation. We also propose and analyze an implementation within microwave circuit-QED, where a strongly-coupled ancilla superconducting qubit can be used in the place of the atomic ensemble to provide high-fidelity coupling to microwave photons.