Fault-tolerant quantum computing with spins using the conditional Faraday rotation

We propose a fault-tolerant scheme for deterministic quantum computing with spins that is based on a quantum teleportation scheme using the conditional Faraday rotation. The phase gate between two sets of noninteracting quantum dots, embedded in microcavities inside a photonic crystal, is mediated by single photons, which yields a Faraday rotation rate high enough for gate operation times of 100 ps. Using sets of quantum dots and error correction codes makes our scheme fault-tolerant. Single-qubit operations on encoded qubits can be implemented by means of the optical Stark effect combined with the optical RKKY interaction.