We propose a scalable fault-tolerant scheme for deterministic quantum computing with spins that is based on a three-particle entanglement produced by the conditional Faraday rotation of the polarization of single photons due to the nonresonant interaction with spins of quantum dots, embedded in microcavities inside a photonic crystal. The resulting conditional phase gate yields switching times of $50\mathrm{ps}$. We show that it acts fault-tolerantly not only on the Calderbank-Shor-Steane quantum error correction codes, but also on Shor’s code in a single shot. Single-qubit operations on Shor’s logical qubits can be implemented by means of the optical Stark effect combined with the optical Ruderman-Kittel-Kasuya-Yosida interaction in a single shot.

• Received 8 July 2005

DOI:https://doi.org/10.1103/PhysRevB.73.075312