Photonic Phase Gate via an Exchange of Fermionic Spin Waves in a Spin Chain

We propose a new protocol for implementing the two-qubit photonic phase gate. In our approach, the phase is acquired by mapping two single photons into atomic excitations with fermionic character and exchanging their positions. The fermionic excitations are realized as spin waves in a spin chain, while photon storage techniques provide the interface between the photons and the spin waves. Possible imperfections and experimental systems suitable for implementing the gate are discussed.