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 pi 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.