Improving the fidelity of optical Zeno gates via distillation

We have modeled the Zeno effect controlled-sign gate of Franson et al. [Phys. Rev. A 70, 062302 (2004)] and shown that high two-photon to one-photon absorption ratios, $\ensuremath{\kappa}$, are needed for high fidelity free-standing operation. Hence we instead employ this gate for cluster state fusion, where the requirement for $\ensuremath{\kappa}$ is less restrictive. With the help of partially offline one-photon and two-photon distillations, we can achieve a fusion gate with unity fidelity but nonunit probability of success. We conclude that for $\ensuremath{\kappa}g2200$, the Zeno fusion gate will out perform the equivalent linear optics gate.