Robust quantum gates on neutral atoms with cavity-assisted photon-scattering

We propose a scheme to achieve quantum computation with neutral atoms whose interactions are catalyzed by single photons. Conditional quantum gates, including an $N$-atom Toffoli gate and nonlocal gates on remote atoms, are obtained through cavity-assisted photon scattering in a manner that is robust to random variation in the atom-photon coupling rate and which does not require localization in the Lamb-Dicke regime. The dominant noise in our scheme is automatically detected for each gate operation, leading to signalled errors which do not preclude efficient quantum computation even if the error probability is close to the unity.