Heralded quantum gates with integrated error detection in optical cavities

We propose and analyze heralded quantum gates between qubits in optical cavities. They employ an auxiliary qubit to report if a successful gate occurred. In this manner, the errors, which would have corrupted a deterministic gate, are converted into a non-unity probability of success: once successful the gate has a much higher fidelity than a similar deterministic gate. Specifically, we describe that a heralded , near-deterministic controlled phase gate (CZ-gate) with the conditional error arbitrarily close to zero and the success probability that approaches unity as the cooperativity of the system, C, becomes large. Furthermore, we describe an extension to near-deterministic N- qubit Toffoli gate with a favorable error scaling. These gates can be directly employed in quantum repeater networks to facilitate near-ideal entanglement swapping, thus greatly speeding up the entanglement distribution.