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

Heralded quantum gates with integrated error detection in optical cavities