Compact quantum gates for hybrid photon–atom systems assisted by Faraday rotation

Abstract

We present some compact circuits for a deterministic quantum computing on the hybrid photon---atom systems, including the Fredkin gate and SWAP gate. These gates are constructed by exploiting the optical Faraday rotation induced by an atom trapped in a single-sided optical microcavity. The control qubit of our gates is encoded on the polarization states of the single photon, and the target qubit is encoded on the ground states of an atom confined in an optical microcavity. Since the decoherence of the flying qubit with atmosphere for a long distance is negligible and the stationary qubits are trapped inside single-sided microcavities, our gates are robust. Moreover, ancillary single photon is not needed and only some linear-optical devices are adopted, which makes our protocols efficient and practical. Our schemes need not meet the condition that the transmission for the uncoupled cavity is balanceable with the reflectance for the coupled cavity, which is different from the quantum computation with a double-sided optical microcavity. Our calculations show that the fidelities of the two hybrid quantum gates are high with the available experimental technology.