A heralded and error-rejecting three-photon hyper-parallel quantum gate through cavity-assisted interactions.

Hyper-parallel quantum computation is a promising and fruitful area of research with its high capacity and low loss rate characters. In this paper, we propose a heralded, compact, scalable, and deterministic error-rejecting scheme for implementing three-photon hyper-parallel Toffoli gate simultaneously acting on polarization and spatial degrees of freedom. It is a practical and unity gate without strong coupling strength limitations, since the undesired performances caused by the side leakage and the limited coupling strength are detected by the single-photon detectors. The success of our proposal can be heralded by the detectors, and the efficiency can be further improved by repeating the operation processes when the detectors are clicked. The evaluation of gate performance with experimental parameters shows that it is feasible with current experimental technology.