One-photon controlled two-photon not gate contributed by weak cross-Kerr nonlinearities

A quantum logic gate is an indispensable fundamental element for completing tasks of quantum information processing, such as quantum computation and scalable quantum networks. With the help of weak cross-Kerr nonlinearities, we propose an efficient optical one-photon controlled two-photon not gate, where polarization modes of photons act as quantum bits, aiming to construct the practical and scalable quantum logic circuits. By adopting one-time nondestructive measurement, this gate can realize the function of two two-photon controlled-not gates, where the polarization bits of two target photons will be flipped when the controlled photon is in the vertical polarization state. After measuring on the coherent state, the suitable operations including swapping of photon states and single-photon transformations are carried out by classical feed forward, conditioned on the measurement outcomes. Simple linear optical elements, and mature techniques containing Homodyne measurement and classical feed forward are applied to enhance the feasibility of the scheme presented here and other scalable logic gates.