Two-photon phase gate with linear optical elements and atom–cavity system

We propose a protocol for implementing π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi $$\end{document} phase gate of two photons with linear optical elements and an atom–cavity system. The evolution of the atom–cavity system is based on the quantum Zeno dynamics. The devices in the present protocol are simple and feasible with current experimental technology. Moreover, the method we proposed here is deterministic with a high fidelity. Numerical simulation shows that the evolution in cavity is efficient and robust. Therefore, the protocol may be helpful for quantum computation field.