Toffoli gate with photonic qubits based on weak cross-Kerr nonlinearities

We design an experimental feasible Toffoli gate, comprising nonlinear optical gates via cross-Kerr nonlinearities (XKNLs) and linear optical devices, on three photonic qubits (photons). The Toffoli gate is a three-qubit universal quantum controlled gate for various quantum information processing schemes. Thus, we propose an efficient method to construct a Toffoli gate using nonlinear optical gates that employ weak XKNLs, quantum bus beams, and photon-number-resolving measurements. Furthermore, to ensure the reliable performance of the Toffoli gate (via XKNLs), we describe an experimental condition to reduce the influence (photon loss and dephasing) of the decoherence effect induced in nonlinear optical gates.