Quantum Toffoli gate in hybrid optomechanical system

An quantum Toffoli gate based on optomechanical system is proposed. By exploring the hybrid optomechanical system, we show that there are equivalence third order Kerr nonlinear effects between optical and mechanical modes. Through parameter analysis, we find that the nonlinear coefficient can be much stronger than the one under natural conditions. By taking advantage of this nonlinear effect, we can achieve high fidelity photon-phonon Toffoli gate. In the presence of dissipation and noise, we calculate the implementation time and fidelity of Toffoli gate. In addition, the application of this protocol in universal fault-tolerant quantum computation is also analyzed. Our study provides an effective platform for hybrid quantum computation.