Abstract
Feasibility study is done for the possibility of universal set of quantum gate implementation based on phononic state via 4th order Duffing nonlinearity in an optomechanical system. The optomechanical system consists of N doubly clamped coupled nanobeam array drived by local static and radio frequency electrical potentials, coupled to a single-mode high finesse optical cavity. The results show that ideal CNOT gate can be implemented only under non-resonance dynamics when the dissipation processes are negligible.