Implementation of controlled-not quantum gate by nonlinear coupled electro-nano-optomechanical oscillators

A feasibility study is done for the possibility of a universal set of quantum gate implementation based on phononic state via fourth-order Duffing nonlinearity in an optomechanical system. The optomechanical system consists of $N$ doubly clamped coupled nanobeam arrays driven by local static and radio frequency electrical potentials, coupled to a single-mode high-finesse optical cavity. The results show that the ideal cnot gate can be implemented only under nonresonance dynamics when the dissipation processes are negligible.