Simulating an all-optical quantum controlled-NOT gate using soliton scattering by a reflectionless potential well

We present a protocol for the quantum controlled-NOT gate which is based on two qubits operation by investigating the soliton scattering through a reflectionless potential well in an optical system. We consider the set up of two input solitons with different intensities scattered by a reflectionless potential well with a control soliton placed at the center of the potential. The two input solitons correspond to the target qubit while either the presence or absence of control soliton in the potential well or the presence or absence of control potential well corresponds to the control qubit. We achieve the desired performance of the quantum logic gate by exploiting the intensity difference between the two input solitons and we find this to be possible within a finite width of a velocity of incidence for the two solitons. The calculation of transport coefficients ensures the feasibility of building a quantum controlled-NOT gate. This protocol demonstrates the prospect of soliton scattering by a potential well for quantum information processing. Especially, the setup with control potential as a control qubit allows realization of the CNOT operation with the negligible amount of radiation.