Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED

We present a simple protocol and quantum circuit for efficient implementation of the N-bit discrete quantum Fourier transform by using two-qubit controlled-NOT gate and SWCZ gate that is a combination of -SWAP and controlled-Z gates in cavity quantum electrodynamics. In this protocol long-lived electronic states in circular Rydberg atoms are used as quantum bits and the one-bit and two-bit quantum gate operations required for implementing the discrete quantum Fourier transform in the quantum circuit can be easily achieved with atom-microwave resonant interaction and atom-cavity interaction occurring only between two nearest-neighbour atoms. We present the detailed experimental procedure and analyse the experimental feasibility.