Quantum fast Fourier transform using multilevel atoms

We propose an implementation of the quantum fast Fourier transform algorithm in an entangled system of multilevel atoms. The Fourier transform occurs naturally in the unitary time evolution of energy eigenstates and is used to de®ne an alternative wave-packet basis for quantum information in the atom. A change of basis from energy levels to wave packets amounts to a discrete quantum Fourier transform within each atom. The algorithm then reduces to a series of conditional phase transforms between two entangled atoms in mixed energy and wave-packet bases. We show how to implement such transforms using wave-packet control of the internal states of the ions in the linear ion-trap scheme for quantum computing.