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Physical Review A

Cavity QED implementation of the discrete quantum Fourier transform

Marlan O. Scully, Muhammad Suhail Zubairy

Published May 8, 2002• 58 citations
Publisher

Abstract

We present a scheme for the implementation of the discrete quantum Fourier transform using cavity quantum electrodynamics. In the proposed scheme a series of atoms whose atomic coherence carries the input state passes through a series of cavities and classical field, and the resulting state in the cavities is the quantum Fourier transform of the input state.

DOI
10.1103/physreva.65.052324

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We present a scheme for the implementation of the discrete quantum Fourier transform using cavity quantum electrodynamics. In the proposed scheme a series of atoms whose atomic coherence carries the input state passes through a series of cavities and classical field, and the resulting state in the cavities is the quantum Fourier transform of the input state.
We propose a scheme for implementing discrete quantum Fourier transform in cavity quantum electrodynamics (QED). The experimental implementation is appealingly simple because the combined effect of the complex controlled- R k gate and SWAP gate operations required for implementing discrete quantum Fourier transform in the naive quantum circuit is replaced by the one-step CR k S gate, which can be directly implemented via atom–cavity interaction with the assistance of classical fields. We propose the detailed experimental procedure and analyze the experimental feasibility. The experimental implementation of the scheme would show the full power of quantum algorithm and would open wide prospects for more complicated quantum computation with atoms in QED.
Possible schemes to implement the basic quantum gates for quantum computation have been presented based on cavity quantum electrodynamics (QED) systems. We then discuss schemes to implement several important quantum algorithms such as the discrete quantum fourier transform (QFT) algorithm and Grover's quantum search algorithm based on these quantum gates. Some other applications of cavity QED based systems including the implementations of a quantum disentanglement eraser and an entanglement amplifier are also discussed.
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.