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Physical Review A

Toffoli gate originating from a single resonant interaction with cavity QED

Changyong Chen, Mang Feng, Kelin Gao

Published Jun 23, 2006• 62 citations
Publisher

Abstract

We propose a potentially practical scheme to implement a three-qubit Toffoli gate by a single resonant interaction in cavity QED. The scheme does not require two-qubit controlled-NOT gates but uses a three-qubit phase gate and two Hadamard gates, where the phase gate can be implemented by only a single resonant interaction of the atoms with the cavity mode. Both the situations with and without cavity decay are considered. We discuss the advantages and the experimental feasibility of our scheme.

DOI
10.1103/physreva.73.064304

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We propose a potentially practical scheme to implement a three-qubit Toffoli gate by a single resonant interaction in cavity QED. The scheme does not require two-qubit controlled-NOT gates but uses a three-qubit phase gate and two Hadamard gates, where the phase gate can be implemented by only a single resonant interaction of the atoms with the cavity mode. Both the situations with and without cavity decay are considered. We discuss the advantages and the experimental feasibility of our scheme.
We propose a potentially practical scheme to implement an approximate three-qubit Toffoli gate by a single resonant interaction in dissipative cavity QED in which the cavity mode decay and atomic spontaneous emission are considered. The scheme does not require two-qubit controlled-NOT gates but uses a three-qubit phase gate and two Hadamard gates, where the approximate phase gate can be implemented by only a single dissipative resonant interaction of atoms with the cavity mode. Discussions are made for the advantages and the experimental feasibility of our scheme.
A scheme for implementing a three-qubit Toffoli gate with atoms sent through a microwave cavity is proposed by choosing nonidentical coupling constants between the atoms and cavity. The scheme can be generalized to implement an NNN-qubit Toffoli gate and the gating time does not change with an increase of the number of qubits.
The Toffoli gate, which has practical applications in the implementation of practical quantum algorithms and quantum error correction, is usually constructed from concatenated two-qubit or qubit-qutrit gates. Here we show that the Toffoli gate for three qubits can be implemented through a single XY\mathit{XY}XY interaction plus two single-qubit rotations. This method greatly simplifies the experimental implementation of the Toffoli gate and promises a much higher fidelity compared to those based on elementary gate decomposition. We present an example for the implementation of the required XY\mathit{XY}XY interaction in cavity QED.
This paper proposes a scheme for realization of a three-qubit Toffoli gate operation using three four-level atoms by a selective atom-field interaction in a cavity quantum electrodynamics system. In the proposed protocol, the quantum information is encoded on the stable ground states of atoms, and atomic spontaneous emission is negligible as the large atom-cavity detuning effectively suppresses the spontaneous decay of the atoms. The influence of the dissipation on fidelity and success probability of the three-qubit Toffoli gate is also discussed. The scheme can also be applied to realize an N -qubit Toffoli gate and the interaction time required does not rise with increasing the number of qubits.
We propose a scheme for realization of three-qubit controlled-phase gate via passing two three-level atoms through a high-Q optical cavity in a cavity QED system. In the presented protocol, the two stable ground states of the atoms act as the two controlling qubits and the zero- and one-photon Fock states of the cavity-field form the target qubit, and no auxiliary state or any measurement is required. The numerical simulation shows that the gate fidelities remain at a high level under the influence of the atomic spontaneous emission, the decay of the cavity mode and deviation of the coupling strength. The experimental feasibility of our proposal is also discussed.