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Physical Review A

Implementing a conditional z gate by a combination of resonant interaction and quantum interference

Xu‐Bo Zou, Yuli Dong, Guang‐Can Guo

Published Sep 19, 2006• 46 citations
Publisher

Abstract

We first propose an experimental scheme to implement a two-qubit conditional $z$ gate with atoms trapped in a high-$Q$ optical cavity. The scheme is based on a combination of resonant interaction and quantum interference. Further, we show that the scheme can be directly generalized to implement an $N$-qubit conditional $z$ gate, and the interaction time required to implement scheme does not change with increasing the number of qubits. This might lead to more efficient construction of quantum circuits and quantum algorithms.

DOI
10.1103/physreva.74.032325

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We first propose an experimental scheme to implement a two-qubit conditional zzz gate with atoms trapped in a high-QQQ optical cavity. The scheme is based on a combination of resonant interaction and quantum interference. Further, we show that the scheme can be directly generalized to implement an NNN-qubit conditional zzz gate, and the interaction time required to implement scheme does not change with increasing the number of qubits. This might lead to more efficient construction of quantum circuits and quantum algorithms.
We present a one-step scheme for direct implementation of an NNN-qubit controlled-phase gate with atoms trapped in a high-QQQ optical cavity without resorting to a sequence of single- and two-qubit gates. The interaction time that is required to implement the scheme does not rise with increasing number of qubits. This might lead to more efficient construction of quantum circuits and quantum algorithms.
We propose a scheme for realizing a two-qubit quantum phase gate between atoms inside a high-QQQ optical cavity. In the scheme, the dispersive interaction between atoms and the cavity field induces photon-number Stark shift, which can yield a resonant interaction inside one selected atom-field subspace and leave the others in a highly dispersive regime. Due to the selective atom-cavity interaction, (1) the scheme only requires commonly addressing the atoms inside the optical cavity during the gate operation, and (2) it can be directly used to implement an NNN-qubit conditional phase gate. These properties can significantly reduce the number of operations for implementing quantum computation and quantum algorithms.
We propose a scheme to implement an NNN-qubit conditional phase gate with NNN neutral atoms which are trapped in a large detuning optical cavity. In our scheme, since the cavity field is only required to be virtually excited, the phase gate operation is insensitive to the cavity decay and the gate can be implemented with a high fidelity.
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.