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Chinese Physics Letters

A Simple Scheme for Two-Qubit Grover Search in Hot Trapped Ions

Zheng Xiao-Juan, Mao-Fa Fang, Hui Xu

Published Oct 29, 2009• 2 citations
Publisher

Abstract

An alternative simple scheme is proposed to implement the two-qubit Grover search algorithm in trapped ions by applying a single standing-wave laser pulse during the two-qubit operation. The scheme is insensitive to the heating of vibrational motion, which is important in view of decoherence. Moreover a third auxiliary internal electronic state is eliminated, and the qubit definitions are the same for both ions, which makes the experiment easier and simpler.

DOI
10.1088/0256-307x/26/11/110301

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An alternative simple scheme is proposed to implement the two-qubit Grover search algorithm in trapped ions by applying a single standing-wave laser pulse during the two-qubit operation. The scheme is insensitive to the heating of vibrational motion, which is important in view of decoherence. Moreover a third auxiliary internal electronic state is eliminated, and the qubit definitions are the same for both ions, which makes the experiment easier and simpler.
We propose a scheme to implement a two-qubit Grover quantum search algorithm. The novelty in the proposal is that the motional state is introduced into the computation and the internal state within a single cold trapped ion. The motional and internal states of the ion are manipulated as two qubits by the laser pulses to accomplish an example of a Grover algorithm based on the two qubits. The composite laser pulses that are applied to implement the Grover algorithm have been designed in detail. The issues concerning measurement and decoherence are discussed.
The desired interference required for quantum computing may be modified by wave-function oscillations for the implementation of quantum algorithms [Phys. Rev. Lett. 84, 1615 (2000)]. To diminish such a detrimental effect, we propose a scheme with trapped ion pairs as qubits and apply the scheme to the Grover search. It will be shown that our scheme cannot only carry out a full Grover search, but can also meet the requirement for scalable hot-ion quantum computing. Moreover, the ion-pair qubits in our scheme are more robust against decoherence and the dissipation caused by the environment than single-particle qubits proposed before.
Following the proposal by [F. Yamaguchi et al. Phys. Rev. A 66, 010302(R) (2002)], we present an alternative way to implement the two-qubit Grover search algorithm in cavity QED. Compared with Yamaguchi et al.'s proposal, with a strong resonant classical field added, our method is insensitive to both the cavity decay and thermal field, and does not require that the cavity remain in the vacuum state throughout the procedure. Moreover, the qubit definitions are the same for both atoms, which makes the experiment easier. The strictly numerical simulation shows that our proposal is good enough to demonstrate a two-qubit Grover's search with high fidelity.