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arXiv:0809.3053 · Journal of the Optical Society of America B

Implementation of a many-qubit Grover search with trapped ultracold ions

Wan-Li Yang, Hua Wei, Changyong Chen, Mang Feng

Published Sep 25, 2008• 7 citations
arXivHTMLPDF

Abstract

We propose a potentially practical scheme for realization of an n-qubit (n>2) conditional phase flip (CPF) gate and implementation of Grover's search algorithm in an ion-trap system. We demonstrate, both analytically and numerically, that our scheme could be achieved efficiently to find a marked state with high fidelity and high success probability. We also show the merits of the proposal that the increase of the ion number can improve the fidelity and success probability of the CPF gate. The required operations for a Grover search are very close to the capabilities of current ion-trap techniques.

DOI
10.1364/josab.25.001720

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We propose a potentially practical scheme for realization of an n-qubit (n>2) conditional phase flip (CPF) gate and implementation of Grover's search algorithm in an ion-trap system. We demonstrate, both analytically and numerically, that our scheme could be achieved efficiently to find a marked state with high fidelity and high success probability. We also show the merits of the proposal that the increase of the ion number can improve the fidelity and success probability of the CPF gate. The required operations for a Grover search are very close to the capabilities of current ion-trap techniques.
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We study the possibility of an implementation of N-qubit (N>3) Grover search in cavity QED, based on a fast operation of N-qubit controlled phase-flip with atoms in resonance with the cavity mode. We demonstrate both analytically and numerically that, our scheme could be achieved efficiently to find a marked state with high fidelity and high success probability. As cavity decay is involved in our quantum trajectory treatment, we could analytically understand the implementation of a Grover search subject to dissipation, which would be very helpful for relevant experiments.
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The Grover quantum search algorithm is a hallmark application of a quantum computer with a well-known speedup over classical searches of an unsorted database. Here, we report results for a complete three-qubit Grover search algorithm using the scalable quantum computing technology of trapped atomic ions, with better-than-classical performance. Two methods of state marking are used for the oracles: a phase-flip method employed by other experimental demonstrations, and a Boolean method requiring an ancilla qubit that is directly equivalent to the state marking scheme required to perform a classical search. We also report the deterministic implementation of a Toffoli-4 gate, which is used along with Toffoli-3 gates to construct the algorithms; these gates have process fidelities of 70.5% and 89.6%, respectively.