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Chinese Physics

Grover search algorithm in an ion trap system

Zheng Shi-Biao

Published Oct 31, 2005• 12 citations
Publisher

Abstract

Two schemes for the implementation of the two-qubit Grover search algorithm in the ion trap system are proposed. These schemes might be experimentally realizable with presently available techniques. The experimental implementation of the schemes would be an important step toward more complex quantum computation in the ion trap system.
DOI
10.1088/1009-1963/14/11/013

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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.
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We propose an ion-trap implementation of Grover's quantum search algorithm for an unstructured database of arbitrary length NNN. The experimental implementation is appealingly simple because the linear ion trap allows for a straightforward construction, in a single interaction step and without a multitude of Hadamard transforms, of the reflection operator, which is the engine of the Grover algorithm. Consequently, a dramatic reduction in the number of the required physical steps takes place, to just O(N)O(\sqrt{N})O(N​), the same as the number of mathematical steps. The proposed setup allows for demonstration of both the original (probabilistic) Grover search and its deterministic variation, and is remarkably robust to imperfections in the register initialization.