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arXiv:quant-ph/0204154

Ion Trap Proposal for Quantum Search

Joonwoo Bae, Younghun Kwon

Published Apr 26, 2002• 0 citations
arXivHTMLPDF

Abstract

In this letter, we show that the laser Hamiltonian can perform the quantum search. We also show that the process of quantum search is a resonance between the initial state and the target state, which implies that Nature already has a quantum search system to use a transition of energy. In addition, we provide the particular scheme to implement the quantum search algorithm based on a trapped ion.

DOI
10.48550/arxiv.quant-ph/0204154

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In this letter, we show that the laser Hamiltonian can perform the quantum search. We also show that the process of quantum search is a resonance between the initial state and the target state, which implies that Nature already has a quantum search system to use a transition of energy. In addition, we provide the particular scheme to implement the quantum search algorithm based on a trapped ion.
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.
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.
We propose an implementation of the Grover's search algorithm in a nonclassical database using a linear chain of trapped ions. The database comprises all collective states with two ionic excitations; hence the number of database entries scales quadratically with the number of ions NNN. The system is initialized in an even superposition of all register states, i.e., in the symmetric Dicke state with NNN ions sharing two excitations. The reflection-about-the-mean operator is produced merely by global addressing of the ion string by an off-resonant pulse with a suitable area, whereas the oracle operator is a control-phase gate. This simplification should allow a demonstration of quantum search in a database of hundreds of elements without needing to synthesize multiqubit quantum gates. The technique does not rely on coherent addition or subtraction of phonons, and hence the ion chain can be sympathetically cooled throughout the process.
The purpose of this article is to review two complementary schemes for quantum computation with trapped ions. We initially discuss the first proposal of quantum computations with cold trapped ions (J. I. Cirac and P. Zoller; Phys. Rev. Lett. 74, 4091, 1995) which requires, prior to any computation, laser cooling to the motional ground state. This proposal is closely related to the physics of generating and manipulating N-particles entangled states in both ion traps and high-Q cavities (cavity quantum electrodynamics). The second scheme is that of quantum computations with hot trapped ions (J.F. Poyatos, J.I. Cirac and P. Zoller; Phys. Rev. Lett. 81, 1322, 1998) which works at finite temperature and resembles physical ideas found in atom interferometry.