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Science 13 May 2005:
Vol. 308. no. 5724, pp. 997 - 1000
DOI: 10.1126/science.1110335
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Reports

Implementation of the Semiclassical Quantum Fourier Transform in a Scalable System

J. Chiaverini,* J. Britton, D. Leibfried, E. Knill, M. D. Barrett,{dagger} R. B. Blakestad, W. M. Itano, J. D. Jost, C. Langer, R. Ozeri, T. Schaetz,{ddagger} D. J. Wineland

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

National Institute of Standards and Technology, Boulder, CO 80305, USA.

{dagger} Present address: Physics Department, University of Otago, Dunedin 9001, New Zealand.

{ddagger} Present address: Max Planck Institut für Quantenoptik, Garching 85748, Germany.

* To whom correspondence should be addressed. E-mail: john.chiaverini{at}boulder.nist.gov

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THIS ARTICLE HAS BEEN CITED BY OTHER ARTICLES:
Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots.
J. R. Petta, A. C. Johnson, J. M. Taylor, E. A. Laird, A. Yacoby, M. D. Lukin, C. M. Marcus, M. P. Hanson, and A. C. Gossard (2005)
Science 309, 2180-2184
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