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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Recent experiments in trapped-ion quantum information processing at NIST

John Chiaverini, M. D. Barrett, R. B. Blakestad, J. Britton, Wayne M. Itano, John D. Jost, Emanuel H. Knill, C. Langer, Dietrich G. Leibfried, Roee Ozeri, Tobias Schaetz, David J. Wineland

Published May 2, 2006• 1 citation
Publisher

Abstract

Atomic ions confined in segmented trap arrays provide a system for quantum information processing. We report on the execution of two simple quantum algorithms, quantum error correction and the quantum Fourier transform, using this implementation. The demonstration of these algorithms in a scalable system is one step towards the execution of useful, large-scale quantum algorithms.

DOI
10.1117/12.682633

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Atomic ions confined in segmented trap arrays provide a system for quantum information processing. We report on the execution of two simple quantum algorithms, quantum error correction and the quantum Fourier transform, using this implementation. The demonstration of these algorithms in a scalable system is one step towards the execution of useful, large-scale quantum algorithms.
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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.
Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40 Ca + ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm.