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Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer

Nature volume 421, pages 48–50 (2003)Cite this article

Abstract

Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch–Jozsa algorithm1,2) requires just one examination step. The Deutsch–Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques3,4, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises3 motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate6, the entanglement of four ions7, quantum state engineering8 and entanglement-enhanced phase estimation9. Here we exploit techniques10,11 developed for nuclear magnetic resonance to implement the Deutsch–Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.

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Figure 1: Quantum circuit for implementing the Deutsch–Jozsa algorithm with basic quantum operations.
Figure 2: Quantum mechanical energy levels relevant for the ion-trap quantum computer.
Figure 3: Time evolution of |〈1∣a〉|2.

References

  1. Deutsch, D. Quantum theory, the Church-Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97–117 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  2. Deutsch, D. & Jozsa, R. Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  3. Chuang, I. I., Vandersypen, I. M. K., Zhou, X., Leung, D. W. & Lloyd, S. Experimental realization of a quantum algorithm. Nature 393, 143–146 (1998)

    Article  ADS  CAS  Google Scholar 

  4. Jones, T. F. & Mosca, M. Implementation of a quantum algorithm to solve Deutsch's problem on a nuclear magnetic resonance quantum computer. J. Chem. Phys. 109, 1648–1653 (1998)

    Article  ADS  CAS  Google Scholar 

  5. Cirac, J. I. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995)

    Article  ADS  CAS  Google Scholar 

  6. Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M. & Wineland, D. J. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714–4717 (1995)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  7. Sackett, C. A. et al. Experimental entanglement of four particles. Nature 404, 256–259 (2000)

    Article  ADS  CAS  Google Scholar 

  8. Roos, Ch. et al. Quantum state engineering on an optical transition and decoherence in a Paul trap. Phys. Rev. Lett. 83, 4713–4716 (1999)

    Article  ADS  CAS  Google Scholar 

  9. Meyer, V. et al. Experimental demonstration of entanglement-enhanced rotation angle estimation using trapped ions. Phys. Rev. Lett. 86, 5870–5873 (2001)

    Article  ADS  CAS  Google Scholar 

  10. Childs, A. M. & Chuang, I. M. Universal quantum computation with two-level trapped ions. Phys. Rev. A 63, 012306 (2001)

    Article  ADS  Google Scholar 

  11. Levitt, M. H. Composite pulses (NMR spectroscopy). Prog. Nucl. Magn. Reson. Spectrosc. 18, 61–122 (1986)

    Article  ADS  CAS  Google Scholar 

  12. Šašura, M. & Bužek, V. Cold trapped ions as quantum information processors. J. Mod. Opt. 49, 1593–1647 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  13. Eschner, J., Raab, Ch., Schmidt-Kaler, F. & Blatt, R. Light interference from single atoms and their mirror images. Nature 413, 495–498 (2001)

    Article  ADS  CAS  Google Scholar 

  14. Guthöhrlein, G. R., Keller, M., Hayasaka, K., Lange, W. & Walther, H. A single ion as a nanoscopic probe of an optical field. Nature 414, 49–51 (2001)

    Article  ADS  Google Scholar 

  15. Mundt, A. B. et al. Coupling a single atomic quantum bit to a high finesse optical cavity. Phys. Rev. Lett. 89, 103001 (2002)

    Article  ADS  CAS  Google Scholar 

  16. Meekhof, D. M., Monroe, C., King, B. E., Itano, W. M. & Wineland, D. J. Generation of nonclassical motional states of a trapped atom. Phys. Rev. Lett. 76, 1796–1799 (1996)

    Article  ADS  CAS  Google Scholar 

  17. Monroe, C., Meekhof, D. M., King, B. E. & Wineland, D. J. A “Schrödinger Cat” superposition state of an atom. Science 272, 1131–1136 (1996)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  18. Dehmelt, H. Proposed 1014Δν > ν laser fluorescence spectroscopy on TI+ mono-ion oscillator. Bull. Am. Phys. Soc. 20, 60 (1975)

    Google Scholar 

  19. Nägerl, H. C. et al. Investigating a qubit candidate: Spectroscopy on the S1/2 to D5/2 transition of a trapped calcium ion in a linear Paul trap. Phys. Rev. A 61, 023405 (2000)

    Article  ADS  Google Scholar 

  20. Häffner, H. et al. Precision measurement and compensation of optical Stark shifts for an ion-trap quantum processor. Preprint available at 〈http://arXiv.org/abs/physics/0212040〉 (2002).

  21. Nielsen, M. A. & Chuang, I. J. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, 2000)

    MATH  Google Scholar 

  22. Schmidt-Kaler, F. et al. Coherence of qubits based on single Ca ions. Preprint available at 〈http://arXiv.org/abs/quant-ph/0211059〉 (2002).

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Acknowledgements

We gratefully acknowledge support by the European Commission (QSTRUCT, QI, QUEST and QUBITS networks), by the Austrian Science Fund (FWF), and by the Institut für Quanteninformation GmbH.

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Authors and Affiliations

  1. Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020, Innsbruck, Austria

    Stephan Gulde, Mark Riebe, Gavin P. T. Lancaster, Christoph Becher, Jürgen Eschner, Hartmut Häffner, Ferdinand Schmidt-Kaler, Isaac L. Chuang & Rainer Blatt

  2. MIT Media Laboratory, Cambridge, Massachusetts, 02139, USA

    Isaac L. Chuang

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  1. Stephan Gulde
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Correspondence to Ferdinand Schmidt-Kaler.

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Gulde, S., Riebe, M., Lancaster, G. et al. Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer. Nature 421, 48–50 (2003). https://doi.org/10.1038/nature01336

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