Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

An algorithmic benchmark for quantum information processing

Nature volume 404, pages 368–370 (2000)Cite this article

Abstract

Quantum information processing offers potentially great advantages over classical information processing, both for efficient algorithms1,2 and for secure communication3,4. Therefore, it is important to establish that scalable control of a large number of quantum bits (qubits) can be achieved in practice. There are a rapidly growing number of proposed device technologies5,6,7,8,9,10,11 for quantum information processing. Of these technologies, those exploiting nuclear magnetic resonance (NMR) have been the first to demonstrate non-trivial quantum algorithms with small numbers of qubits12,13,14,15,16. To compare different physical realizations of quantum information processors, it is necessary to establish benchmark experiments that are independent of the underlying physical system, and that demonstrate reliable and coherent control of a reasonable number of qubits. Here we report an experimental realization of an algorithmic benchmark using an NMR technique that involves coherent manipulation of seven qubits. Moreover, our experimental procedure can be used as a reliable and efficient method for creating a standard pseudopure state, the first step for implementing traditional quantum algorithms in liquid state NMR systems. The benchmark and the techniques can be adapted for use with other proposed quantum devices.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Quantum networks for the cat-state benchmark.
Figure 2: Characteristics of crotonic acid.
Figure 3: Experimental results: spectra of the pseudopure state (red) and the input state after transfer of polarization to the methyl carbon (blue).

Similar content being viewed by others

References

  1. Simon, D. R. On the power of quantum computation. SIAM J. Comput. 26, 1474–1483 (1997).

    Article  MathSciNet  Google Scholar 

  2. Shor, P. W. Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997).

    Article  MathSciNet  Google Scholar 

  3. Wiesner, S. Conjugate coding. Sigact News 15, 78–88 (1983).

    Article  Google Scholar 

  4. Bennett, C., Bessette, F., Brassard, G., Salvail, L. & Smolin, J. Experimental quantum cryptography. J. Cryptol. 5, 3–28 (1992).

    Article  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  6. Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1997).

    Article  ADS  Google Scholar 

  7. Bocko, M. F., Herr, A. M. & Feldman, M. J. Prospects for quantum coherent computation using superconducting electronics. IEEE Trans. Appl. Supercond. 7, 3638–3641 (1997).

    Article  ADS  Google Scholar 

  8. Shnirman, A., Schön, G. & Hermon, Z. Quantum manipulations of small josephson junctions. Phys. Rev. Lett. 79, 2371–2374 (1997).

    Article  ADS  CAS  Google Scholar 

  9. Cory, D. G., Fahmy, A. F. & Havel, T. F. Ensemble quantum computing by nmr-spectroscopy. Proc. Natl Acad. Sci. USA 94, 1634–1639 (1997).

    Article  ADS  CAS  Google Scholar 

  10. Gershenfeld, N. A. & Chuang, I. L. Bulk spin resonance quantum computation. Science 275, 350–356 (1997).

    Article  MathSciNet  CAS  Google Scholar 

  11. Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).

    Article  ADS  CAS  Google Scholar 

  12. Jones, J. A., Mosca, M. & Hansen, R. H. Implementation of a quantum search algorithm on a quantum computer. Nature 392, 344–346 (1998).

    Article  ADS  Google Scholar 

  13. Chuang, I. L., Vandersypen, L. 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 

  14. Cory, D. G. et al. Experimental quantum error correction. Phys. Rev. Lett. 81, 2152–2155 (1998).

    Article  ADS  CAS  Google Scholar 

  15. Nielsen, M. A., Knill, E. & Laflamme, R. Complete quantum teleportation. Nature 396, 52–55 (1998).

    Article  ADS  CAS  Google Scholar 

  16. Marx, R., Fahmy, A. F., Myers, J. M., Bermel, W. & Glaser, S. J. Realization of a 5-bit nmr quantum computer using a new molecular architecture. Preprint quant-ph/9905087 at 〈http://xxx.lanl.gov〉 (1999).

  17. Sörensen, O. W., Eich, G. W., Levitt, M. H., Bodenhausen, G. & Ernst, R. R. Product operator-formalism for the description of nmr pulse experiments. Prog. Nucl. Magn. Reson. Spectrosc. 16 (1983).

  18. Barenco, A. et al. Elementary gates for quantum computation. Phys. Rev. A 52, 3457–3467 (1995).

    Article  ADS  CAS  Google Scholar 

  19. Freeman, R. Spin Choreography (Oxford Univ. Press, 1998).

    Google Scholar 

  20. Schumacher, B. Sending entanglement through noisy quantum channels. Phys. Rev. A 54, 2614–2628 (1996).

    Article  ADS  CAS  Google Scholar 

  21. Shor, P. W. in Proc. Symp. Foundations of Computer Science 56–65 (IEEE, Los Alamitos, California, 1996).

    Google Scholar 

  22. Aharonov, D. & Ben-Or, M. in Proc. 29th Ann. ACM Symp. Theory of Computing 176–188 (Association for Computing Machinery, New York, 1996).

    Google Scholar 

  23. Kitaev, A. Y. Quantum computations: algorithms and error correction. Uspekhi Mat. Nauk. 52, 53–112 (1997).

    Article  MathSciNet  Google Scholar 

  24. Knill, E., Laflamme, R. & Zurek, W. H. Resilient quantum computation. Science 279, 342–345 (1998).

    Article  ADS  CAS  Google Scholar 

  25. Dür, W., Briegel, H.-J., Cirac, J. I. & Zoller, P. Quantum repeaters for based on entanglement purification. Phys. Rev. A 59, 169–181 (1999).

    Article  ADS  Google Scholar 

  26. Emsley, L. & Pines, A. in Proc. Int. School of Physics, Enrico Fermi Vol. CXXIII, 123–266 (North-Holland, Amsterdam, 1994).

    Google Scholar 

  27. Knill, E., Chuang, I. & Laflamme, R. Effective pure states for bulk quantum computation. Phys. Rev. A 57, 3348–3363 (1998).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  28. Weitekamp, D. P., Garbow, J. R. & Pines, A. Determination of dipole coupling constants using heteronuclear multiple quantum nmr. J. Chem. Phys. 77, 2870–2883 (1982).

    Article  ADS  CAS  Google Scholar 

  29. Maffei, P., Elbayed, K., Brondeau, J. & Canet, D. Slice selection in nmr imaging by use of the b1 gradient along the axial direction of a saddle-shaped coil. J. Magn. Reson. 95, 382–386 (1991).

    ADS  Google Scholar 

  30. Vandersypen, L. M. K., Yannoni, C. S., Sherwood, M. H. & Chuang, I. L. Realization of logically labeled effective pure states for bulk quantum computation. Phys. Rev. Lett. 83, 3085–3088 (1999).

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank D. Cory, G. Fernandez, T. Havel, S. Lacelle, D. Lemaster, D. Meyer, C. Unkefer, A. M. Wang and W. H. Zurek for help and discussions.

Author information

Authors and Affiliations

  1. Los Alamos National Laboratory, MS B265, Los Alamos, 87545, New Mexico, USA

    E. Knill, R. Laflamme & R. Martinez

  2. Department of Nuclear Engineering, MIT, Cambridge, 02139, Massachusetts, USA

    C.-H. Tseng

Authors
  1. E. Knill
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Laflamme
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Martinez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C.-H. Tseng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. Knill.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Knill, E., Laflamme, R., Martinez, R. et al. An algorithmic benchmark for quantum information processing. Nature 404, 368–370 (2000). https://doi.org/10.1038/35006012

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/35006012

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing