Skip to main content
SpringerLink
Log in

The theoretic design of NMR pulses program of arbitrary N-qubit Grover’s algorithm and the NMR experiment proof

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

Grover’s quantum searching algorithm is most widely studied in the current quantum computation research, and has been implemented experimentally by NMR (Nuclear Magnetic Resonance) technique. In this article, we design arbitrary N-qubit NMR pulses program of Grover’s algorithm based on the multiple-quantum operator algebra theory and demonstrate 2-qubit pulses program experimentally. The result also proves the validity of the multiple-quantum operator algebra theory

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bennett, C. H., DiVincenzo, D. P., Quantum information and computation, Nature, 2000, 404: 247–255.

    Article  Google Scholar 

  2. Deutsch, D., Quantum theory, the Church-Turing principle and the universal quantum computer, Proc. Roy. Soc. Lond. A, 1985,400:97–117.

    MATH  MathSciNet  Google Scholar 

  3. Shor, P., Proc.35th Ann. Symp. Found Comput. Science, Los Alamilos: IEEE Comp. Soc. Press, 1994: 124–133.

    Book  Google Scholar 

  4. Grover, L. K., Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett., 1997, 79: 325–328.

    Article  Google Scholar 

  5. Feynman, R. P., Simulating physics with computers, Int. J. Theor. Phys., 1982, 21: 467–488.

    Article  MathSciNet  Google Scholar 

  6. Lloyd, S., Universal quantum simulators, Science, 1996, 273: 1073–1078.

    Article  MathSciNet  Google Scholar 

  7. Deutsch, D., Jozsa, R., Rapid solution of problems by quantum computation, Proc. Roy. Soc. Lond. A, 1992, 439: 553–558.

    MATH  MathSciNet  Google Scholar 

  8. DiVincenzo, D. P., Quantum computation, Science, 1995, 270: 255–261.

    Article  MathSciNet  Google Scholar 

  9. Ernst, R. R., Bodenhausen, G., Wokaun, A., Principle of Nuclear Magnetic Resonance in One and Two Dimensions, Oxford: Oxford University Press, 1987.

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  11. Cory, D. G., Fahmy, A. F., Havel, T. F., Ensemble quantum computing by NMR-spectroscopy, Proc. Natl. Acad. Sci. USA, 1997, 94: 1634–1639.

    Article  Google Scholar 

  12. Chuang, I. L., Vandersypen, L. M. K., Zhou, X. et al., Experimental realization of a quantum algorithm, Nature, 1998, 393: 143–146.

    Article  Google Scholar 

  13. Jones, J. A., Mosca, M., Hansen, R. H., Implementation of a quantum search algorithm on a quantum computer, Nature, 1998, 393: 344–346.

    Article  Google Scholar 

  14. Nielsen, M. A., Knill, E., Laflamme, R., Complete quantum teleportation using nuclear magnetic resonance, Nature, 1998, 396: 52–55.

    Article  Google Scholar 

  15. Knill, E., Laflamme, R., Matinez, R. et al., An algorithmic benchmark for quantum information processing, Nature, 2000, 404: 368–370.

    Article  Google Scholar 

  16. Linden, N., Barjat, H., Freeman, R., An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer, Chem. Phys. Lett., 1998, 296: 61–67.

    Article  Google Scholar 

  17. Marx, R., Fahmy, A. F., Myers, J. M. et al., Approaching five-bit NMR quantum computing, Phys. Rev. A, 2000, 62: 12310-1-8.

    Google Scholar 

  18. Chuang, I. L., Gershenfeld, N., Kubinec, M., Experimental implementation of fast quantum searching, Phys. Rev. Lett., 1998,80:3408–3411.

    Article  Google Scholar 

  19. Miao, X., Han, X., Hu, J., Application of product operator formalism to the strong coupled spin (I= 1/2) systems, Science in China, Ser. A, 1993, 36: 1199–1211.

    Google Scholar 

  20. Miao, X., Ye, C., Application of the product operator formalism to spin (I= 1/2) systems under a radio-frequency irradiation, Mol. Phys., 1997, 90: 499–514.

    Article  Google Scholar 

  21. Miao, X. J., Lu, G., Ye, Z. H., Science in China (in Chinese), Ser. A, 1997, 27: 720–730.

    Google Scholar 

  22. Miao, X., Chen, J., Mao, X. A., Selective excitation by radiation damping field for a coupled nuclear spin system, Chem. Phys. Lett., 1999, 304:45–50.

    Article  Google Scholar 

  23. Miao, X., Multiple-quantum operator algebra spaces and description for unitary time evolution of multilevel spin systems, Mol. Phys., 2000, 98: 625–631.

    Article  Google Scholar 

  24. Miao, X., Universal construction of unitary transformation of quantum computation with one- and two-body interactions. http://xxx.lanl.gov/abs/quant-ph/0003068.

  25. Miao, X., Universal construction of quantum computational networks in superconducting Josephson junctions. http://xxx.lanl.gov/abs/quant-ph/0003113.

  26. Miao, X., A convenient method to prepare the effective pure state in a quantum ensemble. http://xxx.lanl.gov/abs/quant-ph/0008094.

  27. Chuang, I. L., Gershenfeld, N. A., Kubinec, M. G. et al., Bulk quantum computation with nuclear magnetic resonance: theory and experiment, Proc. R. Soc. Lond. A, 1998, 454: 447–467.

    Article  MATH  Google Scholar 

  28. Knill, E., Chuang, I. L., Laflamme, R., Effective pure states for bulk quantum computation, Phys. Rev. A, 1998, 57: 3348–3363.

    Article  MathSciNet  Google Scholar 

  29. Luo, R., Liu, M., Mao, X. A., Eliminating systematic error in multiple quantum diffusion measurements by bipolar gradient pulses, Meas. Sci. Technol., 1998, 9: 1347–1350.

    Article  Google Scholar 

  30. Miao, X., Freeman, R., Spin-echo modulation experiments with soft Gaussian pulses, J. Magn. Reson. A, 1996, 119: 90–100.

    Article  Google Scholar 

  31. Miao, X., An explicit criterion for existence of the magnus solution for a coupled spin system under a time-dependent radiofrequency pulse, Phys. Lett. A, 2000, 271: 296–302.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, 430071, Wuhan, China

    Yang Xiaodong & Miao Xijia

Authors
  1. Yang Xiaodong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miao Xijia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miao Xijia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xiaodong, Y., Xijia, M. The theoretic design of NMR pulses program of arbitrary N-qubit Grover’s algorithm and the NMR experiment proof. Sci. China Ser. A-Math. 45, 1610–1619 (2002). https://doi.org/10.1360/02ys9173

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1360/02ys9173

Keywords

Search

Navigation