Skip to main content
SpringerLink
Log in

Experimental implementation of a fixed-point duality quantum search algorithm in the nuclear magnetic resonance quantum system

  • Research Paper
  • Published:
Science China Physics, Mechanics and Astronomy Aims and scope Submit manuscript

Abstract

In this work, we demonstrated a fixed-point quantum search algorithm in the nuclear magnetic resonance (NMR) system. We constructed the pulse sequences for the pivotal operations in the quantum search protocol. The experimental results agree well with the theoretical predictions. The generalization of the scheme to the arbitrary number of qubits has also been given.

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. Grover L K. A fast quantum mechanical algorithm for database search. In: Proceedings of 28th Annual ACM Symposium on Theory of Computing. New York: ACM, 1996. 212

    Google Scholar 

  2. Grover L K. Fixed-point quantum search. Phys Rev Lett, 2005, 95: 150501

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. Brassard G, Hoyer P, Mosca M, et al. Quantum amplitude amplification and estimation. Arxiv: quant-ph/0005055

  5. Long G L. Grover algorithm with zero theoretical failure rate. Phys Rev A, 2001, 64: 022307

    Article  ADS  Google Scholar 

  6. Brassard G, Hoyer P, Tapp A. Quantum counting. In: Proceedings of 25th ICALP of Lecture Notes in Computer Science, 1998. 1443: 820–831

    Article  MathSciNet  Google Scholar 

  7. Benioff P. Quantum computation and information. In: Washington DC AMS Series on Contemporary Mathematics, 2000. 305: 1

    MathSciNet  Google Scholar 

  8. Toyama F M, van Dijk W, Nogami Y, et al. Multiphase matching in the Grover algorithm. Phys Rev A, 2008, 77: 042324

    Article  ADS  Google Scholar 

  9. Mizel A. Critically damped quantum search. Phys Rev Lett, 2009, 102: 150501

    Article  ADS  Google Scholar 

  10. Yan H Y. A new searching problem solved by quantum computers. Chin Phys Lett, 2002, 19(4): 460–462

    Article  ADS  Google Scholar 

  11. Zhong P C, Bao W S. Research on quantum searching algorithms based on phase shifts. Chin Phys Lett, 2008, 25: 2774–2777

    Article  ADS  Google Scholar 

  12. Zhong P C, Bao W S. Quantum mechanical meet-in-the-middle search algorithm for Triple-DES. Chin Sci Bull, 2010, 55(3): 321–325

    Article  Google Scholar 

  13. Hsu L Y. Quantum secret-sharing protocol based on Grover’s algorithm. Phys Rev A, 2003, 68: 022306

    Article  ADS  Google Scholar 

  14. Hao L, Li J L, Long G L. Eavesdropping in a quantum secret sharing protocol based on Grover algorithm and its solution. Sci China Phys Mech Astron, 2010, 53(3): 491–495

    Article  ADS  Google Scholar 

  15. Wang C, Hao L, Song S Y, et al. Quantum direct communication based on quantum search algorithm. Int J Quant Inform, 2010,8: 443–450

    Article  MATH  Google Scholar 

  16. Tulsi T, Grover L K, Patel A. A new algorithm for fixed point quantum search. Quant Inf Comput, 2006, 6: 483–494; also see arXiv: quantph/0505007

    MathSciNet  MATH  Google Scholar 

  17. Li D. Performance of equal phase-shift search for one iteration. Eur Phys J D, 2007, 45: 335–340

    Article  ADS  Google Scholar 

  18. Hoyer P. Arbitrary phases in quantum amplitude amplification. Phys Rev A, 2000, 62: 052304

    Article  ADS  Google Scholar 

  19. Bilham E, Bilham O, Biron D, et al. Analysis of generalized Grover quantum search algorithms using recursion equations. Phys Rev A, 2000, 63: 012310

    Article  ADS  Google Scholar 

  20. Li D, Li X, Huang H, et al. Fixed-point quantum search for different phase shifts. Phys Lett A, 2007, 362: 260–264

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. Long G L. General quantum interference principle and duality computer. Commun Theor Phys, 2006 45: 825–844; also see arXiv: quantph/0512120

    Article  Google Scholar 

  22. Gudder S. Mathematical theory of duality quantum computers. Quant Inf Proc, 2007, 6(1): 37–48

    Article  MathSciNet  MATH  Google Scholar 

  23. Long G L. Mathematical theory of the duality computer in the density matrix formalism. Quant Inf Proc, 2007, 6(1):49–54

    Article  MATH  Google Scholar 

  24. Wang Y Q, Du H K, Dou Y N. Note on generalized quantum gates and quantum operations. Int J Theor Phys, 2008, 47: 2268–2278

    Article  MathSciNet  MATH  Google Scholar 

  25. Du H K, Wang Y Q, Xu J L. Applications of the generalized Luders theorem. J Math Phys, 2008, 49: 013507–013513

    Article  MathSciNet  ADS  Google Scholar 

  26. Long G L, Liu Y. Duality computing in quantum computers. Commun Theor Phys, 2008, 50: 1303–1306

    Article  ADS  Google Scholar 

  27. Long G L, Liu Y, Wang C. Allowable generalized quantum gates. Commun Theore Phys, 2009, 51: 65–67

    Article  ADS  MATH  Google Scholar 

  28. Zou X F, Qiu D W, Wu L H, et al. On mathematical theory of the duality computers. Quant Inf Proc, 2009, 8: 37–50

    Article  MathSciNet  MATH  Google Scholar 

  29. Du H K, Dou Y N. A spectral characterization for generalized quantum gates. J Math Phys, 2009, 50: 032101

    Article  MathSciNet  ADS  Google Scholar 

  30. Chen Z L, Cao H X. A note on the extreme points of positive quantum operations. Int J Theor Phys, 2009, 48: 1669–1671

    Article  MathSciNet  MATH  Google Scholar 

  31. Cao H X, Li L, Chen Z L, et al. Restricted allowable generalized quantum gates. Chin Sci Bull, 2010, 55(20): 2122–2125

    Article  Google Scholar 

  32. Hao L, Liu D, Long G L. An N/4 fixed-point duality quantum search algorithm. Sci China Phys Mech Astron, 2010, 53(9): 1765–1768

    Article  ADS  Google Scholar 

  33. Long G L. Duality quantum computing and duality quantum information processing. Int J Theor Phys, doi: 10.1007/s10773-010-0603-z

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

    Article  MathSciNet  MATH  Google Scholar 

  35. Cory D G, Fahmy A F, Havel T F. Ensemble quantum computing by NMR-spectroscopy. Proc Nat Acad Sci USA, 1997, 94(5): 1634–1639

    Article  ADS  Google Scholar 

  36. Cory D G, Price M D, Havel T F. Nuclear magnetic resonance spectroscopy: An experimentally accessible paradigm for quantum computing. Physica D, 1998, 120(1): 82–101

    Article  ADS  Google Scholar 

  37. Marx R, Fahmy A F, Myers J M, et al. Approaching five-bit NMR quantum computing. Phys Rev A, 2000, 62: 012310–012317

    Article  ADS  Google Scholar 

  38. Liu W Z, Zhang J F, Long G L. Simulation of the four-body interaction in a nuclear magnetic resonance quantum information processor. Chin Sci Bull, 2009, 54(22): 4262–4265

    Article  Google Scholar 

  39. Wei D X, Yang X D, Luo J, et al. NMR experimental implementation of three-parties quantum superdense coding. Chin Sci Bull, 2004, 49(5): 423–426

    MATH  Google Scholar 

  40. Fang X M, Zhu X W, Feng M, et al. Realization of quantum discrete Fourier transform with NMR. Chin Sci Bull, 2000, 45(12): 1071–1075

    Article  MATH  Google Scholar 

  41. Liu W Z, Zhang J F, Deng Z W, et al. Simulation of general three-body interactions in a nuclear magnetic resonance ensemble quantum computer. Sci China Ser G-Phys Mech Astron, 2008, 51(8): 1089–1096

    Article  ADS  MATH  Google Scholar 

  42. Xiao L, Long G L. Fetching marked items from an unsorted database in NMR ensemble computing. Phys Rev A, 2002, 66: 052320–052324

    Article  ADS  Google Scholar 

  43. Barenco A, Bennett C H, Cleve R, et al. Elementary gates for quantum computation. Phys Rev A, 1995, 52: 3457–3467

    Article  ADS  Google Scholar 

  44. Liu Y, Long G L, Sun Y. Analytic one-bit and CNOT gate constructions of general n-qubit controlled gates. Int J Quant Inform, 2008, 6(3): 447–462

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory for Atomic and Molecular NanoSciences and Department of Physics, Tsinghua University, Beijing, 100084, China

    Liang Hao

  2. Tsinghua National Laboratory for Information Science and Technology, Beijing, 100084, China

    GuiLu Long

Authors
  1. Liang Hao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. GuiLu Long
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to GuiLu Long.

Additional information

Contributed by LONG GuiLu

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hao, L., Long, G. Experimental implementation of a fixed-point duality quantum search algorithm in the nuclear magnetic resonance quantum system. Sci. China Phys. Mech. Astron. 54, 936–941 (2011). https://doi.org/10.1007/s11433-011-4327-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-011-4327-8

Keywords

Search

Navigation