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49. Quantum information processing with NMR

This experiment will let you perform a series of simple quantum computations on a two spin system, demonstrating one and two quantum-bit quantum logic gates, and a circuit implementing the Deutsch-Jozsa quantum algorithm. You will use NMR techniques and manipulate the state of a proton and a carbon nucleus in a chloroform molecule, measuring ensemble nuclear magnetization.

WARNING: you should know Matlab well to successfully do this experiment! You will measure:

  • the coupling constant describing the electron-mediated interaction between the proton and carbon nuclear spins of chloroform,
  • the classical input-output truth table for a controlled-not gate
  • the numerical output of the Deutsch-Jozsa quantum algorithm, and
  • optionally, the output and oscillatory behavior of the Grover quantum search algorithm.
  • Student Wiki: Quantum Information processing with NMR

    Download Lab Guide in PDF format

    References (certificates required)

    1. [1961] C. Landauer, "Irreversibility and Heat Generation inthe Computing Process"IBM J. Res. Dev. 5, 183 (1961)
    2. [1973] C.H. Bennett, "Logical Reversibility of Computation", IBM J. Res. Dev. 17, 525 (1973)
    3. [1980] P. Benioff, The Computer as a Physical System: A Microscopic Quantum Mechanical Hamiltonian Model of Comupters as Represented by Turing Machines; Journal of Statistical Physics, Vol. 22, No. 5, (1980)
    4. [1982] R. P. Feynman, Simulating Physics with Computers; Int. J. Theor. Phys. 21, 467 (1982)
    5. [1982] E. Fredkin and T. Toffoli, Conservative Logic; Int. J. Theor. Phys. 21, 219 (1982)
    6. [1985] R. P. Feynman,Quantum Mechanical Computers;, Optics News, p. 11 (1985)
    7. [1985] David Deutsch, "Quantum theory, the Church-Turing principle and the universal quantum computer", Proc. Royal Soc. London A400, p97, 1985.
    8. [1989] David Deutsch, "Quantum computational networks", Proc. Royal Soc. London A425, p73, 1989.
    9. [1990] H. Leff and R. Rex,"Maxwell's Demon: Entropy, Information, Computing" Princeton University Press, (1990)
    10. [1992] David Deutsch and Richard Jozsa, "Rapid solution of problems by quantum computation", Proc. Royal Soc. London A439, p553, 1992
    11. [1994] P.W. Shor, "Algorithms for quantum computation: discrete logarithms and factoring", in Proceedings, 35th Annual Symposium on Foundations of Computer Science, pp. 124-134, IEEE Press, Los Alamitos, CA, (1994)
    12. [1994] D. Simon, "On the power of quantum computation", in Proceedings, 35th Annual Symposium on Foundations of Computer Science, pp. 116-123, IEEE Press, Los Alamitos, CA, (1994)
    13. [1996] L. Grover, "A fast quantum mechanical algorithm for database search", Proceedings of the 28th annual ACM symposium on Theory of computing, pp. 212-219 Philadelphia (1996)
    14. [1997] N. Gershenfeld and I. Chuang , "Bulk Spin-Resonance Quantum Computation", Science 275, 350 (1997)
    15. [1997] D. Cory, A. Fahmy and T. Havel, "Ensemble quantum computing by NMR spectroscopy", Proc. Natl. Acad. Sci., Vol. 94, pp. 1634-1639 (1997)
    16. [1997] I.L. Chuang, N. Gershenfeld, W.S. Warren, "The Usefulness of NMR Quantum Computing", Science, New Series, 277, No. 5332, pp. 1688-1690, (1997)
    17. [1998] I.L. Chuang, N. Gershenfeld and M. Kubinec, "Experimental Implementation of Fast Quantum Searching", Physical Review Letters, Vol. 80, No. 15, 13 April [1998]
    18. [1998] I. L. Chuang, L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd."Experimentalrealization of a quantum algorithm". Nature, 393 no. 6681 pp. 143-146, 1998.
    19. [1998] Neil Gershenfeld and Isaac Chuang, "Quantum Computing with Molecules", Scientific American, June 1998.
    20. [1998] Van Beveren, Some notes on group theory, Chapter 6: "series of matrices and direct products", Feb. 1998
    21. [1998] Aaron Sodickson and David G. Cory, A generalized k-space formalism for treating the spatial aspects of a variety of NMR experiments", 1998
    22. [1999] M. Price, S. Somaroo, C. Tseng, J. Gore, A. Fahmy, T. Havel and D. Cory Construction and Implementation of NMR Quantum Logic Gates for Two Spin System, Journal of Magnetic Resonance, 140, pp. 371-378, 1999
    23. [2000] D. Cory, R. LaFlamme, E. Knill, L. Viola, T. Havel, N. Boulant, G. Boutis, E. Fortunato, S. Lloyd, R. Martinez, C. Negrevergne, M. Pravia, Y. Sharf., G. Teklemariam, Y. Weinstein and W. Zurek, "NMR Based Quantum Information Processing: Achievements and Prospects", Fortschr. Phys. 48, pp. 875-907 (2000)
    24. [2000] I.L. Chuang and M.A.Nielsen, Quantum Computation and Quantum Information : Chapter 1, November 2000
    25. [2001] L. Vandersypen, C. Yannoni and I. Chuang, Liquid State NMR Quantum ComputingThe Encyclopedia of NMR, Edited by D. Grant and R. Harris, John Wiley and Sons (2001)
    26. [2002] T.F. Havel, D.G. Cory, S. Lloyd, N. Boulant, E.M. Fortunato, M.A. Pravia, G. Teklemariam, Y.S. Weinstein, A. Bhattacharyya, and J. Hou, "Quantum Information Processing by nuclear magnetic resonance spectroscopy", Am. J. Phys., Vol. 70, pp345-362, March 2002
    27. [2003] I.L. Chuang, "How proton and carbon spectra arise from density matrices", April 2003
    28. [2003] S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, H. Haffner, F. Schmidt-Kaler, I. Chuang and R. Blatt, "Implementation of the Deutsch-Joza algorithm on an ion-trop quantum computer", Nature 421, 48 (2003)
    29. J. Sakurai Notes on Density Matricesfrom Modern Quantum Mechanics 2nd Edition, 1994

    Selected Resources

    1. Frequently Asked Questions
    2. Oxford Instruments - 200 MHz Superconducting Magnet - Operating Instructions
    3. Shimming Ain't Magic - The Shimming of High Resolution NMR Magnets
    4. The Probehead - Function, Structure and Overview
    5. Quantum Info. Sci. @ MIT
    6. Quantum Information Literature
    7. Bruker Bio-Spin Technical Support

     

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