This is an archived course. A more recent version may be available at ocw.mit.edu.

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

Lab Guide (PDF)

A two spin system.

A two spin system. (Image courtesy of Junior Lab staff.)

References

Deutsch, David. "Quantum Theory, the Church-Turing Principle and the Universal Quantum Computer." Proceedings of the Royal Society of London A400 (1985): 97.

———. "Quantum Computational Networks." Proceedings of the Royal Society of London A425 (1989): 73.

Deutsch, David, and Richard Jozsa. "Rapid Solution of Problems by Quantum Computation." Proceedings of the Royal Society of London A439 (1992): 553.

Chuang, Isaac L. "QIP - Chuang." Science 275 (Jan 17, 1997).

Chuang, Isaac L., Neil Gershenfeld, and M. Kubinec. "Experimental Implementation of Fast Quantum Searching." The Physical Review Letters 80, no. 15 (April 13, 1998).

Chuang, Isaac L., L. M. K. Vandersypen, X. L. Zhou, D. W. Leung, and S. Lloyd. "Experimental Realization of a Quantum Algorithm." Nature 393, no. 6681 (1998): 143-146.

Gershenfeld, Neil, and Isaac Chuang. "Quantum Computing with Molecules." Scientific American (June 1998).

Buy at Amazon Chuang, Isaac L., and Michael A. Nielsen. Quantum Computation and Quantum Information. New York, NY: Cambridge University Press, November 2000, chapter 1. ISBN: 9780521632355.

Havel, T. F., 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." American Journal of Physics 70 (March 2002): 345-362.

Landauer, R. "Irreversibility and Heat Generation in the Computing Process." IBM J Res Dev 183 (1961): 183-191.

Bennett, C. H. "Logical Reversibility of Computation." IBM J Res Dev 525 (1973): 525-532.

Benioff, P. "The Computer as a Physical System: A Microscopic Quantum Mechanical Hamiltonian Model of Computers as Represented by Turing Machines." J Statistical Phys 22 (1980): 563-591.

Feynman, R. P. "Simulating Physics with Computers." Int J Theor Phys 21 (1982): 467-488.

Fredkin, E., and T. Toffoli. "Conservative Logic." Int J Theor Phys 21 (1982): 219-253.

Buy at Amazon Leff, H., and R. Rex. Maxwell's Demon: Entropy, Information, Computing. Princeton, NJ: Princeton University Press, 1991. ISBN: 9780691087276.

Gershenfeld, N., and I. Chuang. "Bulk Spin-Resonance Quantum Computation." Science 275 (1997): 350-356.

Cory, D., A. Fahmy, and T. Havel. "Ensemble Quantum Computing by NMR Spectroscopy." Proc Natl Acad Sci 94 (1997): 1634-1639.

Sodickson, A., and D. G. Cory. "A Generalized k-space Formalism for Treating the Spatial Aspects of a Variety of NMR Experiments." Prog NMR Spec 33 (1998): 77-108.

Price, M., 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." J Mag Res 140 (1999): 371-378.

Cory, D., et al. "NMR Based Quantum Information Processing: Achievements and Prospects." Fortschr Phys 48 (2000): 875-907.

Gulde, S., et al. "Implementation of the Deutsch-Joza Algorithm on an Ion-trop Quantum Computer." Nature 421 (2003): 48.

Buy at Amazon Sakurai, J. "Ensemble Averages and Density Operator." In Modern Quantum Mechanics. 2nd ed. Reading, MA: Addison-Wesley, 1993, pp. 176-180. ISBN: 9780201539295.

Selected Resources

Quantum Info. Sci. @ MIT

Quantum Information Literature

Bruker Bio-Spin Technical Support