A study of quantum error correction by geometric algebra and liquid-state NMR spectroscopy

Molecular Physics

Volumn 98, Issue 17, 2000, Pages 1347-1363

  Sharf, Y ^a   Cory, D G ^a   Somaroo, S S ^b   Havel, T F ^b   Knill, E ^c   Laflamme, R ^c   Zurek, W H ^c  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b HARVARD MEDICAL SCHOOL   (United States)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFUSION; GEOMETRY; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; NUMERICAL METHODS; RELAXATION PROCESSES;

DECOHERENCE; GEOMETRIC ALGEBRA; QUANTUM ERROR CORRECTION;

QUANTUM THEORY;

EID: 0034633387     PISSN: 00268976     EISSN: None     Source Type: Journal    
DOI: 10.1080/002689700413604     Document Type: Article

References (44)

1. Shor, P. W., 1995, Phys. Rev. A, 52, R2493.
2. Steane, A. M., 1996, Phys. Rev. Lett., 77, 793.
3. Knill, E., and Laflamme, R., 1997, Phys. Rev. A, 55, 900.
4. Gottesman, D., 1998, Phys. Rev. A, 57, 127.
5. Steane, A. M., 1998, Phil. Trans R. Soc. Lond. A, 356, 1739.
6. Preskill, J., 1999, Physics Today, 52, 24.
7. Cory, D. G., Fahmy, A. F., and Havel, T. F., 1997, Proc. Natl. Acad. Sci. USA, 94, 1634.
8. Gershenfeld, N. A., and Chuang, I. L., 1997, Science, 275, 350.
9. Cory, D. G., Price, M. D., and Havel, T. F., 1998, Physica D, 120, 82.
10. Chuang, I. L., Gershenfeld, N., Kubinec, M. G., and Leung, D. W., 1998, Proc. R. Soc. Lond. A, 454, 447.
11. Jones, J. A.; Mosca, M., and Hansen, R. H., 1998, Nature, 393, 344.
12. Linden, N., Barjat, H., and Freeman, R. 1998, Chem. Phys. Lett., 296, 61.
13. Chuang, I. L., Vandersypen, L. M. K., Zhou, X., Leung, D. W., and Lloyd, S., 1998, Nature, 393, 143.
14. Nielsen, M. A., Knill, E., and Laflamme, R., 1998, Nature, 396, 52.
15. Cory, D. G., Maas, W., Price, M., Knill, E., Laflamme, R., Zurek, W. H., Havel, T. F., and Somaroo, S. S., 1998, Phys. Rev. Lett., 81, 2152.
16. Havel, T. F., Somaroo, S. S., Tseng, C.-H., and Cory, D. G., 2000, Applicable Algebra in Engineering, Communications and Computing (Berlin: Springer-Verlag), 10, 339.
17. Knill, E., Chuang, I., and Laflamme, R., 1998, Phys. Rev. A, 57, 3348.
18. Warren, W. S., 1997, Science 277, 1688.
19. Somaroo, S. S., Cory, D. G., and Havel, T. F., 1998, Phys. Lett. A, 240, 1.
20. Slichter, C. P., 1990, Principles of Magnetic Resonance, 3rd Edn (Berlin: Springer-Verlag).
21. Abragam, A., 1961, Principles of Nuclear Magnetism (Oxford University Press).
22. Boulat, B., and Range, M., 1994, Molec. Phys., 83, 1021.
23. Sörensen, O. W., Eich, G. W., Levitt, M. H., Bodenhausen, G., and Ernst, R. R., 1983, Progr. NMR Spectrosc., 16, 163.
24. Van Deven, F. J. M., and Hilbers, C. W., 1983, J. magn. Reson., 54, 512.
25. Doran, C. J. L., Lasenby, A. N., and Gull, S. F., 1993, Foundations Phys., 23, 1239.
26. Somaroo, S. S., Lasenby, A. N., and Doran, C. J. L., 1999, J. math. Phys., 40, 3327.
27. Doran, C. J. L., Lasenby, A. N., Gull, S. F., Somaroo, S. S., and Challinor, A. D. 1996, Advances in Imaging and Electron Physics, edited by P. Hawkes (New York: Academic Press) p. 271.
28. Hestenes, D., 1996, Space-Time Algebra (London: Gordon and Breach).
29. Cowan, B., 1997, Nuclear Magnetic Resonance and Relaxation (Cambridge University Press).
30. Giulini, D., Joos, E., Kiefer, C., Kupsch, J., Stamatescu, I.-O., and Zeh, H. D., 1996, Decoherence and the Appearance of a Classical World in Quantum Theory (Berlin: Springer-Verlag).
31. Zurek, W. H., 1991, Physics Today, 43, 36.
32. Zurek, W. H., 1998, Phil. trans R. Soc. Lond. A, 356, 1793.
33. Haroche, S., 1998, Physics Today, 51, 36.
34. Sodickson, A., and Cory, D. G., 1998, Progr. NMR Spectrosc., 33, 77.
35. Ernst, R. R., Bodenhausen, G., and Wokaun, A., 1987, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press).
36. Freeman, R., 1998, Spin Choreography (Oxford University Press).
37. Patt, S. L., 1992, J. magn. Reson., 96, 94.
38. Price, M. D., Somaroo, S. S., Dunlop, A. E., Havel, T. F., and Cory, D. G., 1999, Phys. Rev. A, 60, 2777.
39. Redfield, A. G., 1995, Adv. magn. Reson., 1, 1.
40. Werbelow, L. G., and Grant, D. M., 1977, Adv. magn. Reson., 9, 189.
41. Vold, R. L., and Vold, R. R., 1978, Progr. NMR Spectrosc., 12, 79.
42. Wokaun, A., and Ernst, R. R., 1978, Molec. Phys., 36, 317.
43. Peng, J. W., and Wagner, G., 1994, Nuclear Magnetic Resonance Probes of Molecular Dynamics, edited by R. Tycko (Dordrecht: Kluwer) p. 373.
44. Kumar, P., and Kumar, A., 1996, J. magn. Reson. A., 119, 29.