Experimental realization of a two-bit phase damping quantum code

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 60, Issue 3, 1999, Pages 1924-1943

  Leung, Debbie ^a,b   Vandersypen, Lieven ^b,c   Zhou, Xinlan ^b,c   Sherwood, Mark ^b   Yannoni, Constantino ^b   Kubinec, Mark ^d   Chuang, Isaac ^b,c  

^a STANFORD UNIVERSITY   (United States)

^b IBM ALMADEN RESEARCH CENTER   (United States)

^c STANFORD UNIVERSITY   (United States)

^d UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001754497     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.60.1924     Document Type: Article

References (46)

1. I. Chuang, N. Gershenfeld, and M. Kubinec, Phys. Rev. Lett. 80, 3408 (1998).
2. I. Chuang, L. Vandersypen, X. Zhou, D. Leung, and S. Lloyd, Nature (London) 393, 143 (1998).
3. J. Jones, M. Mosca, and R. Hansen, Nature (London) 393, 344 (1998).
4. J. Jones and M. Mosca, J. Chem. Phys. 109, 1648 (1998).
5. J. Jones and M. Mosca, e-print quant-ph/9808056.
6. N. Gershenfeld and I. Chuang, Science 275, 350 (1997).
7. D. Cory, A. Fahmy, and T. Havel, Proc. Natl. Acad. Sci. USA 94, 1634 (1997).
8. D. Cory, M. Price, and T. Havel, Physica D 120, 82 (1998).
9. I. Chuang, N. Gershenfeld, M. Kubinec, and D. Leung, Proc. R. Soc. London, Ser. A 454, 447 (1998).
10. P. Shor, Phys. Rev. A 52, 2493 (1995).
11. A. Steane, Phys. Rev. Lett. 77, 793 (1996).
12. P. Shor, in Proceedings of the 37th Annual Symposium on theFoundations of Computer Science (IEEE Computer Society Press, Los Alamitos, 1996), pp. 56–65.
13. D. Aharonov and M. Ben-Or, in Proceedings of the 29th Annual ACM Symposium on the Theory of Computing (ACM, New York, 1998), pp. 176–188.
14. J. Preskill, Proc. R. Soc. London, Ser. A 454, 385 (1998).
15. A. Yu. Kitaev, in Quantum Communication, Computing and Measurement, edited by O. Hirota, A. S. Holevo, and C. M. Caves (Plenum, New York, 1997).
16. E. Knill, R. Laflamme, and W. Zurek, Proc. R. Soc. London, Ser. A 454, 365 (1998).
17. D. Gottesman, Phys. Rev. A 57, 127 (1998).
18. I. L. Chuang and R. Laflamme, e-print quant-ph/9511030.
19. D. Cory, M. Price, W. Mass, E. Knill, R. Laflamme, W. Zurek, T. Havel, and S. Somaroo, Phys. Rev. Lett. 81, 2152 (1998).
20. K. Kraus, States, Effects, and Operators: Fundamental Notions of Quantum Theory (Springer, Berlin, 1983).
21. B. Schumacher, Phys. Rev. A 54, 2614 (1996).
22. A. Ekert and C. Macchiavello, Phys. Rev. Lett. 77, 2585 (1996).
23. E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997).
24. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
25. M. A. Nielsen, H. Barnum, C. M. Caves, and B. W. Schumacher, Proc. R. Soc. London, Ser. A 454, 277 (1998).
26. D. Gottesman, Ph.D. thesis, California Institute of Technology, 1997.
27. C. Slichter, Principles of Magnetic Resonance (Springer, Berlin, 1990).
28. A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, Oxford, 1961).
29. D. DiVincenzo, Phys. Rev. A 51, 1015 (1995).
30. A. Barenco, Proc. R. Soc. London, Ser. A 449, 679 (1995).
31. D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995).
32. A. Barenco, C. Bennett, R. Cleve, D. DiVincenzo, N. Margolus, P. Shor, T. Sleater, J. Smolin, and H. Weinfurter, Phys. Rev. A 52, 3457 (1995).
33. M. A. Nielsen (private communication).
34. E. Knill, I. Chuang, and R. Laflamme, Phys. Rev. A 57, 3348 (1998).
35. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, Oxford, 1994).
36. Formic-13C acid and calcium chloride were supplied by Aldrich (respective catalog Nos. 27,941-2 and 23,922-4). Chemicals were used without further purification.
37. We note that J coupling, phase damping, and amplitude damping are noncommuting and simultaneous processes. Moreover, the effects of generalized amplitude damping at finite temperature on deviation density matrices are complicated.
38. The refocusing pulses were applied to spin B; therefore, spin A was not affected directly. Refocusing affected the output indirectly by flipping spin B for half of the storage time during which it was susceptible to amplitude damping.
39. A. Peres, Int. J. Theor. Phys. 38, 799 (1999).
40. Two Hadamard transformations and two controlled nots are needed in the detection code, whereas six Hadamard transformations, four controlled nots, and one Toffoli gate are needed in the correction code. Simulating the Toffoli gate by three controlled nots, the correction code still requires at least three times as many operations as required by the detection code.
41. Despite these observations, it must be kept in mind that the proper figure of merit depends on the application, and our conclusions do not imply advantages for detection codes, or even coding schemes in general. For example, in the exponential signal loss model, each extra bit used in coding reduces the absolute signal strength by half. A similar observation was made by Cory et al. 19.
42. N. Cerf and R. Cleve, Phys. Rev. A 56, 1721 (1997).
43. A. Calderbank, E. Rains, P. Shor, and N. Sloane, IEEE Trans. Inf. Theory 44, 1369 (1998).
44. L. Schulman and U. Vazirani, in Proceedings of the 31st Annual ACM Symposium on Theory of Computing, 1999 (ACM, New York, 1999).
45. The chloroform sample was a 0.5-ml, 0.2 M solution in d6 acetone supplied by Cambridge Isotope Labs., Inc. (catalog No. CLM-262). Experiments were performed at room temperature.
46. (Formula presented)’s for the input and the ancilla, as measured from the line widths, were 0.13 and 0.53 s when carbon was the input, and 0.92 and 0.16 s when proton was the input. The storage times were 0, 37.2, 74.4, 111.6, and 148.8 ms when carbon was the input, and 0, 223, and 446 ms when proton was the input.