Efficient implementation of coupled logic gates for quantum computation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 61, Issue 4, 2000, Pages 423101-423107

  Leung, Debbie W ^a,b   Chuang, Isaac L ^b   Yamaguchi, Fumiko ^a   Yamamoto, Yoshihisa ^a,c  

^a STANFORD UNIVERSITY   (United States)

^b IBM ALMADEN RESEARCH CENTER   (United States)

^c NTT Basic Research Laboratories   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346478227     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. D. DiVincenzo, Science 270, 255 (1995).
2. A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996).
3. R. Josza, in Proceedings of First NASA International Conference on Quantum Computation and Quantum Communication, Palm Springs, FL, 1998, edited by C. Williams (Springer Verlag, New York, 1999); e-print quant-ph/9805086.
4. N. Gershenfeld and I. Chuang, Science 275, 350 (1997).
5. D. Cory, A. Fahmy, and T. Havel, Proc. Natl. Acad. Sci. USA 94, 1634 (1997).
6. D. Cory, M. Price, and T. Havel, Physica D 120, 82 (1998); e-print quant-ph/9709001. ]
7. I. Chuang, N. Gershenfeld, M. Kubinec, and D. Leung, Proc. R. Soc. London, Ser. A 454, 447 (1998).
8. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, Oxford, 1994).
9. C. Slichter, Principles of Magnetic Resonance (Springer, Berlin, 1990).
10. P. Mansfield, Pulsed NMR in Solids, Progress in Nuclear Magnetic Resonance Spectroscopy Vol. 8 (Pergamon Press, Oxford, 1971).
11. M. Mehring, Principles of High Resolution NMR in Solids (Springer, Berlin, 1983).
12. N. Linden, H. Barjat, R. Carbajo, and R. Freeman, e-print quant-ph/9811043. Homonuclear systems were considered, in contrast to the present discussion.
13. D. DiVincenzo, Phys. Rev. A 51, 1015 (1995).
14. A. Barenco, Proc. R. Soc. London, Ser. A 449, 679 (1995).
15. D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995).
16. A. Barenco, C. Bennett, R. Cleve, D. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter, Phys. Rev. A 52, 3457 (1995).
17. A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, Oxford, 1961).
18. Refocusing has been used in many demonstrations of quantum information processing, for instance, see I. Chuang, L. Vandersypen, X. Zhou, D. Leung, and S. Lloyd, Nature (London) 393, 143 (1998); and M. Nielsen, E. Knill, and R. Laflamme, ibid. 395, 52 (1998).
19. Refocusing has been used in many demonstrations of quantum information processing, for instance, see I. Chuang, L. Vandersypen, X. Zhou, D. Leung, and S. Lloyd, Nature (London) 393, 143 (1998); and M. Nielsen, E. Knill, and R. Laflamme, ibid. 395, 52 (1998).
20. The CRC Handbook of Combinatorial Designs edited by C. Colbourn and J. Dinitz (CRC Press, Boca Raton, FL, 1996).
21. ∼njas/hadamard/index.ht-ml
22. J. van Lint and R. Wilson, A Course in Combinatorics (Cambridge University Press, Cambridge, 1992).
23. F. MacWilliams and N. Sloane, The Theory of Error-Correcting Codes (North-Holland, Amsterdam, 1977).
24. For the Walsh-Hadamard transformation commonly used in quantum computation, see for instance, L. Grover, Phys. Rev. Lett. 80, 4329 (1998); and A. Steane, ibid. 77, 793 (1996).
25. For the Walsh-Hadamard transformation commonly used in quantum computation, see for instance, L. Grover, Phys. Rev. Lett. 80, 4329 (1998); and A. Steane, ibid. 77, 793 (1996).
26. J. Hadamard, Bull. Sci. Math., 17, 240 (1893).
27. J. Sylvester, Philos. Mag. 34, 461 (1867).
28. R. E. A. C. Paley, J. Math. Phys. 12, 311 (1933).
29. With a periodic sign matrix, setting the jth row to be the ith row also recouples the jth and the (i + k) th spins when j>i. Similar problems occur when j
30. F. Yamaguchi and Y. Yamamoto, Appl. Phys. A: Mater. Sci. Process. 68, 1 (1999).
31. J. Waugh, L. Huber, and U. Haeberlen, Phys. Rev. Lett. 20, 180 (1968).
32. B. Terhal and D. DiVincenzo, Phys. Rev. A 61, 022301 (2000).
33. J. Rosser and L. Schoenfeld, III. J. Math. 6, 64 (1962).
34. H. Davenport, Multiplicative Number Theory (Springer-Verlag, New York, 1967).