Quantum computation over continuous variables

Physical Review Letters

Volumn 82, Issue 8, 1999, Pages 1784-1787

  Lloyd, Seth ^a   Braunstein, Samuel L ^b  

^a Massachusetts Institute of Technology Cambridge   (United States)

^b BANGOR UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000965389     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.82.1784     Document Type: Article

References (37)

1. D.DiVincenzo, Science, 270, 255(1995).
2. S.Lloyd, Sci. Am., 273, No. 4, 140(1995).
3. S.Lloyd and J. J.-E.Slotine, Phys. Rev. Lett., 80, 4088(1998).
4. S. L.Braunstein, Phys.Rev. Lett., 80, 4084(1998).
5. S. L.Braunstein, Nature (London), 394, 47(1998).
6. S. L.Braunstein and H. J.Kimble, Phys. Rev. Lett., 80, 869(1998).
7. A.Furusawa, et al., Science, 282, 706(1998).
8. D.Deutsch, Proc. R.Soc. London A, 425, 73(1989);
9. A. C.-C.Yao, in Proceedings of the 36th Annual Symposium on Foundations of Computer Science, S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1995), pp. 352-361.
10. M.Reck, et al., Phys. Rev. Lett., 73, 58(1994).
11. N. J. Cerf, C. Adami, and P. G. Kwiat, Phys. Rev. A, 57, R1477 (1998).
12. R. Reck, et al., and, C. Cerf, et al., propose performing arbitrary unitary operations on arms and acting in this exponentially larger space. Local operations on the original variables correspond to highly nonlocal operations in this “unary” representation: To flip a single bit requires one to act on half of the arms of the interferometer.
13. Y.Yamamoto, M.Kitagawa, and K.Igeta, in Proceedings of the 3rd Asia-Pacific Physics Conference, Y. W. Chan, A. F. Leung, C. N. Yang, and K. Young (World Scientific, Singapore, 1988), pp. 779-799;
14. G. J.Milburn, Phys.Rev. Lett., 62, 2124(1989).
15. G. M.Huang, T. J.Tarn, and J. W.Clark, J. Math. Phys. (N.Y.), 24, 2608-2618(1983).
16. Differential Geometric Control Theory, R. W.Brockett, R. S.Millman, and H. J. Sussman (Birkhauser, Boston, 1983);
17. Nonholonomic Motion Planning, Z.Li and J. F. Canney (Kluwer Academic, Boston, 1993).
18. V.Ramakrishna, M. V.Salapaka, M.Dahleh, H.Rabitz, and A.Peirce, Phys. Rev. A, 51, 960-966(1995).
19. S.Lloyd, Phys.Rev. Lett., 75, 346-349(1995).
20. D.Deutsch, A.Barenco, and A.Ekert, Proc. R. Soc. London A, 449, 669-677(1995).
21. S.Lloyd, Science, 273, 1073(1996).
22. L.Blum, M.Shub, and S.Smale, Bull. Am. Math. Soc., 21, 1-46(1989).
23. L. A.Wu, et al., Phys. Rev. Lett., 57, 2520(1986).
24. Q. A.Turchette, et al., Phys. Rev. Lett., 75, 4710-4713(1995).
25. R.Landauer, Nature (London), 335, 779-784(1988).
26. R.Landauer, Phys.Lett. A, 217, 188-193(1996).
27. R.Landauer, Philos. Trans. R. Soc. London A, 335, 367-376(1995)
28. P.Shor, Proceedings of the 37th Annual Symposium on the Foundations of Computer Science (IEEE Computer Society Press, Los Alamitos, 1996), pp. 56-65.
29. D. P.DiVincenzo and P. W.Shor, Phys. Rev. Lett., 77, 3260-3263(1996).
30. R.Laflamme, M.Knill, and W. H.Zurek, Science, 279, 342(1998).
31. D. Aharanov and M. Ben-Or, quant-ph/9611025;
32. J.Preskill, Proc. R.Soc. London A, 454, 385(1998).
33. C. H. Bennett and G. Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, India (IEEE Press, New York, 1984), pp. 175-179
34. A. K.Ekert, et al., Phys. Rev. Lett., 69, 1293(1992).
35. P. D.Townsend, J. G.Rarity, and P. R.Tapster, Electron. Lett., 29, 1291(1993);
36. R. J.Hughes, et al in Advances in Cryptology: Proceedings of Crypto 96 (Springer-Verlag, New York, 1997), pp. 329-343;
37. A.Muller, et al., Appl. Phys. Lett., 70, 793(1997).