Universal quantum simulators

Science

Volumn 273, Issue 5278, 1996, Pages 1073-1078

  Lloyd, Seth ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; COMPUTER MODEL; COMPUTER SIMULATION; COMPUTER SYSTEM; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; QUANTUM CHEMISTRY; SYSTEM ANALYSIS;

EID: 0029838223     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.273.5278.1073     Document Type: Article

References (68)

1. P. Benioff, J. Stat. Phys. 22, 563 (1980); Phys. Rev. Lett. 48, 1581 (1982); J. Stat. Phys. 29, 515 (1982); Ann. N.Y. Acad. Sci. 480, 475 (1986).
2. P. Benioff, J. Stat. Phys. 22, 563 (1980); Phys. Rev. Lett. 48, 1581 (1982); J. Stat. Phys. 29, 515 (1982); Ann. N.Y. Acad. Sci. 480, 475 (1986).
3. P. Benioff, J. Stat. Phys. 22, 563 (1980); Phys. Rev. Lett. 48, 1581 (1982); J. Stat. Phys. 29, 515 (1982); Ann. N.Y. Acad. Sci. 480, 475 (1986).
4. P. Benioff, J. Stat. Phys. 22, 563 (1980); Phys. Rev. Lett. 48, 1581 (1982); J. Stat. Phys. 29, 515 (1982); Ann. N.Y. Acad. Sci. 480, 475 (1986).
5. R. P. Feynman, Opt. News 11, 11 (1985) ; Found. Phys. 16, 507 (1986); Int. J. Theor. Phys. 21, 467 (1982).
6. R. P. Feynman, Opt. News 11, 11 (1985) ; Found. Phys. 16, 507 (1986); Int. J. Theor. Phys. 21, 467 (1982).
7. R. P. Feynman, Opt. News 11, 11 (1985) ; Found. Phys. 16, 507 (1986); Int. J. Theor. Phys. 21, 467 (1982).
8. W. H. Zurek, Phys. Rev. Lett. 53, 391 (1984).
9. A. Peres, Phys. Rev. A 32, 3266 (1985).
10. N. Margolus, Ann. N.Y. Acad. Sci. 480, 487 (1986); in Complexity, Entropy, and the Physics of Information, vol. 8 of Santa Fe Institute Series, W. H. Zurek, Ed. (Addison-Wesley. Redwood City, CA, 1991), pp. 273-288.
11. N. Margolus, Ann. N.Y. Acad. Sci. 480, 487 (1986); in Complexity, Entropy, and the Physics of Information, vol. 8 of Santa Fe Institute Series, W. H. Zurek, Ed. (Addison-Wesley. Redwood City, CA, 1991), pp. 273-288.
12. D. Deutsch, Proc. R Soc. London Ser. A 400, 97 (1985).
13. See, however, D. Deutsch and R. Jozsa, ibid. 439, 553 (1992), for an interesting oracle problem that can be performed more quickly by quantum computers.
14. D. Deutsch, ibid. 425, 73 (1989).
15. Y. Yamamoto, M. Kitegawa, K. lgeta, in Proceedings of the 3rd Asia-Pacific Physics Conference, Y. W. Chan, A. F. Lenng, C. N. Yang, K. Young, Eds. (World Scientific, Singapore, 1988), pp. 779-799.
16. G. J. Milburn, Phys. Rev. Lett. 62, 2124 (1989).
17. R. Landauer, Int. J. Theor. Phys. 21, 283 (1982); Found. Phys. 16, 551 (1986); Nature 335, 779 (1988); in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, Eds. (Academic Press, Boston, 1989), pp. 17-29; Phys. Today 42, 119 (October 1989); in Proceedings ol the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 28 to 31 August 1989 (Physical Society of Japan, Tokyo, 1990), p. 407; Physica A 168, 75 (1990); Phys. Today 44, 23 (May 1991); in Proceedings of the Workshop on Physics of Computation II, Dallas, 17 to 20 November 1994, D. Matzke, Ed. (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 54-58.
18. R. Landauer, Int. J. Theor. Phys. 21, 283 (1982); Found. Phys. 16, 551 (1986); Nature 335, 779 (1988); in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, Eds. (Academic Press, Boston, 1989), pp. 17-29; Phys. Today 42, 119 (October 1989); in Proceedings ol the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 28 to 31 August 1989 (Physical Society of Japan, Tokyo, 1990), p. 407; Physica A 168, 75 (1990); Phys. Today 44, 23 (May 1991); in Proceedings of the Workshop on Physics of Computation II, Dallas, 17 to 20 November 1994, D. Matzke, Ed. (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 54-58.
19. R. Landauer, Int. J. Theor. Phys. 21, 283 (1982); Found. Phys. 16, 551 (1986); Nature 335, 779 (1988); in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, Eds. (Academic Press, Boston, 1989), pp. 17-29; Phys. Today 42, 119 (October 1989); in Proceedings ol the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 28 to 31 August 1989 (Physical Society of Japan, Tokyo, 1990), p. 407; Physica A 168, 75 (1990); Phys. Today 44, 23 (May 1991); in Proceedings of the Workshop on Physics of Computation II, Dallas, 17 to 20 November 1994, D. Matzke, Ed. (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 54-58.
20. R. Landauer, Int. J. Theor. Phys. 21, 283 (1982); Found. Phys. 16, 551 (1986); Nature 335, 779 (1988); in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, Eds. (Academic Press, Boston, 1989), pp. 17-29; Phys. Today 42, 119 (October 1989); in Proceedings ol the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 28 to 31 August 1989 (Physical Society of Japan, Tokyo, 1990), p. 407; Physica A 168, 75 (1990); Phys. Today 44, 23 (May 1991); in Proceedings of the Workshop on Physics of Computation II, Dallas, 17 to 20 November 1994, D. Matzke, Ed. (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 54-58.
21. R. Landauer, Int. J. Theor. Phys. 21, 283 (1982); Found. Phys. 16, 551 (1986); Nature 335, 779 (1988); in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, Eds. (Academic Press, Boston, 1989), pp. 17-29; Phys. Today 42, 119 (October 1989); in Proceedings ol the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 28 to 31 August 1989 (Physical Society of Japan, Tokyo, 1990), p. 407; Physica A 168, 75 (1990); Phys. Today 44, 23 (May 1991); in Proceedings of the Workshop on Physics of Computation II, Dallas, 17 to 20 November 1994, D. Matzke, Ed. (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 54-58.
22. R. Landauer, Int. J. Theor. Phys. 21, 283 (1982); Found. Phys. 16, 551 (1986); Nature 335, 779 (1988); in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, Eds. (Academic Press, Boston, 1989), pp. 17-29; Phys. Today 42, 119 (October 1989); in Proceedings ol the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 28 to 31 August 1989 (Physical Society of Japan, Tokyo, 1990), p. 407; Physica A 168, 75 (1990); Phys. Today 44, 23 (May 1991); in Proceedings of the Workshop on Physics of Computation II, Dallas, 17 to 20 November 1994, D. Matzke, Ed. (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 54-58.
23. R. Landauer, Int. J. Theor. Phys. 21, 283 (1982); Found. Phys. 16, 551 (1986); Nature 335, 779 (1988); in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, Eds. (Academic Press, Boston, 1989), pp. 17-29; Phys. Today 42, 119 (October 1989); in Proceedings ol the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 28 to 31 August 1989 (Physical Society of Japan, Tokyo, 1990), p. 407; Physica A 168, 75 (1990); Phys. Today 44, 23 (May 1991); in Proceedings of the Workshop on Physics of Computation II, Dallas, 17 to 20 November 1994, D. Matzke, Ed. (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 54-58.
24. R. Landauer, Int. J. Theor. Phys. 21, 283 (1982); Found. Phys. 16, 551 (1986); Nature 335, 779 (1988); in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, Eds. (Academic Press, Boston, 1989), pp. 17-29; Phys. Today 42, 119 (October 1989); in Proceedings ol the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 28 to 31 August 1989 (Physical Society of Japan, Tokyo, 1990), p. 407; Physica A 168, 75 (1990); Phys. Today 44, 23 (May 1991); in Proceedings of the Workshop on Physics of Computation II, Dallas, 17 to 20 November 1994, D. Matzke, Ed. (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 54-58.
25. R. Landauer, Int. J. Theor. Phys. 21, 283 (1982); Found. Phys. 16, 551 (1986); Nature 335, 779 (1988); in Nanostructure Physics and Fabrication, M. A. Reed and W. P. Kirk, Eds. (Academic Press, Boston, 1989), pp. 17-29; Phys. Today 42, 119 (October 1989); in Proceedings ol the 3rd International Symposium on Foundations of Quantum Mechanics, Tokyo, 28 to 31 August 1989 (Physical Society of Japan, Tokyo, 1990), p. 407; Physica A 168, 75 (1990); Phys. Today 44, 23 (May 1991); in Proceedings of the Workshop on Physics of Computation II, Dallas, 17 to 20 November 1994, D. Matzke, Ed. (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 54-58.
26. K. Obermayer, W. G. Teich, G. Mahler, Phys. Rev. B 37, 8096 (1988); W. G. Teich, K. Obermayer, G. Mahler, ibid., p. 8111 ; W. G. Teich and G. Mahler, Phys. Rev. A 45, 3300 (1992).
27. K. Obermayer, W. G. Teich, G. Mahler, Phys. Rev. B 37, 8096 (1988); W. G. Teich, K. Obermayer, G. Mahler, ibid., p. 8111 ; W. G. Teich and G. Mahler, Phys. Rev. A 45, 3300 (1992).
28. K. Obermayer, W. G. Teich, G. Mahler, Phys. Rev. B 37, 8096 (1988); W. G. Teich, K. Obermayer, G. Mahler, ibid., p. 8111 ; W. G. Teich and G. Mahler, Phys. Rev. A 45, 3300 (1992).
29. S. Lloyd, Science 261, 1569 (1993); ibid. 263, 695 (1994).
30. S. Lloyd, Science 261, 1569 (1993); ibid. 263, 695 (1994).
31. P. Shor, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, 20 to 22 November 1994, S. Goldwasser, Ed. (IEEE Computer Society. Los Alamitos, CA, 1994), p. 124.
32. D. P. DiVincenzo, Science 270, 255 (1995).
33. _, Phys. Rev. A 50, 1015 (1995).
34. A. Barenco, D. Deutsch, A. Ekert, R. Jozsa, Phys. Rev. Lett. 74, 4083 (1995).
35. T. Sleator and H. Weinfurter, ibid., p. 4087.
36. G. M. Palma. K.-A. Suominem, A. Ekert, Proc. R Soc. London Ser. A 452, 567 (1996).
37. S. Lloyd, Phys. Rev. Lett. 75, 346 (1995).
38. D. Deutsch, A. Barenco, A. Ekert, Proc. R. Soc. London Ser. A 449, 669 (1995).
39. J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
40. Q. A. Turchette, C. J. Hood, W. Lange, H. Mabuchi, H. J. Kimble, ibid. 75, 4710 (1995).
41. C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, D. J. Wineland, ibid., p. 4714.
42. W. G. Unruh, Phys. Rev. A 51, 992 (1995).
43. M. Brune et al., Phys. Rev. Lett. 72, 3339 (1994); P. Domokos, J. M. Raimond, M. Brune, S. Haroche, Phys. Rev. A 52, 3554 (1995).
44. M. Brune et al., Phys. Rev. Lett. 72, 3339 (1994); P. Domokos, J. M. Raimond, M. Brune, S. Haroche, Phys. Rev. A 52, 3554 (1995).
45. R. Landauer, Philos. Trans. R. Soc. London Ser. A 353, 367 (1995); in Proceedings of the Drexel-4 Symposium on Quantum Nonintegrability: Quantum Classical Correspondence, D. H. Feng and B. L. Hu, Eds. (International Press, Boston, 1996).
46. R. Landauer, Philos. Trans. R. Soc. London Ser. A 353, 367 (1995); in Proceedings of the Drexel-4 Symposium on Quantum Nonintegrability: Quantum Classical Correspondence, D. H. Feng and B. L. Hu, Eds. (International Press, Boston, 1996).
47. I. L. Chuang, R. Laflamme, P. W. Shor, W. H. Zurek, Science 270, 1633 (1995).
48. P. W. Shor, Phys. Rev. A 52, 2493 (1995); A. R. Calderbank and P. W. Shor, Phys. Rev. A, in press; A. Steane, in preparation.
49. P. W. Shor, Phys. Rev. A 52, 2493 (1995); A. R. Calderbank and P. W. Shor, Phys. Rev. A, in press; A. Steane, in preparation.
50. P. W. Shor, Phys. Rev. A 52, 2493 (1995); A. R. Calderbank and P. W. Shor, Phys. Rev. A, in press; A. Steane, in preparation.
51. M. H. Kalos, Ed., Monte Carlo Methods in Quantum Problems (Reidel, Dordrecht, Netherlands, 1984).
52. K. Binder, Ed., The Monte Carlo Method in Condensed Matter Physics (Springer-Verlag, New York, 1995).
53. C. Rebbi, Ed., Lattice Gauge Theories and Monte Carlo Simulations (World Scientific, Singapore, 1983).
54. W. S. Warren, D. P. Weitekamp, A. Pines, J. Chem. Phys. 73, 2084 (1980).
55. V. Ramakrishna, M. V. Salapaka, M. Dahleh, H. Rabitz, A. Peirce, Phys. Rev. A 51, 960 (1995).
56. A. Yao, in Proceedings of the 34th Annual Symposium on Foundations of Computer Science, S. Goldwasser, Ed. (IEEE Computer Society, Los Alamitos, CA, 1995), p. 352.
57. H. Mabuchi and H. J. Kimble, Opt. Lett. 19, 749 (1993); A. B. Matsko, S. P. Vyatchanin, H. Mabuchi, H. J. Kimble, Phys. Lett. A 192, 175 (1994); H. J. Kimble et al., in Proceedings of the International Conference on Atomic Physics; A. S. Parkins, P. Marte, P. Zoller, H. J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).
58. H. Mabuchi and H. J. Kimble, Opt. Lett. 19, 749 (1993); A. B. Matsko, S. P. Vyatchanin, H. Mabuchi, H. J. Kimble, Phys. Lett. A 192, 175 (1994); H. J. Kimble et al., in Proceedings of the International Conference on Atomic Physics; A. S. Parkins, P. Marte, P. Zoller, H. J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).
59. H. Mabuchi and H. J. Kimble, Opt. Lett. 19, 749 (1993); A. B. Matsko, S. P. Vyatchanin, H. Mabuchi, H. J. Kimble, Phys. Lett. A 192, 175 (1994); H. J. Kimble et al., in Proceedings of the International Conference on Atomic Physics; A. S. Parkins, P. Marte, P. Zoller, H. J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).
60. H. Mabuchi and H. J. Kimble, Opt. Lett. 19, 749 (1993); A. B. Matsko, S. P. Vyatchanin, H. Mabuchi, H. J. Kimble, Phys. Lett. A 192, 175 (1994); H. J. Kimble et al., in Proceedings of the International Conference on Atomic Physics; A. S. Parkins, P. Marte, P. Zoller, H. J. Kimble, Phys. Rev. Lett. 71, 3095 (1993).
61. t as well. See, for example, R. W. Brockett, R. S. Millman, H. J. Sussman, Eds., Differential Geometric Control Theory (Birkhauser, Boston, 1983), and Z. Li and J. F. Canney, Eds., Nonholonomic Motion Planning (Kluwer Academic, Boston, 1993).
62. t as well. See, for example, R. W. Brockett, R. S. Millman, H. J. Sussman, Eds., Differential Geometric Control Theory (Birkhauser, Boston, 1983), and Z. Li and J. F. Canney, Eds., Nonholonomic Motion Planning (Kluwer Academic, Boston, 1993).
63. The extra factor of N is required to conform with the normal rules for phases of fermions on a lattice in second quantized form. See, for example, A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971), and J. W. Negele and H. Ormand, Quantum Many-Particle Systems (Addison-Wesley, Redwood City, CA, 1988).
64. The extra factor of N is required to conform with the normal rules for phases of fermions on a lattice in second quantized form. See, for example, A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971), and J. W. Negele and H. Ormand, Quantum Many-Particle Systems (Addison-Wesley, Redwood City, CA, 1988).
65. K. Kraus, States, Effects, and Operations: Fundamental Notions of Quantum Theory (Springer-Verlag, Berlin, 1983).
66. There is an extra subtlety in the open system case. For the quantum analog simulation of open systems to be efficient, the time evolution of the open system must be a finite-order quantum Markov process, that is, the environment must have finite time and space correlation lengths.
67. C. B. Murray, C. R. Kagan, M. G. Bawendi, Science 270, 1335 (1995).
68. Supported in part by grant N00014-95-1-0975 from the Office of Naval Research. This work is part of the Quantum Information and Computation project (QUIC).