The challenge of quantum computer simulations of physical phenomena

Nuclear Physics B - Proceedings Supplements

Volumn 106-107, Issue , 2002, Pages 151-158

  Ortiz, G ^a   Knill, E ^a   Gubernatis, J E ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036524754     PISSN: 09205632     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0920-5632(01)01654-1     Document Type: Article

References (15)

1. R. Landauer in Feynman and Computation, edited by A. J. G. Hey (Perseus Books, Reading, 1999).
2. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
3. For a history about quantum simulations see, for example, Ref. [2].
4. G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, Phys. Rev. A 64 (2001) 22319.
5. Probabilistic simulations of quantum systems on a CC are mainly performed with the use of the Monte Carlo method, which has the property that the probability distributions achieved represent the desired information efficiently. But they often require exponential sampling to obtain the desired expectation with sufficient accuracy.
6. D. S. Abrams and S. Lloyd, Phys. Rev. Lett. 79 (1997) 2586.
7. R. Somma, G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme, quant-ph/0108146.
8. C.D. Batista and G. Ortiz, Phys. Rev. Lett. 86 (2001) 1082. C.D. Batista and G. Ortiz, unpublished preprint.
9. j.
10. j - 1.
11. We are aware of at least one case where the sign problem can be mapped onto a 3-SAT problem, i.e., an NP-complete problem [7]. Therefore, one cannot yet claim that a QC can solve "all" sign problems, otherwise one would claim that one is solving all NP-complete problems and this has not been rigorously established.
12. C. Negrevergne et al., unpublished preprint.
13. D. G. Cory, A. F. Fahmy, and T. F. Havel, P. Natl. Acad. Sci. USA 94 (1997) 1634.
14. N. A. Gershenfeld and I. L. Chuang, Science 275 (1997) 350.
15. C. Miquel, J. P. Paz, M. Saraceno, E. Knill, R. Laflamme, and C. Negrevergne, quant-ph/0109072.