Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 66, Issue 2, 2002, Pages 022317/1-022317/12

  Nielsen, Michael A ^a   Bremner, Michael J ^a   Dodd, Jennifer L ^a   Childs, Andrew M ^a,b   Dawson, Christopher M ^b  

^a UNIVERSITY OF QUEENSLAND   (Australia)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036701960     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.66.022317     Document Type: Article

References (38)

1. D. Deutsch, Proc. R. Soc. London, Ser. A 400, 97 (1985).
2. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
3. J. Preskill, Physics 229: Advanced Mathematical Methods of Physics-Quantum Computation and Information (California Institute of Technology, Pasadena, California, 1998), http://www.theory.caltech.edu/people/preskill/ph229/
4. J.L. Dodd, M.A. Nielsen, M.J. Bremner, and R.T. Thew, Phys. Rev. A 65, 040301(R) (2002).
5. C. P. Slichter, Principles of Magnetic Resonance (Springer, Berlin, 1996).
6. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, Oxford, 1994).
7. J.A. Jones and E. Knill, J. Magn. Reson. 141, 322 (1999).
8. D.W. Leung, I.L. Chuang, F. Yamaguchi, and Y. Yamamoto, Phys. Rev. A 61, 042310 (2000).
9. A. Barenco, C.H. Bennett, R. Cleve, D.P. DiVicenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter, Phys. Rev. A 52, 3457 (1995).
10. J.L. Brylinski and R. Brylinski, e-print arXiv:quant-ph/0108062.
11. D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995).
12. S. Lloyd, Phys. Rev. Lett. 75, 346 (1995).
13. N. Weaver, J. Math. Phys. 41, 240 (2000).
14. W. Dür, G. Vidal, J.I. Cirac, N. Linden, and S. Popescu, Phys. Rev. Lett. 87, 137901 (2001).
15. P. Wocjan, D. Janzing, and T. Beth, Quantum Inform. Comput. 2, 117 (2002).
16. C.H. Bennett, J.I. Cirac, M.S. Leifer, D.W. Leung, N. Liden, S. Popescu, and G. Vidal, e-print arXiv:quant-ph/0107035v1.
17. G. Vidal and J.I. Cirac, e-print arXiv:quant-ph/0108076.
18. D. W. Leung and G. Vidal, e-print arXiv:quant-ph/0107035v2, updated version of Ref. [16]. Appendix C.
19. H. Rabitz, R. De Vive-Riedle, M. Motzkus, and K. Kompa, Science 288, 824 (2000).
20. S.G. Schirmer, A.I. Solomon, and J.V. Leahy, e-print arXiv:quant-ph/0108114v1.
21. D. Janzing, P. Wocjan, and T. Beth, e-print arXiv:quant-ph/0106085.
22. D.W. Leung, e-print arXiv:quant-ph/0107041.
23. D. Gottesman, in Quantum Computing and Quantum Communications: First NASA International Conference, edited by C. P. Williams (Springer-Verlag, Berlin, 1999).
24. Euclid, Elements (Cambridge University Press, Cambridge, England, 1908).
25. J.-P. Serre, Linear Representations of Finite Groups, Graduate Texts in Mathematics Vol. 42 (Springer-Verlag, New York, 1977).
26. M.A. Nielsen, Phys. Rev. A 63, 022114 (2001).
27. R. Bhatia, Matrix Analysis (Springer-Verlag, New York, 1997).
28. A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and its Applications (Academic Press, New York, 1979).
29. P. M. Alberti and A. Uhlmann, Stochasticity and Partial Order: Doubly Stochastic Maps and Unitary Mixing (Dordrecht, Boston, 1982).
30. A. Uhlmann, Wiss. Z.-Karl-Marx-Univ. Leipzig, Math.-Naturwiss. Reihe 20, 633 (1971).
31. A. Wehrl, Rev. Mod. Phys. 50, 221 (1978).
32. M. A. Nielsen and G. Vidal, Quantum Inform. Comput. 1, 76 (2001).
33. C.H. Bennett, J.I. Cirac, M.S. Leifer, D.W. Leung, S. Popescu, and G. Vidal, e-print arXiv:quant-ph/0107035v2, updated version of Ref. [16].
34. P. Wocjan, M. Roetteler, D. Janzing, and T. Beth, Quantum Inform. Comput. 2, 133 (2002).
35. S. Lloyd and L. Viola, Phys. Rev. A 65, 010101 (2002).
36. D. Bacon, A.M. Childs, I.L. Chuang, J. Kempe, D.W. Leung, and X. Zhou, Phys. Rev. A 63, 012306 (2001).
37. This term was coined in a 1998 conversion between one of us (M.A.N.) and Raymond Laflamme.
38. Our thanks go to Ben Schumacher, who contributed to the discovery of this theorem.