Theory of decoherence-free fault-tolerant universal quantum computation

Physical Review A. Atomic, Molecular, and Optical Physics

Volumn 63, Issue 4, 2001, Pages 423071-4230729

  Kempe, J ^a,b   Bacon, D ^a   Lidar, D A ^a,c   Whaley, K B ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b TELECOM PARISTECH   (France)

^c UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

DECOHERENCE-FREE SUBSPACES (DFS); QUANTUM ERROR CORRECTING CODES (QECC); QUBITS;

ERROR CORRECTION; HAMILTONIANS; HIGH ENERGY PHYSICS; INFORMATION ANALYSIS; MARKOV PROCESSES; MATRIX ALGEBRA;

QUANTUM THEORY;

EID: 3543055458     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (65)

1. P.W. Shor, in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994), p. 124.
2. L.K. Grover, Phys. Rev. Lett. 79, 325 (1997).
3. C.H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W.K. Wootters, Phys. Rev. Lett. 70, 1895 (1993).
4. C.H. Bennett and P.W. Shor, IEEE Trans. Inf. Theory 44, 2724 (1998).
5. Abbreviations frequently used in this paper are QECC = quantum error correcting code, DFS = decoherence-free subsystem (or subspace, if no confusion can arise), WCD/SCD = weak/ strong collective decoherence, and the irrep=irreducible representation.
6. P.W. Shor, Phys. Rev. A 52, R2493 (1995).
7. A.M. Steane, Phys. Rev. Lett. 77, 793 (1996).
8. E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997).
9. D. Gottesman, Phys. Rev. A 54, 1862 (1997).
10. P.W. Shor, in Proceedings of the 37th Symposium on Foundations of Computing (IEEE Computer Society Press, Los Alamitos, CA, 1996), p. 56.
11. D. Aharonov and M. Ben-Or, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC) (ACM, New York, 1997).
12. D. Aharonov and M. Ben-Or, LANL Report No. quant-ph/9906129, 1999 (unpublished).
13. A.Yu. Kitaev, Russian Math. Surveys 52, 1191 (1996).
14. E. Knill, R. Laflamme, and W. Zurek, Science 279, 342 (1998).
15. J. Preskill, Proc. R. Soc. 454, 385 (1998).
16. G. Palma, K. Suominen, and A. Ekert, Proc. R. Soc. London, Ser. A 452, 567 (1996).
17. L.-M. Duan and G.-C. Guo, Phys. Rev. Lett. 79, 1953 (1997).
18. L.-M. Duan and G.-C. Guo, Phys. Rev. A 57, 737 (1998).
19. P. Zanardi and M. Rasetti, Mod. Phys. Lett. B 11, 1085 (1997).
20. P. Zanardi, Phys. Rev. A 56, 4445 (1997).
21. P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997).
22. P. Zanardi, Phys. Rev. A 57, 3276 (1998).
23. P. Zanardi and M. Rasetti, Phys. Rev. A 57, 3276 (1998).
24. D.A. Lidar, I.L. Chuang, and K.B. Whaley, Phys. Rev. Lett. 81, 2594 (1998).
25. D.A. Lidar, D. Bacon, and K.B. Whaley, Phys. Rev. Lett. 82, 4556 (1999).
26. D.A. Lidar, D. Bacon, J. Kempe, and K.B. Whaley, Phys. Rev. A 63, 022306 (2001).
27. D. Bacon, D.A. Lidar, and K.B. Whaley, Phys. Rev. A 60, 1944 (1999).
28. D.A. Lidar, D. Bacon, J. Kempe, and K.B. Whaley, Phys. Rev. A 61, 052307 (2000).
29. M. Durdevich, H.E. Makaruk, and R. Owczarek, LANL Report No. quant-ph/0003134, 2000 (unpublished).
30. P. Zanardi and F. Rossi, Phys. Rev. Lett. 81, 4572 (1998).
31. P. Zanardi and F. Rossi, Phys. Rev. B 59, 8170 (1999).
32. L. Viola and S. Lloyd, Phys. Rev. A 58. 2733 (1998).
33. L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999).
34. L.-M. Duan and G. Guo, LANL Report No. quant-ph/9807072, 1998 (unpublished).
35. P. Zanardi, Phys. Lett. A 258, 77 (1999).
36. P. Zanardi, Phys. Rev. A 63, 012301 (2001).
37. P. Zanardi, Phys. Rev. A 60, R729 (1999).
38. A. Beige, D. Braun, and P.L. Knight, New J. Phys. 2 (2000).
39. A. Beige, D. Braun, B. Tregenna, and P.L. Knight, Phys. Rev. Lett. 85, 1762 (2000).
40. D. Bacon, J. Kempe, D.A. Lidar, and K.B. Whaley, Phys. Rev. Lett. 85, 1758 (2000).
41. D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995).
42. A. Barenco, Proc. R. Soc. London. Ser. A 449, 679 (1995).
43. D. P. DiVincenzo, Phys. Rev. A 51, 1015 (1995).
44. S. Lloyd, Phys. Rev. A 75, 346 (1995).
45. T. Sleator and H. Weinfurter, Phys. Rev. Lett. 74, 4087 (1995).
46. D. P. DiVincenzo, D. Bacon, J. Kempe, G. Burkard, and K. B. Whaley, Nature (London) 408, 339 (2000).
47. L. Duan and G. Guo, Phys. Lett. A 255, 209 (1999).
48. E. Knill, R. Laflamme, and L. Viola, Phys. Rev. Lett. 84, 2525 (2000).
49. L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 85, 3520 (2000).
50. H. Carmichael, An Open Systems Approach to Quantum Optics, No. m18 in Lecture Notes in Physics (Springer-Verlag, Berlin, 1993).
51. D. Gottesman, Phys. Rev. A 57, 127 (1997).
52. G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
53. R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Applications, No. 286 in Lecture Notes in Physics (Springer-Verlag, Berlin, 1987).
54. S. De Filippo, Phys. Rev. A 62, 052307 (2000).
55. N.P. Landsman, LANL Report No. math-ph/9807030, 1998 (unpublished).
56. K. Kraus. States, Effects and Operations, Fundamental Notions of Quantum Theory (Academic, Berlin, 1983).
57. L.-M. Duan and G.-C. Guo, Phys. Rev. A 57, 737 (1998).
58. J.P. Paz and W.H. Zurek, Proc. R. Soc. London, Ser. A 454, 355 (1998).
59. D. Barenco, C.H. Bennett, R. Cleve, D.P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter, Phys. Rev. A 52, 3457 (1995).
60. R.H. Dicke, Phys. Rev. 93, 99 (1954).
61. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).
62. D. P. DiVincenzo, G. Burkard, D. Loss, and E.V. Sukhorukov, in Quantum Mesoscopic Phenomena and Mesoscopic Devices in Microelectronics., edited by LO. Kulk and R. Ellialtioglu (NATO Advanced Study Institute, Turkey, 1999).
63. R. Laflamme, C. Miquel, J.P. Paz, and W.H. Zurek, Phys. Rev. Lett. 77, 198 (1996).
64. D. Gottesman, J. Mod. Opt. 47, 333 (2000).
65. R.N. Cahn, Semi-Simple Lie Algebras and Their Representations (Benjamin/Cummings, Reading, MA, 1984), available online at http://www-physics.lbl.gov/rncahn/book.html.