Decoherence-free subspaces for multiple-qubit errors. II. Universal, fault-tolerant quantum computation

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 63, Issue 2, 2001, Pages 022307-022301

  Lidar, Daniel A ^a,c   Bacon, Dave ^a   Kempe, Julia ^a,b   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);

CORRELATION METHODS; FAILURE ANALYSIS; MATHEMATICAL MODELS; TENSORS;

QUANTUM THEORY;

EID: 0035251190     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.63.022307     Document Type: Article

References (50)

1. H. K. Lo, S. Popescu, and T. P. Spiller, Introduction to Quantum Computation and Information (World Scientific, Singapore, 1999).
2. C. Williams and S. Clearwater, Explorations in Quantum Computing (Springer-Verlag, New York, 1998).
3. A. M. Steane, Rep. Prog. Phys. 61, 117 (1998); e-print quant-ph/9708022.
4. D. Aharonov, e-print quant-ph/9812037.
5. R. Cleve, e-print quant-ph/9906111.
6. R. Alicki and K. Lendi, in Quantum Dynamical Semigroups and Applications, Lecture Notes in Physics (Springer-Verlag, Berlin, 1987).
7. K. Kraus, States, Effects and Operations, Fundamental Notions of Quantum Theory (Academic, Berlin, 1983).
8. D. Bacon, D. A. Lidar, and K. B. Whaley, Phys. Rev. A 60, 1944 (1999); e-print quant-ph/9902041.
9. M. A. Nielsen, C. M. Caves, B. Schumacher, and H. Barnum, Proc. R. Soc. London, Ser. A 454, 277 (1998); e-print quant-ph/9706064.
10. P. W. Shor, Phys. Rev. A 52, 2493 (1995).
11. A. R. Calderbank and P. W. Shor, Phys. Rev. A 54, 1098 (1996).
12. A. M. Steane, Phys. Rev. Lett. 77, 793 (1996).
13. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996).
14. A. Yu. Kitaev, Russ. Math. Surveys 52, 1191 (1996).
15. D. Gottesman, Phys. Rev. A 54, 1862 (1996); e-print quant-ph/9604038.
16. E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997).
17. A. M. Steane, in Introduction to Quantum Computation and Information, edited by H. K. Lo, S. Popescu, and T. P. Spiller (World Scientific, Singapore, 1999), p. 184.
18. P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997); e-print quant-ph/9705044.
19. P. Zanardi and M. Rasetti, Mod. Phys. Lett. B 11, 1085 (1997); e-print quant-ph/9710041.
20. L.-M. Duan and G.-C. Guo, Phys. Rev. A 57, 737 (1998).
21. L.-M. Duan and G.-C. Guo, Phys. Lett. A 243, 265 (1998).
22. D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. 81, 2594 (1998); e-print quant-ph/9807004.
23. D. A. Lidar, D. Bacon, and K. B. Whaley, Phys. Rev. Lett. 82, 4556 (1999); e-print quant-ph/9809081.
24. E. Knill, R. Laflamme, and L. Viola, Phys. Rev. Lett. 84, 2525 (2000); e-print quant-ph/9908066.
25. L. Duan and G. Guo, Phys. Lett. A 255, 209 (1999); e-print quant-ph/9809057.
26. D. Bacon, J. Kempe, D. A. Lidar, and K. B. Whaley, Phys. Rev. Lett. 85, 1758 (2000); e-print quant-ph/9909058.
27. J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, Phys. Rev. A (to be published): available as e-print quant-ph/0004064.
28. E. M. Rains, R. H. Hardin, P. W. Shor, and N. J. A. Sloane, Phys. Rev. Lett. 79, 953 (1997).
29. D. A. Lidar, D. Bacon, J. Kempe, and K. B. Whaley, preceding paper, Phys. Rev. A 63, 022306 (2000).
30. P. Zanardi, Phys. Rev. A 60, R729 (1999), e-print quant-ph/ 9901047.
31. A. Beige, D. Braun, B. Tregenna, and P. L. Knight, Phys. Rev. Lett. 85, 1762 (2000).
32. P. W. Shor, in Proceedings of the 37th Symposium on Foundations of Computing (IEEE Computer Society Press, Los Alamitos, CA. 1996), p. 56; e-print quant-ph/9605011.
33. P. Boykin, T. Mor, M. Pulver, V. Roychowdhury, and F. Vatan, in 40th Annual Symposium on Foundations of Computer Science (IEEE Comput. Soc., Los Alamitos, CA, 1999), p. 486; e-print quant-pn/9906054.
34. D. Gottesman, Phys. Rev. A 57, 127 (1997); e-print quant-ph/ 9702029.
35. E. Knill, R. Laflamme, and W. Zurek, Proc. R. Soc. London, Ser. A 454, 365 (1998); e-print quant-ph/9702058.
36. D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995).
37. D. P. DiVincenzo, Phys. Rev. A 51, 1015 (1995).
38. T. Sleator and H. Weinfurter, Phys. Rev. Lett. 74, 4087 (1995).
39. S. Lloyd, Phys. Rev. Lett. 75, 346 (1995).
40. D. Gottesman, e-print quant-ph/9807006.
41. A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, IEEE Trans. Inf. Theory 44, 1369 (1998); e-print quant-ph/9608006.
42. A. 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).
43. M.E. Rose, Elementary Theory of Angular Momentum (Dover, New York, 1995).
44. D. Loss and D. P. DiVincenzo, Phys. Rev. A 57, 120 (1998); e-print quant-ph/9701055.
45. D. Gottesman, Ph.D. thesis, California Institute of Technology, Pasadena, CA, 1997; e-print quant-ph/9705052.
46. C. Slichter, in Principles of Magnetic Resonance, Springer Series in Solid-State Sciences Vol. 1 (Springer, Berlin, 1996).
47. R. Bhatia, in Matrix Analysis, Graduate Texts in Mathematics Vol. 169 (Springer-Verlag, New York, 1997).
48. D. Aharonov and M. Ben-Or, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing (STOC) (ACM, New York, 1997), p. 46; e-print quant-ph/9611025.
49. C. Zalka, e-print quant-ph/9612028.
50. E. Knill, R. Laflamme, and W. Zurek, Science 279, 342 (1998).