Decoherence-free subspaces for multiple-qubit errors. I. Characterization

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 63, Issue 2, 2001, Pages 022306-022301

  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);

CODES (SYMBOLS); ERROR CORRECTION; MATHEMATICAL MODELS; MATRIX ALGEBRA; NUCLEAR MAGNETIC RESONANCE;

QUANTUM THEORY;

EID: 0035250890     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.63.022306     Document Type: Article

References (46)

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. L.-M. Duan and G.-C. Guo, Phys. Rev. A 57, 737 (1998).
4. L. Duan and G. Guo, Phys. Rev. A 58, 3491 (1998).
5. P. Zanardi and M. Rasetti, Phys. Rev. Lett. 79, 3306 (1997).
6. P. Zanardi and M. Rasetti, Mod. Phys. Lett. B 11, 1085 (1997).
7. P. Zanardi, Phys. Rev. A 57, 3276 (1998).
8. A. D. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. 81, 2594 (1998).
9. D. A. Lidar, D. Bacon, and K. B. Whaley, Phys. Rev. Lett. 82, 4556 (1999).
10. D. Bacon, D. A. Lidar, and K. B. Whaley, Phys. Rev. A 60, 1944 (1999).
11. P. W. Shor, Phys. Rev. A 52, 2493 (1995).
12. A. M. Steane, Phys. Rev. Lett. 77, 793 (1996).
13. D. Gottesman, Phys. Rev. A 54, 1862 (1996).
14. E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997).
15. L. Viola and S. Lloyd, Phys. Rev. A 58, 2733 (1998).
16. L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999).
17. L.-M. Duan and G. Guo, e-print quant-ph/9807072.
18. P. Zanardi, Phys. Lett. A 258, 77 (1999).
19. D. Bacon, J. Kempe, D. A. Lidar, and K. B. Whaley, Phys. Rev. Lett. 85, 1758 (2000).
20. J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, Phys. Rev. A (to be published).
21. D. A. Lidar, D. Bacon, J. Kempe, and K. B. Whaley, Phys. Rev. A 61, 052307 (2000).
22. C. Slichter, Principles of Magnetic Resonance, Vol. 1 of Springer Series in Solid-State Sciences (Springer, Berlin, 1996).
23. D. S. Chemla, in Nonlinear Optics in Semiconductors, edited by R. K. Wiliardson and A. C. Beers (Academic Press, New York, 1998).
24. W. Jones and N. March, Theoretical Solid State Physics (Dover. New York, 1985), Vol. 2.
25. D. A. Lidar, D. Bacon, J. Kempe, and K. B. Whaley, following paper, Phys. Rev. A 63, 022307 (2001).
26. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. A. P. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987).
27. D. P. DiVincenzo, Phys. Rev. A 51, 1015 (1995).
28. S. Lloyd, Phys. Rev. Lett. 75, 346 (1995).
29. A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVenceezo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter, Phys. Rev. A 52, 3457 (1995).
30. R. Bhatia, Matrix Analysis, Vol. 169 of Graduate Texts in Mathematics (Springer-Verlag, New York, 1997).
31. N. Gershenfeld and I. L. Chuang, Science 275, 350 (1997).
32. J. Preskill, in Introduction to Quantum Computation and Information, edited by H. K. Lo, S. Popeseu, and T. P. Spiller (World Scientific, Singapore, 1999).
33. P. Boykin, T. Mor, M. Pulver, V. Roychowdhury, and F. Vatan, e-print quant-ph/9906054.
34. I. L. Chuang and M. A. Nielsen, J. Mod. Opt. 44, 2455 (1997).
35. C. Gardiner, Quantum Noise, Vol. 56 of Springer Series in Synergetics (Springer-Verlag, Berlin, 1991).
36. K. Kraus, States, Effects and Operations, Fundamental Notions of Quantum Theory (Academic, Berlin, 1983).
37. B. Schumacher, Phys. Rev. A 54, 2614 (1996).
38. A. Peres, e-print quant-ph/9906023.
39. N. March, W. H. Young, and S. Sampanthar, The Many-Body Problem in Quantum Mechanics (Dover, New York, 1995).
40. L.-M. Duan and G.-C. Guo, Phys. Rev. A 59, 4058 (1999).
41. S. Bandyopadhyay, A. Balandin, V. P. Roychowdhury, and F. Vatan, Superlatt. Microstruct. 23, 445 (1998); further detail in e-print quant-ph/9704019.
42. I. V. Schensted, A Course on the Application of Group Theory to Quantum Mechanics (NEO Press, Peaks Island, ME, 1976).
43. M. A. Nielsen and C. M. Caves, Phys. Rev. A 55, 2547 (1997).
44. J. F. Cornwell, Group Theory in Physics: An Introduction (Academic, San Diego, 1997).
45. D. Jaksch, H.-J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, Phys. Rev. Lett. 82, 1975 (1999).
46. M. B. Ruskai, Phys. Rev. Lett. 85, 194 (2000).