Operator quantum error-correcting subsystems for self-correcting quantum memories

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 73, Issue 1, 2006, Pages

  Bacon, Dave ^a  

^a Department of Computer Science and Engineering University of Washington ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ERROR ANALYSIS; ERROR CORRECTION; HAMILTONIANS; SIGNAL ENCODING;

HILBERT SPACE; QUANTUM ERROR-CORRECTING SUBSYSTEMS; QUANTUM MEMORIES;

QUANTUM THEORY;

EID: 33144457448     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.73.012340     Document Type: Article

References (62)

1. W. G. Unruh, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.51.992 51, 992 (1995).
2. R. Landauer, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(96)00453-7 217, 187 (1996).
3. E. Bernstein and U. Vazirani, Proceedings of the 25th Annual ACM Symposium on Theory of Computation (ACM Press, 1993), pp. 11-20.
4. D. Simon, in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science, edited by, S. Goldwasser, (IEEE Computer Society, Los Alamitos, CA, 1994), pp. 116-123.
5. P. W. Shor, in Proceedings of the 35th Annual Symposium on the Foundations of Computer Science (Ref.), pp. 124-134.
6. R. Raz, Proceedings of the 31st ACM Symposium on Theory of Computing (ACM Press, NY, 1999), pp. 358-367.
7. P. W. Shor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.52.R2493 52, R2493 (1995).
8. A. M. Steane, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.4741 54, 4741 (1996).
9. E. Knill and R. Laflamme, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.55.900 55, 900 (1997).
10. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.54.3824 54, 3824 (1996).
11. E. Knill, R. Laflamme, and W. H. Zurek, Science SCIEAS 0036-8075 10.1126/science.279.5349.342 279, 342 (1998).
12. E. Knill, R. Laflamme, and W. H. Zurek, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 10.1098/rspa.1998.0166 454, 365 (1998).
13. P. W. Shor, Proceedings of the 37th Symposium on the Foundations of Computer Science (IEEE, Los Alamitos, CA, 1996), pp. 56-65.
14. D. Aharonov and M. Ben-Or, Proceedings of the 29th Annual ACM Symposium on Theory of Computing (ACM Press, NY, 1997), pp. 176-188.
15. D. Gottesman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.127 57, 127 (1998).
16. A. Kitaev, Ann. Phys. ANPYA2 0003-3804 303, 2 (2003).
17. J. Preskill, Introduction to Quantum Computation and Information (World Scientific, New Jersey, 1998), pp. 213-269.
18. E. Knill, R. Laflamme, and L. Viola, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2525 84, 2525 (2000).
19. L. Viola, E. Knill, and R. Laflamme, Constructing qubits in physical systems, e-print quant-ph/0101090.
20. J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.042307 63, 042307 (2001).
21. D. Bacon, Ph. D. thesis, University of California at Berkeley, Berkeley, CA, 2001 (unpublished).
22. P. Zanardi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.012301 63, 012301 (2001).
23. P. Zanardi and S. Lloyd, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.067902 90, 067902 (2003).
24. A. Shabani and D. Lidar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.042303 72, 042303 (2005).
25. L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.3520 85, 3520 (2000).
26. L. A. Wu and D. A. Lidar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.207902 88, 207902 (2002).
27. D. Kribs, R. Laflamme, and D. Poulin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.180501 94, 180501 (2005).
28. D. Kribs, R. Laflamme, D. Poulin, and M. Lesosky, e-print quant-ph/0504189.
29. P. Zanardi and M. Rasetti, Mod. Phys. Lett. B MPLBET 0217-9849 10.1142/S0217984997001304 11, 1085 (1997).
30. D. A. Lidar, I. L. Chuang, and K. B. Whaley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.81.2594 81, 2594 (1998).
31. M. Nielsen and D. Poulin, e-print quant-ph/0506069.
32. D. Gottesman, Ph. D. thesis, California Insitute of Technology, Pasadena, CA (1997) (unpublished).
33. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quatum Information (Cambridge University Press, New York, 2000).
34. J. F. Cornwell, Group Theory in Physics: An Introduction (Academic Press, San Diego, CA, 1997).
35. G. James and M. Liebeck, Representations and Characters of Groups (Cambridge University Press, Cambridge, UK, 2001).
36. E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1499754 43, 4452 (2002).
37. R. W. Ogburn and J. Preskill, Lect. Notes Comput. Sci. LNCSD9 0302-9743 1509, 341 (1999).
38. B. Douçut, M. Feigel'man, L. Ioffe, and A. Ioselevich, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.71.024505 71, 024505 (2005).
39. J. Dorier, F. Becca, and F. Mila, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.72.024448 72, 024448 (2005).
40. A. M. Turing, Proc. London Math. Soc. PLMTAL 42, 230 (1936).
41. A. M. Turing, A. M Turing's ACE Report of 1946 and Other Papers (North-Holland, Amsterdam, 982).
42. J. von Neumann, in Automata Studies (Princeton University Press, Princeton, NJ, 1956), pp. 329-378.
43. A. Kitaev, Russ. Math. Surveys RMSUAF 0036-0279 10.1070/ RM1997v052n06ABEH002155 52, 1191 (1995).
44. M. Plischke and B. Bergersen, Equilibrium Statistical Physics (World Scientific, Singapore, 1994).
45. J. P. Barnes and W. S. Warren, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.856 85, 856 (2000).
46. C. Wang, J. Harrington, and J. Preskill, Ann. Phys. ANPYA2 0003-3804 303, 31 (2003).
47. M. H. Freedman, A. Kitaev, M. Larsen, and Z. Wang, e-print quant-ph/0101025.
48. C. Nayak and K. Shtengel, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.64.064422 64, 064422 (2001).
49. D. Bacon, K. R. Brown, and K. B. Whaley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.247902 87, 247902 (2001).
50. J. Brink and Z. Wang, Quantum Inf. Process. QIPUAT 1570-0755 2, 81 (2003).
51. M. Freedman, Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-002- 0785-1 234, 129 (2003).
52. M. Freedman, C. Nayak, and K. Shtengel, e-print cond-mat/0309120.
53. A. Hamma, P. Zanardi, and X. Wen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.062319 69, 062319 (2004).
54. M. Freedman, C. Nayak, K. Shtengel, K. Walker, and Z. Wang, Ann. Phys. ANPYA2 0003-3804 310, 428 (2004).
55. M. Freedman, C. Nayak, and K. Shtengel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.147205 94, 147205 (2004).
56. M. Freedman, C. Nayak, and K. Shtengel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.066401 94, 066401 (2005).
57. A. Kitaev, e-print cond-mat/0506438.
58. I. Duetsch, G. Brennen, and P. Jessen, Fortschr. Phys. FPYKA6 0015-8208 10.1002/1521-3978(200009)48:9/11<925::AID-PROP925>3.0.CO;2-A 48, 925 (2000).
59. L. M. Duan, E. Demler, and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.090402 91, 090402 (2003).
60. G. Vidal, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.147902 91, 147902 (2003).
61. F. Verstraete and J. Cirac, e-print cond-mat/0407066.
62. M. Reimpell and R. F. Werner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.080501 94, 080501 (2005).