Optimal and efficient decoding of concatenated quantum block codes

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 74, Issue 5, 2006, Pages

  Poulin, David ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BLOCK CODES; DECODING; ERROR CORRECTION; MONTE CARLO METHODS;

DEPOLARIZING CHANNEL; MESSAGE PASSING ALGORITHMS; NOISY CHANNEL; QUANTUM ERROR CORRECTION;

QUANTUM ELECTRONICS;

EID: 33751271619     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.74.052333     Document Type: Article

References (33)

1. P. W. Shor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.52.R2493 52, R2493 (1995);
2. A. M. Steane, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 452, 2551 (1996);
3. E. Knill and R. Laflamme, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.55.900 55, 900 (1997).
4. P. W. Shor, in Proceedings of the 37th Symposium on the Foundations of Computer Science (IEEE Press, Los Alamitos, CA, 1996), pp. 56â€" 65;
5. A. Y. Kitaev, in Proceedings of the Third International Conference on Quantum Communication and Measurement, edited by, O. Hirota, A. S. Holevo, and, C. M. Caves, (Plenum, New York, 1997), pp. 181â€"188;
6. E. Knill, R. Laflamme, and W. H. Zurek, Philos. Trans. R. Soc. London, Ser. A PTRMAD 0962-8428 454, 365 (1998);
7. D. Aharonov and M. Ben-Or, in Proc. 29th Ann. ACM Symp. on Theory of Computing (ACM, New York, 1997);
8. J. Preskill, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 10.1098/rspa.1998.0167 454, 385 (1998).
9. E. R. Berlekamp, R. J. McEliece, and H. van Tilborg, IEEE Trans. Inf. Theory IETTAW 0018-9448 10.1109/TIT.1978.1055873 24, 384 (1978).
10. T. Richardson and R. Urbanke, Modern Coding Theory (to be published)
11. available online at http://lthcwww.epfl.ch/mct/
12. D. J. C. MacKay, Information Theory, Inference and Learning Algorithms (Cambridge University Press, Cambridge, England, 2003).
13. R. G. Gallager, Low Density Parity Check Codes (MIT Press, Cambridge, MA, 1963).
14. H. Ollivier and J.-P. Tillich, in Proceedings of 26th Symposium on Information Theory in the Benelux (Brussels, 2005), p. 149.
15. T. Camara, H. Ollivier, and J.-P. Tillich, e-print quant-ph/0502086.
16. D. J. C. MacKay, G. Mitchison, and P. L. McFadden, IEEE Trans. Inf. Theory IETTAW 0018-9448 50, 2315 (2004).
17. H. Ollivier and J.-P. Tillich, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.032304 74, 032304 (2006).
18. A. Y. Kitaev, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/S0003-4916(02) 00018-0 303, 2 (2003).
19. R. Laflamme, C. Miquel, J.-P. Paz, and W. H. Zurek, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77.198 77, 198 (1996);
20. 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).
21. A. M. Steane, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.77. 793 77, 793 (1996).
22. B. Rahn, A. C. Doherty, and H. Mabuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.032304 66, 032304 (2002).
23. D. Poulin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95. 230504 95, 230504 (2005).
24. D. Gottesman, Ph.D. thesis, California Institute of Technology, Pasadena, 1997;
25. e-print quant-ph/9705052.
26. I. Markov and Y. Shi, e-print quant-ph/0511069.
27. S. Aji and R. McEliece, IEEE Trans. Inf. Theory IETTAW 0018-9448 46, 325 (2000).
28. G. Forney, Concatenated Codes (MIT Press, Cambridge, MA, 1966).
29. D. P. DiVincenzo, P. W. Shor, and J. A. Smolin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.57.830 57, 830 (1998).
30. G. Smith and J. A. Smolin, e-print quant-ph/0604107.
31. H. Ollivier, D. Poulin, and J.-P. Tillich (to be published).
32. E. Knill, Nature (London) NATUAS 0028-0836 10.1038/nature03350 434, 39 (2005).
33. A. Fletcher, P. Shor, and M. Win, e-print quant-ph/0606035.