Nonbinary codeword-stabilized quantum codes

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 78, Issue 6, 2008, Pages

  Chen, Xie ^a   Zeng, Bei ^a   Chuang, Isaac L ^a,b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b Department of Electrical Engineering and Computer Science   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARTIFICIAL INTELLIGENCE; IMAGE CODING; INFORMATION THEORY;

ADDITIVITY; BINARY STATES; CORRECTING CODES; EFFICIENT CONSTRUCTIONS; ERROR PATTERNS; NON BINARIES; NONBINARY CODES; PRIME DIMENSIONS; QUANTUM CODES; QUANTUM ERRORS; SEARCH PROBLEMS; SEARCH SPACES; SPECIFIC STRUCTURES; STABILIZER CODES;

CODES (SYMBOLS);

EID: 57649139227     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.78.062315     Document Type: Article

References (27)

1. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes (North-Holland, Amsterdam, 1977).
2. A. Ashikhmin and E. Knill, IEEE Trans. Inf. Theory 47, 3065 (2001). 10.1109/18.959288
3. M. Hamada, in Proceedings of the IEEE International Symposium on Information Theory (IEEE, New York, 2003), p. 480.
4. D. Aharonov and M. Ben-Or, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing (Association for Computing Machinery, New York, 1997), pp. 176-188.
5. E. M. Rains, IEEE Trans. Inf. Theory 45, 1827 (1999). 10.1109/18.782103
6. D. Gottesman, in Lecture Notes in Computer Science (Springer, Berlin, 1999), pp. 302-313.
7. M. Grassl, T. Beth, and M. Roetteler, Int. J. Quantum Inf. 2, 55 (2004). 10.1142/S0219749904000079
8. A. Cross, G. Smith, J. Smolin, and B. Zeng, e-print arXiv:0708.1021v4.
9. I. Chuang, A. Cross, G. Smith, J. Smolin, and B. Zeng, e-print arXiv:0803.3232v1.
10. M. Grassl and M. Roetteler, e-print arXiv:0801.2150v1.
11. M. Grassl and M. Roetteler, e-print arXiv:0801.2144v1.
12. S. Yu, Q. Chen, and C. Oh, e-print arXiv:0709.1780v1.
13. V. Arvind, P. P. Kurur, and K. Parthasarathy, e-print arXiv:0210097v1.
14. V. Aggarwal and R. Calderbank, IEEE Trans. Inf. Theory 54, 1700 (2008). 10.1109/TIT.2008.917720
15. D. Hu, W. Tan, M. Zhao, Q. Chen, S. Yu, and C. H. Oh, e-print arXiv:0801.0831v1.
16. S. Y. Looi, L. Yu, V. Gheorghiu, and R. B. Griffiths, Phys. Rev. A 78, 042303 (2008). 10.1103/PhysRevA.78.042303
17. S. D. Bartlett, H. de Guise, and B. C. Sanders, Phys. Rev. A 65, 052316 (2002). 10.1103/PhysRevA.65.052316
18. B. C. Sanders, S. D. Bartlett, and H. de Guise, in Proceedings, ICSSUR'01, edited by, D. Han, Y. S. Kim, B. E. A. Saleh, A. V. Sergienko and, M. C. Teich, (Boston, MA, 2002).
19. J. Daboul, X. Wang, and B. C. Sanders, J. Phys. A 36, 2525 (2003). 10.1088/0305-4470/36/10/312
20. D. Gottesman, A. Kitaev, and J. Preskill, Phys. Rev. A 64, 012310 (2001). 10.1103/PhysRevA.64.012310
21. J. Patera and H. Zassenhaus, J. Math. Phys. 29, 665 (1988). 10.1063/1.528006
22. E. Knill, e-print arXiv:quant-ph/9608048v2.
23. E. Hostens, J. Dehaene, and B. D. Moor, Phys. Rev. A 71, 042315 (2005). 10.1103/PhysRevA.71.042315
24. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
25. D. Schlingemann, e-print arXiv:quant-ph/0111080.
26. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, Phys. Rev. A 54, 3824 (1996). 10.1103/PhysRevA.54.3824
27. E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997). 10.1103/PhysRevA.55.900