Spatially correlated qubit errors and burst-correcting quantum codes

IEEE Transactions on Information Theory

Volumn 45, Issue 5, 1999, Pages 1703-1708

  Vatan, Farrokh ^a   Roychowdhury, Vwani P ^a   Anantram, M P ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b NASA AMES RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CODING ERRORS; CORRELATION THEORY; ERROR CORRECTION; ONE DIMENSIONAL; RANDOM PROCESSES;

ADDITIVE CODES; BURST ERRORS; CYCLIC CODES; GILBERT-VARSHAMOV BOUND; QUANTUM ERROR CORRECTING CODE;

CODES (SYMBOLS);

EID: 0032636507     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.771250     Document Type: Article

References (20)

1. K. A. S. Abdel-Ghaffar, R. J. McEliece, A. M. Odlyzko, and H. C. A. van Tilborg, "On the existence of optimum cyclic burst-correcting codes," IEEE Trans. Inform. Theory, vol. IT-32, pp. 768-775, Nov. 1986.
2. C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and W. K. Wootters, "Mixed state entanglement and quantum error correction," Phys. Rev. A, vol. 54, no. 5, pp. 3824-3851, 1996.
3. A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, "Quantum error correction and orthogonal geometry," Phys. Rev. Lett., vol. 78, no. 3, pp. 405-408, 1997.
4. _, "Quantum error correction via codes over GF(4)," IEEE Trans. Inform. Theory, vol. 44, pp. 1369-1387, July 1998.
5. A. R. Calderbank and P. W. Shor, "Good quantum error-correcting codes exit," Phys. Rev. A, vol. 54, no. 2, pp. 1098-1105, 1996.
6. J. I. Cirac and P. Zoller, "Quantum computations with cold trapped ions," Phys. Rev. Lett., vol. 74, no. 20, pp. 4091-4094, 1995.
7. P. Fire, "A class of multipleor-correcting binary codes for non-independent errors," Tech. Rep., Sylvania Rep. RSL-E-2, Sylvania Reconnaissance Syst. Lab., Mountain View, CA, 1959.
8. D. Gottesman, "A class of quantum error-correcting codes saturating the quantum hamming bound," Phys. Rev. A, vol. 54, no. 3, pp. 1862-1868, 1996.
9. M. Grassl, Th. Beth, and T. Pellizzari, "Codes for the quantum erasure channel," Phys. Rev. A, vol. 56, no. 1, pp. 33-38, 1997.
10. E. Knill and R. Laflamme, "A theory of quantum error-correcting codes," Phys. Rev. A, vol. 55, no. 2, pp. 900-911, 1997.
11. R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, "Perfect quantum error correction code," Phys. Rev. Lett., vol. 77, no. 1, pp. 198-201, 1996.
12. S. Lloyd, "A potentially realizable quantum computer," Science, vol. 261, pp. 1569-1571, 1993.
13. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes. Amsterdam, The Netherlands: North-Holland, 1977.
14. C. M. Melas and E. Gorog, "A note on extending certain codes to correct error bursts in longer messages," IBM J. Res. Develop., vol. 7, pp. 151-152, 1963.
15. G. M. Palma, K. A. Suominen, and A. K. Ekert, "Quantum computers and dissipation," Proc. Roy. Soc. London, Ser. A, vol. 452, pp. 567-584, 1996.
16. W. W. Peterson and E. J. Weldon Jr., Error-Correcting Codes, 2nd ed. Boston, MA: MIT Press, 1972.
17. E. Rains, private communication, Apr. 1997.
18. P. W. Shor, "Scheme for reducing decoherence in quantum memory," Phys. Rev. A, vol. 52, no. 4, pp. 2493-2496, 1995.
19. A. M. Steane, "Error correcting codes in quantum theory," Phys. Rev. Lett., vol. 77, no. 5, pp. 793-797, 1996.
20. A. M. Steane, "Multiple particle interference and quantum error correction," Proc. Roy. Soc. London, Ser. A, vol. 452, pp. 2551-2577, 1996.