Overhead and noise threshold of fault-tolerant quantum error correction

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 68, Issue 4 A, 2003, Pages

  Steane, Andrew M ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CODES (SYMBOLS); COMPUTATIONAL COMPLEXITY; DATA STORAGE EQUIPMENT; ENCODING (SYMBOLS); ERROR CORRECTION; FAILURE ANALYSIS; FAULT TOLERANT COMPUTER SYSTEMS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS; PROBABILITY;

CALDERBANK-SHOR-STEANE CODE; CONCATENATED CODE; FAULT-TOLERANT QUANTUM ERROR CORRECTION; GOLAY CODE; HAMMING CODE; QUANTUM ALGORITHM; QUANTUM COMPUTATION;

QUANTUM THEORY;

EID: 0141983069     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. P.W. Shor, Phys. Rev. A 52, R2493 (1995).
2. A.M. Steane, Phys. Rev. Lett. 77, 793 (1996).
3. A.R. Calderbank and P.W. Shor, Phys. Rev. A 54, 1098 (1996).
4. A.M. Steane, Proc. R. Soc. London, Ser. A 452, 2551 (1996).
5. P.W. Shor, in Proceedings of the 35th Annual Symposium on Fundamentals of Computer Science (IEEE Press, Los Alamitos, 1996), pp. 56-65.
6. D.P. DiVincenzo and P.W. Shor, Phys. Rev. Lett. 77, 3260 (1996).
7. J. Preskill, Proc. R. Soc. London, Ser. A 454, 385 (1998).
8. D. Gottesman, Phys. Rev. A 57, 127 (1998).
9. D. Gottesman and I.L. Chuang, Nature (London) 402, 390 (1999).
10. A.Y. Kitaev, in Quantum Communication, Computing and Measurement, Proceedings of the 3rd International Conference of Quantum Communication and Measurement, edited by O. Hirota, A.S. Holevo, and C.M. Caves (Plenum Press, New York, 1997), pp. 181-188.
11. E. Knill, R. Laflamme, and W.H. Zurek, Science 279, 342 (1998).
12. A.M. Steane, Nature (London) 399, 124 (1999).
13. A.M. Steane, Fortschr. Phys. 46, 443 (1997).
14. A.M. Steane, e-print quant-ph/0202036.
15. D. Aharonov and M. Ben-Or, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing, edited by F.T. Leighton and P. Shor (ACM, New York, 1998), p. 176.
16. A.M. Steane, Phys. Rev. Lett. 78, 2252 (1997).
17. A.Y. Kitaev, e-print quant-ph/9707021.
18. D. Gottesman, Ph.D. thesis, California Institute of Technology, 1997 (unpublished).
19. A.M. Steane, Quant. Inf. Comp. 2, 297 (2002).
20. A.M. Steane, Decoherence and its Implications in Quantum Computation and Information Transfer (IOS Press, Amsterdam, 2001), pp. 284-298.
21. E. Knill and R. Laflamme, Phys. Rev. A 55, 900 (1997).
22. E. Knill, R. Laflamme, and L. Viola, Phys. Rev. Lett. 84, 2525 (2000).
23. R. Alicki, M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. A 65, 062101 (2002).
24. C. Zalka, e-print quant-ph/9612028 v2.
25. W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, England, 1994).
26. J. Preskill, in Introduction to Quantum Computation, edited by H.-K. Lo, S. Popescu, and T. Spiller (World Scientific, Singapore, 1998), pp. 213-269.
27. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes (North-Holland, Amsterdam, 1977).
28. A.M. Steane, Phys. Rev. A 54, 4741 (1996).
29. A.R. Calderbank, E.M. Rains, P.W. Shor, and N.J.A. Sloane, IEEE Trans. Inf. Theory 44, 1369 (1998).