Effects of a random noisy oracle on search algorithm complexity

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 68, Issue 5, 2003, Pages 523131-5231311

  Shenvi, Neil ^a   Brown, Kenneth R ^a   Whaley, K Birgitta ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CODES (SYMBOLS); COMPUTER SCIENCE; ERROR CORRECTION; QUANTUM THEORY; SEARCH ENGINES; SPURIOUS SIGNAL NOISE;

DENSITY-MATRIX APPROACH; QUANTUM SEARCH;

FAULT TOLERANT COMPUTER SYSTEMS;

EID: 0942289431     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. P.W. Shor, Phys. Rev. A 52, R2493 (1995).
2. J. Preskill, Proc. R. Soc. London, Ser. A 454, 385 (1998).
3. D. Bacon, J. Kempe, D.A. Lidar, and K.B. Whaley, Phys. Rev. Lett. 85, 1758 (2000).
4. D. Abrams and C. Williams, e-print quant-ph/9908083.
5. E. Novak, J. Complex. 17, 2 (2001).
6. G. Brassard, P. Hoyer, M. Mosca, and A. Tapp, e-print quant-ph/0005055.
7. G.L. Long, Y.S. Li, W.L. Zhang, and C.C. Tu, Phys. Rev. A 61, 042305 (1999).
8. J. Hsieh, C.-M. Li, and D.-S. Chuu, e-print quant-ph/0209073.
9. B. Pablo-Norman and M. Ruiz-Altaba, Phys. Rev. A 61, 012301 (1999).
10. D. Shapira, S. Mozes, and O. Biham, Phys. Rev. A 67, 042301 (2003).
11. J. Bae and Y. Kwon, e-print quant-ph/0211186.
12. E. Farhi and S. Gutmann, Phys. Rev. A 57, 2403 (1998).
13. E. Farhi, J. Goldstone, S. Gutmann, and M. Sipser, e-print quant-ph/0001106.
14. L.K. Grover, in Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (ACM, New York, 1996), p. 212.
15. L.K. Grover, Phys. Rev. Lett. 79, 4709 (1997).
16. C.H. Bennett, E. Bernstein, G. Brassard, and U.V. Vazirani, SIAM J. Comput. 26, 1510 (1997).
17. M. Boyer, G. Brassard, P. Hoyer, and A. Tapp, Fortsch. Phys.- Prog. Phys. 46, 493 (1998).
18. D.E. Knuth, The Art of Computer Programming (Addison-Wesley, Reading, MA, 1973), Vol. 1.
19. M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
20. A. Messiah, Quantum Mechanics (Interscience, New York, 1961).
21. It should be noted that this analysis applies only in the limit of large N, which is what we mean when we talk of algorithmic complexity in the first place.
22. K. Blum, Density Matrix Theory and Applications (Plenum Press, New York, 1981).