Experimental realization of an order-finding algorithm with an NMR quantum computer

Physical Review Letters

Volumn 85, Issue 25, 2000, Pages 5452-5455

  Vandersypen, Lieven M K ^a,b   Steffen, Matthias ^a,b   Breyta, Gregory ^b   Yannoni, Costantino S ^b   Cleve, Richard ^c   Chuang, Isaac L ^b  

^a STANFORD UNIVERSITY   (United States)

^b IBM ALMADEN RESEARCH CENTER   (United States)

^c UNIVERSITY OF CALGARY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; ELECTRON TRAPS; ELECTRONS; FOURIER TRANSFORMS; IONS; MOLECULAR DYNAMICS; MOLECULES; NUCLEAR MAGNETIC RESONANCE; SEMICONDUCTOR QUANTUM DOTS;

ELECTRON SPINS; ION TRAPS; NUCLEAR MAGNETIC RESONANCE QUANTUM COMPUTER; ORDER FINDING ALGORITHM; SHOR QUANTUM ALGORITHM;

QUANTUM THEORY;

EID: 0034499812     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.85.5452     Document Type: Article

References (32)

1. C. A. Sackett et al., Nature (London) 404, 256 (2000).
2. E. Knill, R. Laflamme, R. Martinez, and C.-H. Tseng, Nature (London) 404, 368 (2000). However, in current room temperature NMR experiments, entangling operations are performed on a density matrix so close to the identity matrix that the state remains separable, as shown by S. L. Braunstein et al., Phys. Rev. Lett. 83, 1054 (1999).
3. E. Knill, R. Laflamme, R. Martinez, and C.-H. Tseng, Nature (London) 404, 368 (2000). However, in current room temperature NMR experiments, entangling operations are performed on a density matrix so close to the identity matrix that the state remains separable, as shown by S. L. Braunstein et al., Phys. Rev. Lett. 83, 1054 (1999).
4. N. Gershenfeld and I. L. Chuang, Science 275, 350 (1997).
5. D. G. Cory, A. F. Fahmy, and T. F. Havel, Proc. Natl. Acad. Sci. U.S.A. 94, 1634 (1997).
6. I. L. Chuang, N. Gershenfeld, and M. Kubinec, Phys. Rev. Lett. 80, 3408 (1998).
7. J. A. Jones, M. Mosca, and R. H. Hansen, Nature (London) 393, 344 (1998).
8. L. M. K. Vandersypen et al., Appl. Phys. Lett. 76, 646 (2000).
9. I. L. Chuang, L. M. K. Vandersypen, X. Zhou, D. W Leung, and S. Lloyd, Nature (London) 393, 143 (1998).
10. J. A. Jones and M. Mosca, J. Chem. Phys. 109, 1648 (1998).
11. R. Marx et al., Phys. Rev. A 62, 012310 (2000).
12. J. A. Jones, Special issue on Experimental Proposals for Quantum Computation [Fortschr. Phys.]; quant-ph/ 0002085.
13. P. Shor, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science (IEEE Computer Society Press, Los Alamitos, CA, 1994), p. 124.
14. A. Ekert and R. Jozsa, Rev. Mod. Phys. 68, 733 (1996).
15. R. Cleve, A. Ekert, C. Macchiavello, and M. Mosca, Proc. R. Soc. London Sect. A 454, 339 (1998).
16. R. Schack and C. M. Caves, Phys. Rev. A 60, 4354 (1999).
17. A. Y. Kitaev, quant-ph/9511026.
18. M. Steffen, L. M. K. Vandersypen, and I. L. Chuang, J. Magn. Reson. 146, 369 (2000).
19. R. Cleve, in Proceedings of the 15th Annual IEEE Conference on Computational Complexity, Firenze, Italy (IEEE Computer Society Press, Los Alamitos, CA, 2000), p. 54.
20. D. Coppersmith, IBM Research Report No. RC19642, 1994.
21. Y. S. Weinstein, S. Lloyd, and D. G. Cory, quant-ph/ 9906059.
22. M. Green, N. Mayne, and F. G. A. Stone, J. Chem. Soc. (A), 902 (1968).
23. If r were independent of the value of y, the second register would not have to be prepared in an effective pure state, but in general r may depend on y so all five spins were made effective pure in all spectra shown.
24. R. Freeman, Spin Choreography (Spektrum, Oxford, 1997).
25. E. Knill, I. L. Chuang, and R. Laflamme, Phys. Rev. A 57, 3348 (1998).
26. L. J. Schulman and U.V. Vazirani, in Proceedings of the 31st Annual ACM Symposium on Theory of Computing, Atlanta, GA, 1999 (Association for Computing Machinery, New York, 1999), p. 322.
27. S. L. Patt, J. Magn. Reson. 96, 94 (1992).
28. L. Emsley and G. Bodenhausen, Chem. Phys. Lett. 168, 297 (1990).
29. N. Linden, Ē Kupče, and R. Freeman, Chem. Phys. Lett. 311, 321 (1999).
30. It is not clear, however, that the bitwise average outputs of the QFT suffice to determine r for permutations on arbitrary n. Instead, classical postprocessing on the quantum computer [3] can be used to compute r.
31. B. E. Kane, Nature (London) 393, 133 (1998).
32. D. Loss and D. DiVincenzo, Phys. Rev. A 57, 120 (1998).