Quantum walks, quantum gates, and quantum computers

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 75, Issue 6, 2007, Pages

  Hines, Andrew P ^a,b   Stamp, P C E ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DEGREES OF FREEDOM (MECHANICS); EXCITED STATES; FOURIER TRANSFORMS; GRAPH THEORY; HAMILTONIANS;

HAMILTONIAN LANGUAGE; QUANTUM GATES; QUANTUM WALKS; QUBIT SYSTEMS;

QUANTUM COMPUTERS;

EID: 34547287377     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.75.062321     Document Type: Article

References (39)

1. For an introduction to solid-state physics, see A. W. Ashcroft and N. D. Mermin, Solid-State Physics (Holt, Rinehart, and Winston, New York, 1976).
2. An introduction to quantum dynamics on disordered lattices and graphs is in J. M. Ziman, Models of Disorder (Cambridge University Press, Cambridge, England, 1979).
3. An introduction to the quantum magnetism of lattice spin systems is given by P. Fazekas, Electron Correlation and Magnetism (World Scientific, Singapore, 1999);
4. the topic of spin glasses, and related work in optimization and neural network theory, is treated in K. H. Fischer and J. A. Hertz, Spin Glasses (Cambridge University Press, Cambridge, England, 1991)
5. and M. Mezard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
6. Optical lattice systems are reviewed in I. Bloch, Nat. Phys. ZZZZZZ 1745-2473 1, 23 (2005), and references therein.
7. Treatments of statistical mechanics emphasizing methods useful for degrees of freedom on lattices and other graphs include D. C. Mattis, Statistical Mechanics Made Simple (World Scientific, Singapore, 2003)
8. and L. P. Kadanoff, Statistical Physics: Statics, Dynamics, and Renormalisation (World Scientific, Singapore, 2000).
9. J. Kempe, Contemp. Phys. CTPHAF 0010-7514 10.1080/00107151031000110776 44, 307 (2003).
10. E. Farhi and S. Gutmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.915 58, 915 (1998).
11. A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. A. Spielman, Proceedings of the 35th ACM Symposium on Theory of Computing (STOC, San Diego, CA, 2003), pp. 59-68.
12. N. Shenvi, J. Kempe, and K. Birgitta Whaley, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052307 67, 052307 (2003).
13. J. Kempe, Probab. Theory Relat. Fields PTRFEU 0178-8051 10.1007/s00440-004-0423-2 133, 215 (2005).
14. A. Ambainis, Int. J. Quantum Inf. ZZZZZZ 0219-7499 1, 407 (2003).
15. A. M. Childs, E. Farhi, and S. Gutmann, Quantum Inf. Process. QIPUAT 1570-0755 10.1023/A:1019609420309 1, 35 (2002).
16. S. Aaronson and A. Ambainis, Theory of Computing 1, 47 (2005);
17. A. Ambainis, J. Kempe, and A. Rivosh, Proceedings of the 16th ACM-SIAM SODA (SIAM, Vancouver, B.C., 2005), pp. 1099-1108.
18. A. M. Childs and J. Goldstone, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.022314 70, 022314 (2004);
19. A. M. Childs and J. Goldstone, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.042312 70, 042312 (2004).
20. B. C. Travaglione and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032310 65, 032310 (2002);
21. W. Dür, R. Raussendorf, V. M. Kendon, and H.-J. Briegel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.052319 66, 052319 (2002);
22. K. Eckert, J. Mompart, G. Birkl, and M. Lewenstein, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.012327 72, 012327 (2005);
23. B. C. Sanders, S. D. Bartlett, B. Tregenna, and P. L. Knight, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.042305 67, 042305 (2003).
24. S. Fujiwara, H. Osaki, I. M. Buluta, and S. Hasegawa, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.032329 72, 032329 (2005).
25. D. Bouwmeester, I. Marzoli, G. P. Karman, W. Schleich, and J. P. Woerdman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.61.013410 61, 013410 (1999).
26. C. A. Ryan, M. Laforest, J. C. Boileau, and R. Laflamme, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.062317 72, 062317 (2005).
27. R. P. Feynman and F. L. Vernon, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(63)90068-X 24, 118 (1963).
28. A. J. Leggett, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.30.1208 30, 1208 (1984).
29. N. V. Prokof'ev and P. C. E. Stamp, Rep. Prog. Phys. RPPHAG 0034-4885 10.1088/0034-4885/63/4/204 63, 669 (2000).
30. P. C. E. Stamp, Stud. Hist. Philos. Mod. Phys. ZZZZZZ 1355-2198 37, 467 (2006).
31. A. Hines and P. C. E. Stamp (unpublished).
32. N. V. Prokof'ev and P. C. E. Stamp, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74.020102 74, 020102 (R) (2006).
33. R. P. Feynman, Found. Phys. FNDPA4 0015-9018 10.1007/BF01886518 16, 507 (1986).
34. V. Kendon, Int. J. Quantum Inf. ZZZZZZ 0219-7499 4, 791 (2006).
35. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000).
36. M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, and C. M. Dawson, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.022317 66, 022317 (2002).
37. M. J. Bremner, C. M. Dawson, J. L. Dodd, A. Gilchrist, A. W. Harrow, D. Mortimer, M. A. Nielsen, and T. J. Osborne, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.247902 89, 247902 (2002).
38. M. A. Nielsen, M. R. Dowling, M. Gu, and A. C. Doherty, Science SCIEAS 0036-8075 10.1126/science.1121541 311, 1133 (2006).
39. A. P. Hines, G. J. Milburn, and P. C. E. Stamp (unpublished).