Searching via walking: How to find a marked clique of a complete graph using quantum walks

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 81, Issue 6, 2010, Pages

  Hillery, Mark ^a   Reitzner, Daniel ^b   Bužek, Vladimír ^b  

^a CITY UNIVERSITY OF NEW YORK   (United States)

^b INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLETE GRAPHS; QUANTITATIVE COMPARISON; QUANTUM CIRCUIT; QUANTUM SEARCH; QUANTUM WALK; SUBGRAPHS;

GRAPH THEORY;

EID: 77953724148     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.81.062324     Document Type: Article

References (34)

1. Y. Aharonov, L. Davidovich, and N. Zagury, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.48.1687 48, 1687 (1993).
2. D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani, in Proceedings of the 33rd STOC (ACM, New York, 2001), p. 50.
3. E. Farhi and S. Gutmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.915 58, 915 (1998).
4. A. Ambainis, SIAM J. Comput. SMJCAT 0097-5397 10.1137/S0097539705447311 37, 210 (2007).
5. A. M. Childs and J. Eisenberg, Quantum Inf. Comput. 5, 593 (2005).
6. A. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. Spielman, in Proceedings of the 35th STOC (ACM, New York, 2003), p. 59.
7. A. M. Childs, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102. 180501 102, 180501 (2009).
8. E. Farhi, J. Goldstone, and S. Gutmann, arXiv: quant-ph/0702144.
9. V. Kendon, Math. Struct. Comp. Sci. MCSCEA 0960-1295 10.1017/ S0960129507006354 17, 1169 (2007).
10. M. Santha, in Proceedings of the 5th TAMC (Springer, New York, 2008), p. 31.
11. J. Kempe, Contemp. Phys. 0010-7514 10.1080/00107151031000110776 44, 307 (2003).
12. 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).
13. M. Karski, L. Forster, J.-M. Choi, A. Steffen, W. Alt, D. Meschede, and A. Widera, Science SCIEAS 0036-8075 10.1126/science.1174436 325, 174 (2009).
14. H. B. Perets, Y. Lahini, F. Pozzi, M. Sorel, R. Morandotti, and Y. Silberberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.100.170506 100, 170506 (2008).
15. P. L. Knight, E. Roldán, and J. E. Sipe, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.020301 68, 020301 (R) (2003).
16. H. Jeong, M. Paternostro, and M. S. Kim, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.012310 69, 012310 (2004).
17. 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).
18. A. Schreiber, K. N. Cassemiro, V Potoček, A. Gabris, P. J. Mosley, E. Andersson, I. Jex, and Ch. Silberhorn, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.050502 104, 050502 (2010).
19. B. C. Travaglione and G. J. Milburn, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.032310 65, 032310 (2002).
20. P. Xue, B. C. Sanders, and D. Leibfried, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.183602 103, 183602 (2009).
21. H. Schmitz, R. Matjeschk, Ch. Schneider, J. Glueckert, M. Enderlein, T. Huber, and T. Schaetz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett. 103.090504 103, 090504 (2009).
22. F. Zähringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt, and C. F. Roos, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.100503 104, 100503 (2010).
23. M. A. Broome, A. Fedrizzi, B. P. Lanyon, I. Kassal, A. Aspuru-Guzik, and A. G. White, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.153602 104, 153602 (2010).
24. N. Shenvi, J. Kempe, and K. Birgitta Whaley, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.67.052307 67, 052307 (2003).
25. A. Ambainis, J. Kempe, and A. Rivosh, in Proceedings of the 16th ACM-SIAM SODA (SIAM, Philadelphia, 2005), p. 1099.
26. A. M. Childs and J. Goldstone, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.022314 70, 022314 (2004).
27. F. Magniez, M. Santha, and M. Szegedy, SIAM J. Comput. SMJCAT 0097-5397 10.1137/050643684 37, 413 (2007).
28. A. M. Childs, E. Farhi, J. Goldstone, and S. Gutmann, Quantum Inf. Comput. 2 (3), 181 (2002).
29. D. Lu, J. Zhu, P. Zou, X. Peng, Y. Yu, S. Zhang, Q. Chen, and J. Du, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.81.022308 81, 022308 (2010).
30. M. Hillery, J. Bergou, and E. Feldman, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.032314 68, 032314 (2003).
31. D. Reitzner, M. Hillery, E. Feldman, and V. Bužek, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.79.012323 79, 012323 (2009).
32. T. Mackay, S. Bartlett, L. Stephenson, and B. Sanders, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/35/12/304 35, 2745 (2002).
33. H. Krovi and T. A. Brun, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.062332 75, 062332 (2007).
34. I. Jex, S. Stenholm, and A. Zeilinger, Opt. Commun. OPCOB8 0030-4018 10.1016/0030-4018(95)00078-M 117, 95 (1995).