Quantum walks on necklaces and mixing

International Journal of Quantum Information

Volumn 10, Issue 2, 2012, Pages

  Kieferová, Mária ^a   Nagaj, Daniel ^a  

^a INSTITUTE OF PHYSICS   (Slovakia)

Author keywords

Continous quantum walks; cyclical graph; mixing

Indexed keywords

EID: 84859541589     PISSN: 02197499     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219749912500256     Document Type: Article

References (29)

1. N. Metropolis, A. W. Rosenbluth, N. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. Phys. 21 (1953) 1087.
2. W. K. Hastings, Biometrika 57 (1970) 97.
3. S. Kirkpatrick, C. D. Gelatt Jr. and M. P. Vecchi, Science 220 (1983) 671.
4. J. Černý, J. Opt. Theory. Appl. 45 (1985) 41.
5. M. Jerrum and A. Sinclair, SIAM J. Comput. 22 (1993) 1087.
6. M. Jerrum, A. Sinclair and E. Vigoda, J. ACM 51(4) (2004) 671.
7. D. Aharonov, A. Ambainis, J. Kempe and U. Vazirani, Quantum walks on graphs, in STOC '01: Proc. Thirty-Third Annual ACM Symp. Theory of Computing (ACM, New York, NY, USA, 2001), pp. 50-59. (Pubitemid 32865717)
8. E. Farhi, S. Gutmann, Phys. Rev. A 58(2) (1998) 915.
9. A. Ambainis, E. Bach, A. Nayak, A. Vishwanath and J. Watrous, One-dimensional quantum walks, in STOC '01: Proc. Thirty-Third Annual ACM Symp. Theory of Computing (ACM, New York, NY, USA, 2001), pp. 37-49. (Pubitemid 32865716)
10. M. Santha, Quantum walk based search algorithms, in Proc. 5th Theory and Applications of Models of Computation (TAMC08), Lectures Notes on Computer Science, Vol. 4978 (2008), pp. 31-46.
11. A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann and D. A. Spielman, Exponential algorithmic speedup by quantum walk, in Proc. 35th ACM Symp. Theory of Computing (2003), pp. 59-68.
12. E. Farhi, J. Goldstone and S. Gutmann, Theor. Comput. 4(1) (2007) 169, quant-ph/0702144.
13. A. M. Childs, Phys. Rev. Lett. 102 (2009) 180501.
14. F. L. Marquezino and R. Portugal, Phys. Rev. A 82 (2010) 042341.
15. C. Moore and A. Russell, Proc. 6th Int. Workshop on Randomization and Approximation Techniques (RANDOM 2002), Cambridge, MA, LNCS, Vol. 2483 (Springer-Verlag, Berlin, 2002), pp. 164-178.
16. A. Ahmadi, R. Belk, C. Tamon and C. Wendler, Quant. Inf. Comput. 3(6) (2003) 611.
17. P. Lo, S. Rajaram, D. Schepens, D. Sullivan, C. Tamon and J. Ward, Quant. Inf. Comput. 6(4&5) (2006) 370.
18. T. Osborne, Hamiltonian complexity, arXiv:1106.5875 (2011).
19. M. A. Nielsen and I. L. Chuang, Quantum Information and Computation (Cambridge University Press, Cambridge, UK, 2000).
20. R. Feynman, Opt. News 11 (1985) 11.
21. J. Kempe, A. Kitaev and O. Regev, SIAM J. Comput. 35(5) (2006) 1070.
22. D. Nagaj and S. Mozes, J. Math. Phys. 48 (2007) 2104.
23. D. de Falco and D. Tamascelli, J. Phys. A: Math. Gen. 37 (2004) 909.
24. D. Nagaj, J. Math. Phys. 51(6) (2010) 062201.
25. A. Mizel, D. A. Lidar and M. Mitchell, Phys. Rev. Lett. 99 (2008) 070502.
26. D. Aharonov, D. Gottesman, S. Irani and J. Kempe, The power of quantum systems on a line, in Proc. 48th IEEE FOCS, (2007), pp. 373-383.
27. D. Nagaj, arXiv:1002.0420 (2010).
28. L. Eldar and O. Regev, Quantum SAT for a qutrit-cinquit pair is QMA1-complete, ICALP 2008, eds. L. Aceto et al., Part I, LNCS, Vol. 5125 (Springer-Verlag Berlin, Heidelberg, 2008), pp. 881-892.
29. D. Nagaj and P. Wocjan, Phys. Rev. A 78 (2008) 032311.