Quantum navigation and ranking in complex networks

Scientific Reports

Volumn 2, Issue , 2012, Pages

  Sánchez Burillo, Eduardo ^a   Duch, Jordi ^b   Gómez Gardeñes, Jesús ^a   Zueco, David ^a,c  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b UNIVERSITAT ROVIRA I VIRGILI   (Spain)

^c FUNDACIÓN ARAID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84866141224     PISSN: None     EISSN: 20452322     Source Type: Journal    
DOI: 10.1038/srep00605     Document Type: Article

References (46)

1. Marchiori, M. Comp. Net. & ISDN Sys. 29, 1225 (1997).
2. Brin, S. & Page, L. The anatomy of a large-scale hypertextual web search engine. Comput. Netw. ISDN Syst. 30, 107-117 (1998).
3. Allesina, S. & Pascual, M. Googling food webs: can an eigenvector measure species importance for coextinctions? PLoS Comput. Biol. 5, e1000494 (2009).
4. Radicchi, F., Fortunato, S., Markines, B. & Vespignani, A. Diffusion of scientific credits and the ranking of scientists. Phys. Rev. E 80, 056103 (2009).
5. Goshal, G. & Barabási, A.-L. Ranking stability and super-stable nodes in complex networks. Nature Communications 2, 394 (2011).
6. Albert, R. & Barabási, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47-97 (2002).
7. Boccaletti, S., Latora, V.,Moreno, Y., Chavez & Hwang, D.-U. Complex networks: Structure and dynamics. Phys. Rep. 424, 175-308 (2006). (Pubitemid 43135890)
8. Newman, M. E. J. The structure and function of complex networks. SIAM Review 45, 167-256 (2003).
9. Vespignani, A. Modelling dynamical processes in complex socio-technical systems. Nature Physics 8, 32-39 (2012).
10. Watts, D. J. & Strogatz, S. H. Collective dynamics of 'small-world' networks. Nature 393, 440-442 (1998). (Pubitemid 28292183)
11. Szabó, G.& Fáth G. Evolutionary games on graphs. Phys. Rep. 446, 97-216 (2007).
12. Castellano, C., Fortunato, S. & Loreto, V. Statistical physics of social dynamics. Rev. Mod. Phys. 81, 591 (2009).
13. Roca, C. P., Cuesta, J. A. & Sánchez, A. Evolutionary game theory: temporal and spatial effects beyond replicator dynamics. Physics of Life Reviews 6, 208-249 (2009).
14. Arenas, A.,Díaz-Guilera, A., Kurths, J., Moreno, Y.& Zhou,C. Synchronization in complex networks. Phys. Rep. 469, 93-153 (2008).
15. Dorogovtsev, S. N., Goltsev, A. V. & Mendes, J. F. F. Critical phenomena in complex networks. Rev Mod. Phys. 80, 1275 (2008).
16. Mülken, O. & Blumen, A. Continuous-time quantum walks: Models for coherent transport on complex networks. Phys. Rep 502, 37-87 (2011).
17. Kempe, J. Quantum random walks - an introductory overview. Contemporary Physics 44, 307-327 (2003). (Pubitemid 36937887)
18. Kendon, V. A random walk approach to quantum algorithms. Phil. Trans. R. Soc. A 364, 3407-3422 (2006). (Pubitemid 44954199)
19. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge University Press, 2004).
20. Whitfield, J. D., Rodríguez-Rosario, C. A.& Aspuru-Guzik A. Quantum stochastic walks: A generalization of classical random walks and quantum walks. Phys. Rev. A 81, 022323 (2010).
21. Paparo, G. D. & Martín-Delgado, M. A. Google in a Quantum Network. Scientific Reports 2, 444 (2012).
22. Rivas, A. & Huelga, S. F. Open Quantum Systems. An Introduction. (Springer, 2011).
23. Blanchard, Ph. & Volchenkov, D. Introduction to Random Walks and Diffusions on Graphs and Databases. (Springer, 2011).
24. Grifoni, M. & Hänggi, P. Coherent and Incoherent Quantum Stochastic Resonance. Phys. Rev. Lett. 76, 1611-1614 (1996). (Pubitemid 126639875)
25. Huelga, S. F. & Plenio, M. B. Stochastic Resonance Phenomena in Quantum Many-Body Systems. Phys. Rev. Lett 98, 170601 (2007).
26. Collini, E.,Wong, C. Y.,Wilk, K. E., Curmi, P. M. G., Brumer, P. & Scholes, G. D. Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature. Nature 463, 644-647 (2010).
27. Plenio, M. B. & Huelga, S. F. Dephasing-assisted transport: quantum networks and biomolecules. New. J. Phys. 10, 113019 (2008).
28. Mohseni, M., Rebentrost, P., Lloyd, S. & Aspuru-Guzik, A. Environment-Assisted Quantum Walks in Photosynthetic Energy Transfer. J. Chem. Phys. 129, 174106 (2008).
29. Delvenne, J. C. & Libert, A. S. Centrality measures and thermodynamic formalism for complex networks. Phys. Rev. E 83, 046117 (2011).
30. Ulanowicz, R. E., Bondavalli, C. & Egnotovich, M. S. Network Analysis of Trophic Dynamics in South Florida Ecosystem. FY97: The Florida Bay Ecosystem, 20688-20038 (1998).
31. White, J. G., Southgate, E., Thompson, J. N. & Brenner, S. The structure of the nervous system of the nematode C. Elegans. Phil. Trans. R. Soc. London 314, 1-340 (1986).
32. Colizza, V., Pastor-Satorras, R.& Vespignani, A. Reaction-diffusion processes and metapopulation models in heterogeneous networks. Nature Physics 3, 276-282 (2007).
33. Newman, M. E. J. Finding community structure in networks using the eigenvectors of matrices. Phys. Rev. E 74, 036104 (2006).
34. Kendall, M. G. & Babington Smith, B. The Problem of m Rankings. Ann. Math. Statist. 10, 275-287 (1939).
35. Perdomo-Ortiz, A., Dickson, N., Drew-Brook, M., Rose, G. & Aspuru-Guzik, A. Finding low-energy conformations of lattice protein models by quantum annealing. Scientific Reports 2, 571 (2012).
36. Kimble, H. J. The quantum internet. Nature (London) 453, 1023 (2008).
37. Galindo, A. & Martín-Delgado, M. A. Information and computation: Classical and quantum aspects. Rev. Mod. Phys. 74, 347-423 (2002).
38. Acín, A., Cirac, J. I. & Lewenstein, M. Entanglement percolation in quantum networks. Nature Physics 3, 256-259 (2007).
39. Cuquet, M. & Calsamiglia, J. Entanglement Percolation in Quantum Complex Networks. Phys. Rev. Lett. 103, 240503 (2009).
40. Perseguers, S., Lewenstein, M., Acín, A. & Cirac, J. I. Quantum random networks Nature Physics 6, 539-543 (2010).
41. Wei, Z. W, Wang, B. H. & Han, X. P. Quantum Small-world Networks. arXiv:1111.0407.
42. Fleming, G. R.,Huelga, S. F.& Plenio, M. B. Focus on quantum effects and noise in biomolecules. New J. Phys. 13, 115002 (2011).
43. Szegedy, M. Quantum Speed-Up ofMarkov Chain Based Algorithms. Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, 32-41 (2004). (Pubitemid 40575264)
44. Spohn, H. An algebraic condition for the approach to equilibrium of and open N-level system. Lett. Math. Phys. 2, 33 (1977).
45. Garnerone, S., Zanardi, P. & Lidar, D. A. Adiabatic quantum algorithm for search engine ranking. Phys. Rev. Lett. 108, 230506 (2012).
46. Van Kampen, N. G. Stochastic processes in physics and chemistry. (North Holland, 3rd ed. 2007).