Powerlaw scaling for the adiabatic algorithm for searchengine ranking
Abstract
An important method for search engine result ranking works by finding the principal eigenvector of the “Google matrix.” Recently, a quantum algorithm for generating this eigenvector as a quantum state was presented, with evidence of an exponential speedup of this process for some scalefree networks. Here we show that the run time depends on features of the graphs other than the degree distribution, and can be altered sufficiently to rule out a general exponential speedup. According to our simulations, for a sample of graphs with degree distributions that are scalefree, with parameters thought to closely resemble the Web, the proposed algorithm for eigenvector preparation does not appear to run exponentially faster than the classical case.
 Publication:

Physical Review A
 Pub Date:
 September 2013
 DOI:
 10.1103/PhysRevA.88.032307
 arXiv:
 arXiv:1211.2248
 Bibcode:
 2013PhRvA..88c2307F
 Keywords:

 03.67.Ac;
 03.67.Lx;
 89.20.Hh;
 Quantum algorithms protocols and simulations;
 Quantum computation;
 World Wide Web Internet;
 Quantum Physics;
 Physics  Physics and Society
 EPrint:
 6 pages, 4 figures