  An important method for search engine result ranking works by finding the
principal eigenvector of the "Google matrix." Recently, a quantum algorithm for
preparing this eigenvector and evidence of an exponential speedup for some
scale-free networks were presented. 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. For a sample of graphs
with degree distributions that more closely resemble the Web than in previous
work, the proposed algorithm for eigenvector preparation does not appear to run
exponentially faster than the classical case.
