Power law scaling for the adiabatic algorithm for search engine ranking

TL;DR

This paper investigates the quantum algorithm for search engine ranking, revealing that its runtime advantage over classical methods depends on specific graph features and may not be exponentially faster for Web-like networks.

Contribution

The study demonstrates that the quantum speedup for eigenvector computation is not universal and depends on graph properties beyond degree distribution.

Findings

Quantum algorithm's runtime varies with graph features.

No exponential speedup for Web-like networks.

Degree distribution alone does not determine quantum advantage.

Abstract

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.