Comparing classical and quantum PageRanks

TL;DR

This paper compares classical and quantum PageRank algorithms, introducing new quantum measures, and demonstrates their effectiveness in distinguishing network types and highlighting important nodes.

Contribution

It presents a comparative analysis of quantum PageRank algorithms, introduces an alternative quantum measure, and evaluates their performance on various network types.

Findings

Quantum PageRank distinguishes network types effectively.

Quantum measures better highlight secondary hubs.

Evolution time does not scale significantly with network size.

Abstract

Following recent developments in quantum PageRanking, we present a comparative analysis of discrete-time and continuous-time quantum-walk-based PageRank algorithms. For the discrete-time case, we introduce an alternative PageRank measure based on the maximum probabilities achieved by the walker on the nodes. We demonstrate that the required time of evolution does not scale significantly with increasing network size. We affirm that all three quantum PageRank measures considered here distinguish clearly between outerplanar hierarchical, scale-free, and Erd\"os-R\'enyi network types. Relative to classical PageRank and to different extents, the quantum measures better highlight secondary hubs and resolve ranking degeneracy among peripheral nodes for the networks we studied in this paper.