Resolving degeneracies in Google search via quantum stochastic walks

TL;DR

This paper introduces quantum stochastic walks to enhance Google's PageRank algorithm, effectively resolving degeneracies and improving ranking accuracy without increasing convergence time.

Contribution

It presents two novel quantum walk schemes that outperform classical PageRank in resolving degeneracies and sometimes reduce convergence time.

Findings

QSW schemes resolve degeneracies better than CPR.

QSW schemes achieve similar or faster convergence.

QSW schemes produce more accurate, degeneracy-free rankings.

Abstract

The Internet is one of the most valuable technologies invented to date. Among them, Google is the most widely used search engine. The PageRank algorithm is the backbone of Google search, ranking web pages according to relevance and recency. We employ quantum stochastic walks (QSWs) to improve the classical PageRank (CPR) algorithm based on classical continuous time random walks. We implement QSW via two schemes: only incoherence and dephasing with incoherence. PageRank using QSW with only incoherence or QSW with dephasing and incoherence best resolves degeneracies that are unresolvable via CPR and with a convergence time comparable to that for CPR, which is generally the minimum. For some networks, the two QSW schemes obtain a convergence time lower than CPR and an almost degeneracy-free ranking compared to CPR.