Google In A Photonic Lattice

TL;DR

This paper proposes implementing Quantum PageRank using a stochastic quantum walk of correlated photons in a photonic lattice, evolving via the Lindblad master equation to determine page rankings.

Contribution

It introduces a novel photonic lattice-based method for Quantum PageRank using correlated photons and Lindblad evolution, advancing quantum algorithms for network analysis.

Findings

Demonstrates feasibility of quantum walk-based PageRank in photonic systems

Shows the stationary state encodes page rankings effectively

Provides a framework for experimental realization of quantum network algorithms

Abstract

The quantum version of Google PageRank has recently been investigated by various groups and shown to be quadratically faster in time than the classical PageRank algorithm. In this paper we propose the implementation of Quantum PageRank by a stochastic quantum walk of correlated photons in a photonic waveguide lattice, where we allow the density matrix to evolve according to the Lindblad-Kossakowski master equation. This yields a stationary state, the diagonal of whose density matrix gives the page ranking.