Quantum walk based algorithm on scale free networks

Abstract

The classification of information contained in complex networks such as the WWW is a central problem in network science for its technological impact. A highly successful methodology for this purpose is Google’s PageRank algorithm. It allows to measure the importance or relevance of a web page depending on the relationship between pages and its connections, i.e, the hyperlink structure.

Finding ways to apply the advantages of quantum computers to real world computational tasks is an active research area. In this thesis, we implement a quantum gate-based algorithm that replicates the behaviour of the Quantum PageRank algorithm. We present a comprehensive analysis with the Szegedy quantum walk formalism. The implementation procedure is based in the quantum circuit model of quantum computing. Here, we review a Quantum PageRank algorithm and illustrate the main findings. We show the behaviour of the quantum PageRank algorithm using the IBM’s Q experience framework for quantum computing. We investigate the behavior of the Quantum PageRank algorithm using quantum walks by giving explicit connections with corresponding classical algorithm. We make a comparative analysis of our findings and discuss the capabilities of a quantum computing platform applied to the Quantum PageRank algorithm. Within the restrictions imposed by hardware, we implement a multiple-controlled gate using ancilla qubits and all other elements required for implementing our quantum algorithm.