Quantum Motif Clustering

TL;DR

This paper introduces three quantum algorithms for motif-based graph clustering, achieving significant speedups over classical methods, and analyzes their effectiveness and limitations in various graph settings.

Contribution

It presents novel quantum algorithms for motif clustering, utilizing Grover search and approximate counting, and extends theoretical understanding of motif clustering with multiple anchor nodes.

Findings

Quantum algorithms achieve square-root speedups over classical methods.

Spectral clustering performance remains stable with constant errors in edge weights.

Analysis clarifies the capabilities and limitations of motif clustering with multiple anchor nodes.

Abstract

We present three quantum algorithms for clustering graphs based on higher-order patterns, known as motif clustering. One uses a straightforward application of Grover search, the other two make use of quantum approximate counting, and all of them obtain square-root like speedups over the fastest classical algorithms in various settings. In order to use approximate counting in the context of clustering, we show that for general weighted graphs the performance of spectral clustering is mostly left unchanged by the presence of constant (relative) errors on the edge weights. Finally, we extend the original analysis of motif clustering in order to better understand the role of multiple `anchor nodes' in motifs and the types of relationships that this method of clustering can and cannot capture.