Quantum community detection via deterministic elimination

TL;DR

This paper introduces a quantum algorithm, deteQt, for large-scale community and botnet detection in complex networks, leveraging quantum state encoding and a novel readout technique to improve scalability and accuracy.

Contribution

It presents a new quantum workflow for community detection that encodes graph properties into quantum states and includes a deterministic readout method to enhance solution filtering.

Findings

Reduces sample complexity from exponential to polynomial

Enables large-scale community and botnet detection with quantum speedup

Provides a novel quantum readout technique for solution verification

Abstract

We propose a quantum algorithm for calculating the structural properties of complex networks and graphs. The corresponding protocol -- deteQt -- is designed to perform large-scale community and botnet detection, where a specific subgraph of a larger graph is identified based on its properties. We construct a workflow relying on ground state preparation of the network modularity matrix or graph Laplacian. The corresponding maximum modularity vector is encoded into a $\log(N)$-qubit register that contains community information. We develop a strategy for ``signing'' this vector via quantum signal processing, such that it closely resembles a hypergraph state, and project it onto a suitable linear combination of such states to detect botnets. As part of the workflow, and of potential independent interest, we present a readout technique that allows filtering out the incorrect solutions deterministically. This can reduce the scaling for the number of samples from exponential to polynomial. The approach serves as a building block for graph analysis with quantum speed up and enables the cybersecurity of large-scale networks.