Topological network analysis using a programmable photonic quantum processor

TL;DR

This paper introduces a programmable photonic quantum processor that can analyze complex network topologies by identifying structures like $k$-cliques and Betti numbers, revealing topological phase transitions and percolation phenomena.

Contribution

It presents a novel quantum computing platform capable of directly uncovering topological features in complex networks using Gaussian boson sampling.

Findings

Successfully identified weighted $k$-cliques in networks

Estimated Betti numbers from sampling results

Observed topological phase transitions and clique percolation

Abstract

Understanding topological features in networks is crucial for unravelling complex phenomena across fields such as neuroscience, condensed matter, and high-energy physics. However, identifying higher-order topological structures -- such as $k$-cliques, fundamental building blocks of complex networks -- remains a significant challenge. Here we develop a universal programmable photonic quantum processor that enables the encoding of arbitrary complex-weight networks, providing a direct pathway to uncovering their topological structures. We demonstrate how this quantum approach can identify weighted $k$-cliques and estimate Betti numbers by leveraging the Gaussian boson sampling algorithm's ability to preferentially select high-weight, dense subgraphs. The unique capabilities of our programmable quantum processor allow us to observe topological phase transitions and identify clique percolation phenomena directly from the entropy of the sampling results. These findings showcase how photonic quantum computing can be applied to analyse the topological characteristics of real-world complex networks, opening new possibilities for quantum-enhanced data analysis.