Topological network analysis using a programmable photonic quantum processor

• URL: http://arxiv.org/abs/2507.08157v2
• Date: Mon, 14 Jul 2025 14:59:25 GMT
• Title: Topological network analysis using a programmable photonic quantum processor
• Authors: Shang Yu, Jinzhao Sun, Zhenghao Li, Ewan Mer, Yazeed K Alwehaibi, Oscar Scholin, Gerard J. Machado, Kuan-Cheng Chen, Aonan Zhang, Raj B Patel, Ying Dong, Ian A. Walmsley, Vlatko Vedral, Ginestra Bianconi,
• Abstract summary: We develop a universal programmable quantum processor that enables the encoding of arbitrary complex-weight networks.<n>We show how this quantum approach can identify weighted $k$-cliques and estimate Betti numbers.<n>These findings showcase how photonic quantum computing can be applied to analyse the topological characteristics of real-world networks.
• Score: 3.0018652145221614
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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