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Astronomy and Computing

Exploring the potential of Quantum Graph Neural Networks in analyzing Large-Scale Structure of Universe

Farida Farsian, Francesco Schillirò, Andrea A. Bulgarelli, C. Burigana, V. F. Cardone, Luca Cappelli, Irene Graziotti, Massimo Meneghetti, Giuseppe Murante, N. Parmiggiani, Alessandro Rizzo, Giuseppe Sarracino, R. Scaramella, V. Testa, T. Trombetti

Published Mar 5, 2026• 1 citation
Publisher

Abstract

The large-scale structure (LSS) of the Universe, characterized by the distribution of clusters, filaments, walls, and voids, encodes fundamental information about cosmology and structure formation. Standard cosmological analyses, based on abundances as well as two-point and higher-order correlation functions, have been widely used to extract information from LSS. While powerful, these techniques can only access a subset of the full information content, leaving much of the encoded structure underexploited. This motivates the use of more flexible approaches capable of learning directly from the raw, graph-like nature of the cosmic web without relying on strong compression or dimensionality reduction. Recent advances in machine learning, particularly graph neural networks (GNNs), provide a natural framework for this task by capturing the non-Euclidean connectivity of cosmic structures. Building on these developments, recent progress in quantum machine learning (QML) offers an intriguing opportunity to further enhance representation power through quantum-enhanced models. In this work, we investigate the potential of quantum graph neural networks (QGNNs) as an alternative computational framework for analyzing LSS, focusing on structure identification and classification with an emphasis on distinguishing clusters and voids. Leveraging the hybrid quantum–classical paradigm implemented in PennyLane, we construct variational quantum circuits to encode graph representations of cosmological data and compare their performance against state-of-the-art classical GNNs. Our study evaluates the accuracy and expressivity of QGNNs relative to classical models, with particular attention to their ability to capture complex correlations in sparse, high-dimensional astrophysical datasets. Preliminary results indicate that QGNNs achieve comparable classification performance, while highlighting both the opportunities and current limitations of quantum-enhanced approaches in cosmological applications.

DOI
10.1016/j.ascom.2026.101095

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The large-scale structure (LSS) of the Universe, characterized by the distribution of clusters, filaments, walls, and voids, encodes fundamental information about cosmology and structure formation. Standard cosmological analyses, based on abundances as well as two-point and higher-order correlation functions, have been widely used to extract information from LSS. While powerful, these techniques can only access a subset of the full information content, leaving much of the encoded structure underexploited. This motivates the use of more flexible approaches capable of learning directly from the raw, graph-like nature of the cosmic web without relying on strong compression or dimensionality reduction. Recent advances in machine learning, particularly graph neural networks (GNNs), provide a natural framework for this task by capturing the non-Euclidean connectivity of cosmic structures. Building on these developments, recent progress in quantum machine learning (QML) offers an intriguing opportunity to further enhance representation power through quantum-enhanced models. In this work, we investigate the potential of quantum graph neural networks (QGNNs) as an alternative computational framework for analyzing LSS, focusing on structure identification and classification with an emphasis on distinguishing clusters and voids. Leveraging the hybrid quantum–classical paradigm implemented in PennyLane, we construct variational quantum circuits to encode graph representations of cosmological data and compare their performance against state-of-the-art classical GNNs. Our study evaluates the accuracy and expressivity of QGNNs relative to classical models, with particular attention to their ability to capture complex correlations in sparse, high-dimensional astrophysical datasets. Preliminary results indicate that QGNNs achieve comparable classification performance, while highlighting both the opportunities and current limitations of quantum-enhanced approaches in cosmological applications.
Graph Neural Networks (GNNs) are now one of the key tools to model relational and non-Euclidean data in multiagent systems, infrastructure networks and even molecular modeling applications. Nevertheless, in very dense or noisy graph topologies, classical message-passing architectures may experience scalability and representational degeneration, especially due to over-smoothing and insufficient higher-order dependency information. The recent developments in quantum machine learning indicate that hybrid quantum-classical models can also provide an alternative feature representation by projecting relational data to parameterized quantum circuits. This article presents a Quantum-Enhanced Graph Neural Network (QGNN) architecture that extends variational quantum circuits with graph learning pipelines, based on classical learning. Parameters are represented as parameterized qubits, and relational dependencies are represented as structured entanglement mappings. We benchmark the regimes where quantum-enhanced relational encoding proves to be more robust and stable through the swarm coordination, molecular property prediction, and financial transaction network. We also elaborate on the issue of scalability, hardware issues, and practical aspects of near-term hybrid implementations and give a critical view of the changing role of quantum methods in computational intelligence systems.
Graph Neural Networks (GNNs) are now one of the key tools to model relational and non-Euclidean data in multiagent systems, infrastructure networks and even molecular modeling applications. Nevertheless, in very dense or noisy graph topologies, classical message-passing architectures may experience scalability and representational degeneration, especially due to over-smoothing and insufficient higher-order dependency information. The recent developments in quantum machine learning indicate that hybrid quantum-classical models can also provide an alternative feature representation by projecting relational data to parameterized quantum circuits. This article presents a Quantum-Enhanced Graph Neural Network (QGNN) architecture that extends variational quantum circuits with graph learning pipelines, based on classical learning. Parameters are represented as parameterized qubits, and relational dependencies are represented as structured entanglement mappings. We benchmark the regimes where quantum-enhanced relational encoding proves to be more robust and stable through the swarm coordination, molecular property prediction, and financial transaction network. We also elaborate on the issue of scalability, hardware issues, and practical aspects of near-term hybrid implementations and give a critical view of the changing role of quantum methods in computational intelligence systems.
Quantum computing has been a prominent research area for decades, inspiring transformative fields such as quantum simulation, quantum teleportation, and quantum machine learning (QML), which are undergoing rapid development. Within QML, hybrid classical-quantum algorithms like Quantum Neural Networks (QNNs) and Variational Quantum Classifiers (VQCs) have shown promise in leveraging quantum circuits and classical optimizers to classify classical data efficiently. Simultaneously, classical machine learning has made significant strides in graph classification, employing Graph Neural Networks (GNNs) to analyze systems ranging from large-scale structures like the Large Hadron Collider to molecular and biological systems like proteins and DNA. Combining the advancements in quantum computing and graph classification presents a unique opportunity to develop quantum algorithms capable of extracting features from graphs and performing their classification effectively. In this paper, we propose a novel quantum encoding framework for graph classification using VQCs. Unlike existing approaches such as PCA-VQC, which rely on dimensionality reduction techniques like Principal Component Analysis (PCA) and may lead to information loss, our method preserves the integrity of graph data. Furthermore, our encoding approach is optimized for Noise-Intermediate Scale Quantum (NISQ) devices, requiring a limited number of qubits while achieving comparable or superior classification performance to PCA-VQC. By constructing slightly more complex circuits tailored for graph encoding, we demonstrate that VQCs can effectively classify graphs within the constraints of current quantum hardware.
Graph Neural Networks (GNNs) are powerful machine learning models that excel at analyzing structured data represented as graphs, demonstrating remarkable performance in applications like social network analysis and recommendation systems. However, classical GNNs face scalability challenges when dealing with large-scale graphs. This paper proposes frameworks for implementing GNNs on quantum computers to potentially address the challenges. We devise quantum algorithms corresponding to the three fundamental types of classical GNNs: Graph Convolutional Networks, Graph Attention Networks, and Message-Passing GNNs. A complexity analysis of our quantum implementation of the Simplified Graph Convolutional (SGC) Network shows potential quantum advantages over its classical counterpart, with significant improvements in time and space complexities. Our complexities can have trade-offs between the two: when optimizing for minimal circuit depth, our quantum SGC achieves logarithmic time complexity in the input sizes (albeit at the cost of linear space complexity). When optimizing for minimal qubit usage, the quantum SGC exhibits space complexity logarithmic in the input sizes, offering an exponential reduction compared to classical SGCs, while still maintaining better time complexity. These results suggest our Quantum GNN frameworks could efficiently process large-scale graphs. This work paves the way for implementing more advanced Graph Neural Network models on quantum computers, opening new possibilities in quantum machine learning for analyzing graph-structured data.
Quantum computing offers a promising avenue to reduce growing machine learning model complexity as required in large language models and simulation models for weather forecasts, financial forecasts, or engineering. Graph neural networks are a particular class of machine learning models that have garnered much attention for their ability to deal well with structured data. We investigate how to enhance existing GNNs and find through the inductive bias that quantum circuits are used best to encode node features. The proposed Quantum Feature Embeddings (QFEs) turn raw input features into quantum states, enabling non-linear and entangled representations. In particular, QFEs provide normalized, non-redundant weight matrices in an exponentially larger feature space and require much fewer qubits than fully quantum graph neural networks. On standard graph benchmark datasets, we showcase that for the same parameter count QFEs perform better than their classical counterpart, and are able to match the performance of an exponentially larger model. Finally, we study the potential benefit of using a hybrid quantum graph neural network over a classic alternative on a concrete use case, laser cutting. We find that the proposed model has the performance and thus the near-term potential to uplift these business applications.
Quantum computing offers a promising avenue to reduce growing machine learning model complexity as required in large language models and simulation models for weather forecasts, financial forecasts, or engineering.Graph neural networks are a particular class of machine learning models that have garnered much attention for their ability to deal well with structured data.We investigate how to enhance existing GNNs and find through the inductive bias that quantum circuits are used best to encode node features.The proposed Quantum Feature Embeddings (QFEs) turn raw input features into quantum states, enabling non-linear and entangled representations.In particular, QFEs provide normalized, non-redundant weight matrices in an exponentially larger feature space and require much fewer qubits than fully quantum graph neural networks.On standard graph benchmark datasets, we showcase that for the same parameter count QFEs perform better than their classical counterpart, and are able to match the performance of an exponentially larger model.Finally, we study the potential benefit of using a hybrid quantum graph neural network over a classic alternative on a concrete use case, laser cutting.We find that the proposed model has the performance and thus the near-term potential to uplift these business applications.