Graph Neural Networks (GNNs) excel at learning from graph-structured data but are limited to modeling pairwise interactions, insufficient for capturing higher-order relationships present in many real-world systems. Topological Deep Learning (TDL) has allowed for systematic modeling of hierarchical higher-order interactions by relying on combinatorial topological spaces such as simplicial complexes. In parallel, Quantum Neural Networks (QNNs) have been introduced to leverage quantum mechanics for enhanced computational and learning power. In this work, we present the first Quantum Topological Deep Learning Model: Quantum Simplicial Networks (QSNs), being QNNs operating on simplicial complexes. QSNs are a stack of Quantum Simplicial Layers, which are inspired by the Ising model to encode higher-order structures into quantum states. Experiments on synthetic classification tasks show that QSNs can outperform classical simplicial TDL models in accuracy and efficiency, demonstrating the potential of combining quantum computing with TDL for processing data on combinatorial topological spaces.
Graph Neural Networks (GNNs) excel at learning from graph-structured data but are limited to modeling pairwise interactions, insufficient for capturing higher-order relationships present in many real-world systems. Topological Deep Learning (TDL) has allowed for systematic modeling of hierarchical higher-order interactions by relying on combinatorial topological spaces such as simplicial complexes. In parallel, Quantum Neural Networks (QNNs) have been introduced to leverage quantum mechanics for enhanced computational and learning power. In this work, we present the first Quantum Topological Deep Learning Model: Quantum Simplicial Networks (QSNs), being QNNs operating on simplicial complexes. QSNs are a stack of Quantum Simplicial Layers, which are inspired by the Ising model to encode higher-order structures into quantum states. Experiments on synthetic classification tasks show that QSNs can outperform classical simplicial TDL models in accuracy and efficiency, demonstrating the potential of combining quantum computing with TDL for processing data on combinatorial topological spaces.
This paper presents the concept of quantum neural networks (QNN), a new framework that combines quantum computing with topological data analysis to process data defined on simplicial complexes. Based on the fundamentals of topological signal processing and variational quantum circuits, QNN aim to use the structure of simplicial complexes to perform efficient calculations and extract higher-order relational patterns from data. The proposed architecture uses quantum layers (QL), which map interactions between simplices into quantum circuits, providing both in-order and inter-order interactions. The paper describes two QL variants: basic and schematic, providing flexibility for applications with varying complexity. In addition, the paper explores the theoretical foundations of simplicial complexes, quantum neural networks, and the interaction between classical and quantum approaches in data encoding, state evolution and optimization. By leveraging quantum algorithms and eliminating current hardware limitations, QNN promise scalability and enhanced performance for applications in optimization, numerical simulation, and complex systems modeling. This research demonstrates the potential of QNN to advance the field of quantum machine learning, paving the way for future developments of quantum algorithms and their practical applications.
Representing and learning from graphs is essential for developing effective machine learning models tailored to non-Euclidean data. While Graph Neural Networks (GNNs) strive to address the challenges posed by complex, high-dimensional graph data, Quantum Neural Networks (QNNs) present a compelling alternative due to their potential for quantum parallelism. However, much of the current QNN research tends to overlook the vital connection between quantum state encoding and graph structures, which limits the full exploitation of quantum computational advantages. To address these challenges, this paper introduces a quantum graph Hamiltonian neural network (QGHNN) to enhance graph representation and learning on noisy intermediate-scale quantum computers. Concretely, a quantum graph Hamiltonian learning method (QGHL) is first created by mapping graphs to the Hamiltonian of the topological quantum system. Then, QGHNN based on QGHL is presented, which trains parameters by minimizing the loss function and uses the gradient descent method to learn the graph. Experiments on the PennyLane quantum platform reveal that QGHNN outperforms all assessment metrics, achieving the lowest mean squared error of0.004and the maximum cosine similarity of99.8%, which shows that QGHNN not only excels in representing and learning graph information, but it also has high robustness ability. QGHNN can reduce the impact of quantum channel noise and has significant potential application in future research of quantum knowledge graphs and recommendation systems.
This paper introduces a novel type of Graph Neural Network (GNN) called Topological Quantum Graph Neural Networks (TQNN). TQNN leverages the inherent topological structure of graphs and the strengths of Graph Neural Networks (GNNs) to enhance model recognition and prediction capabilities. We propose a new architecture that utilizes a modified graph representation and a quantum-inspired transformation to improve the network's ability to capture complex relationships and patterns within data. The core mechanism involves incorporating a quantum-inspired transformation into the graph representation, which enables the network to represent and process information in a fundamentally different way, leading to significant improvements in performance across various tasks. This work presents a new approach to GNNs that addresses limitations of existing methods, offering a promising pathway for enhanced machine learning performance.
This paper introduces a novel approach to graph neural networks (GNNs) – the 'Quantum Adaptive Graph Neural Network' – leveraging quantum self-adaptation to enhance both expressiveness and computational efficiency. Traditional GNNs often struggle with the inherent complexities of graph data and require substantial computational resources. We propose a new architecture that employs quantum mechanics to simulate graph structures, allowing the network to learn more robust representations. This approach, dubbed Quantum Adaptive Graph Neural Network (QAGNN), utilizes quantum machine learning algorithms to improve the network's ability to capture intricate relationships within the graph. The paper details the core mechanism, its mathematical foundations, and preliminary experimental results demonstrating significant improvements in various graph classification tasks compared to traditional GNNs. We present a comprehensive analysis of the QAGNN's performance and discuss potential future research directions.
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.
Quantum Neural Networks (QNNs) represent a novel paradigm in neural network architecture, leveraging quantum mechanics to potentially surpass classical neural networks in terms of learning capabilities and expressiveness. This paper investigates the learning of topological layers within QNNs, proposing a dynamic structure optimization method that systematically evolves the network's representation to achieve enhanced model performance. We explore a framework where the network's topology, represented as a dynamic structure, is continuously refined through a series of learning steps. The core mechanism focuses on optimizing the network's representation by manipulating the underlying topology, ultimately leading to improved generalization and robustness. This research introduces a novel approach to learning topological layers, offering a potential pathway toward more sophisticated and adaptable neural network models.