Quantum Simplicial Neural Networks

2025-01-09

AI Summary

Existing graph neural networks (GNNs) model only pairwise relationships and thus struggle to capture higher-order topological interactions; quantum neural networks (QNNs) and topological deep learning (TDL) remain largely disconnected, limiting progress in learning higher-order relational structures inherent in complex mathematical objects. Method: We propose the first quantum topological deep learning model tailored for simplicial complexes—integrating QNNs with simplicial TDL for the first time. Our approach introduces an Ising-inspired quantum simplicial layer that encodes higher-order relations into quantum states and enables differentiable learning via variational quantum circuits. Contribution/Results: The model jointly leverages topological expressivity and quantum parallelism. On synthetic classification tasks, it achieves significantly higher accuracy and faster inference than classical simplicial TDL baselines, empirically validating the effectiveness and novelty of quantum–topological co-modeling for higher-order relational learning.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Web data generation and simulation

Abstract

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.

Problem

• Graph Neural Networks
• Quantum Neural Networks
• Topological Deep Learning

Innovation

• Quantum Simplicial Neural Networks
• Topological Deep Learning
• Quantum Computing