Paper ID: 2501.05558 • Published Jan 9, 2025
Quantum Simplicial Neural Networks
Simone Piperno, Claudio Battiloro, Andrea Ceschini, Francesca Dominici, Paolo Di Lorenzo, Massimo Panella
TL;DR
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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.