标题： 量子单纯形神经网络 显示英文标题

标题： Quantum Simplicial Neural Networks

摘要： 图神经网络（GNNs）在从图结构数据中学习方面表现出色，但仅限于建模成对交互，这对于捕捉许多现实系统中存在的高阶关系是不够的。 拓扑深度学习（TDL）通过依赖组合拓扑空间（如单纯复形）实现了对分层高阶交互的系统建模。 同时，量子神经网络（QNNs）被引入以利用量子力学来增强计算和学习能力。 在这项工作中，我们提出了第一个量子拓扑深度学习模型： 量子单纯网络（QSNs），即在单纯复形上运行的QNNs。 QSNs是由量子单纯层组成的堆栈，这些层受到伊辛模型的启发，将高阶结构编码到量子态中。 在合成分类任务上的实验表明，QSNs在准确性和效率方面可以超越经典的单纯TDL模型，证明了将量子计算与TDL结合处理组合拓扑空间数据的潜力。 显示英文摘要

摘要： 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.