Extending Graph Transformers with Quantum Computed Aggregation

Recently, efforts have been made in the community to design new Graph Neural Networks (GNN), as limitations of Message Passing Neural Networks became more apparent. This led to the appearance of Graph Transformers using global graph features such as Laplacian Eigenmaps. In our paper, we introduce a GNN architecture where the aggregation weights are computed using the long-range correlations of a quantum system. These correlations are generated by translating the graph topology into the interactions of a set of qubits in a quantum computer. This work was inspired by the recent development of quantum processing units which enables the computation of a new family of global graph features that would be otherwise out of reach for classical hardware. We give some theoretical insights about the potential benefits of this approach, and benchmark our algorithm on standard datasets. Although not being adapted to all datasets, our model performs similarly to standard GNN architectures, and paves a promising future for quantum enhanced GNNs. Graph machine learning is an expanding field of research with applications in chemistry (Gilmer et al., 2017), biology (Zitnik et al., 2018), drug design (Konaklieva, 2014), social networks (Scott, 2011), computer vision (Harchaoui & Bach, 2007), science (Sanchez-Gonzalez et al., 2020). In the past few years, much effort has been put into the design of Graph Neural Networks (GNN) (Hamilton). The goal is to learn a vector representation of the nodes while incorporating information about the graph. The learned information is then processed according to the original problem.