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This work introduces a new equivariant quantum circuit (EQC) for learning tasks on weighted graphs, such as images, social networks, and molecules. The EQC uses both node and edge features to solve tasks such as the Traveling Salesman Problem (TSP). The EQC is an ansatz for cases where encoding node features is sufficient, and is an example of “geometric quantum learning” in the vein of the classical field of geometric deep learning. This work motivates further study of such ansatzes for quantum machine learning (QML) as they are a pre-requisite to efficiently apply quantum models on any practically relevant learning task in the near-term.
