  This paper introduces a novel architecture for Quantum Graph Neural Networks,
which is significantly different from previous approaches found in the
literature. The proposed approach produces similar outcomes with respect to
previous models but with fewer parameters, resulting in an extremely
interpretable architecture rooted in the underlying physics of the problem. The
architectural novelties arise from three pivotal aspects. Firstly, we employ an
embedding updating method that is analogous to classical Graph Neural Networks,
therefore bridging the classical-quantum gap. Secondly, each layer is devoted
to capturing interactions of distinct orders, aligning with the physical
properties of the system. Lastly, we harness SWAP gates to emulate the
problem's inherent symmetry, a novel strategy not found currently in the
literature. The obtained results in the considered experiments are encouraging
to lay the foundation for continued research in this field.
