Neutral-atom quantum features as complementary structural encodings for graph learning
Structural descriptors provide graph neural networks (GNNs) with positional and topological inductive biases. However, widely used classical encodings based on random walks or Laplacian spectra emphasize specific structural statistics of a graph, leaving room for alternative descriptors. Neutral-atom quantum processing units (QPUs) can realize graph-dependent Rydberg Hamiltonians, allowing graph topology to be probed through dynamical correlation measurements. In this work, we use these measurements as quantum graph features (QGFs), providing a complementary, hardware-derived family of structural encoding that is not accurately described by classical features derived from Laplacian and adjacency matrices, even when supplemented with an extended set of random-walk, geometric descriptors and classical physical models. By appropriately selecting the quench parameters of the Hamiltonian, we access two characteristic correlation regimes with distinct structural signatures: antiferromagnetic-like and ferromagnetic-like. On an intrinsic information benchmark of 15 topological and spectral probing tasks, quantum and hybrid quantum-classical features match or surpass classical descriptors on local topological properties. When supplied to message-passing, attention, and graph-transformer backbones, hybrid quantum-classical features yield improvements that are within cross-fold noise on most cells but sign-consistent across architectures. When comparing noiseless, shot-sampled emulation-derived quantum features with a neutral-atom QPU implementation, the downstream hybrid results with compressed hardware features match their emulated counterparts within $0.01$ F$_1$ on all backbones. On a synthetic family of ladder graphs, QGFs distinguish two specific classes, outperforming the strongest classical structural descriptors by a margin exceeding cross-fold variability.