Quantum Evolution Kernel for Node-Attributed Graphs

Abstract

We present a novel approach to embed node-attributed graphs onto neutral-atom quantum computers, and propose an application to digit recognition. Our approach extends PASQAL's quantum evolution kernel (QEK) by introducing a node-level feature encoding based on three-level quantum states. To this purpose, we present a prototype showing how the resulting embedding can be leveraged to extract correlation-based information for classification tasks. The entire quantum process is simulated using Pasqal's Pulser library, which inevitably imposes constraints on the size of the experimental datasets. We compare our method with classical baselines to evaluate its potential. We show that, for the digit recognition task, our method achieves a higher mean accuracy than the more commonly used Jensen-Shannon distance-based methods by utilizing the Wasserstein distance.

The paper studies how to incorporate continuous node attributes into neutral-atom quantum evolution kernels for graph classification. It extends a Rydberg-based graph embedding by using local Raman pulses to encode feature pairs in two hyperfine ground states, followed by interaction-driven evolution involving a third, Rydberg state. Atom positions encode graph connectivity, while the hyperfine populations modulate participation in Rydberg excitation. Measurements yield graph-level distributions of excitation fractions and pairwise correlations. Exponentiated one-dimensional Wasserstein-$1$ distances define positive-semidefinite kernels, combined through optimized weights and used in support-vector classification. The construction is evaluated entirely through Pulser simulations on MNIST images converted into graphs with four node features: coordinates and two local angular descriptors. Simulations restrict graphs to at most nine nodes and use 500 shots per circuit. Evolution time is optimized on 200 training examples, selecting $t=240.1\,\mathrm{ns}$. Classification uses varying training sizes, five random seeds, and a fixed balanced test set of 150 examples. Wasserstein kernels achieve higher mean accuracy than the tested Jensen–Shannon, Hellinger, and Euclidean alternatives; including node features improves performance over the featureless quantum kernel. The resulting model performs comparably to a positional Weisfeiler–Lehman kernel but below the combined-feature WL kernel and a graph convolutional network. The stated limitations include small simulated datasets, graph filtering and geometric hardware constraints, and classical $O(|V|^2)$ correlation post-processing. No hardware experiment or computational or learning advantage is demonstrated; establishing such an advantage remains open.