Quantum Evolution Kernel for Node-Attributed Graphs

Manuel Padovani; Alessandra Di Pierro; Claudia Daffara

quant-phOct 27, 2026

Quantum Evolution Kernel for Node-Attributed Graphs

Authors: Manuel Padovani, Alessandra Di Pierro, Claudia Daffara

Organizations: Department of Computer Science, University of Verona, Verona, Italy

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.

Figures & tables

Figure 1: The picture shows the pipeline from the raw image to the final graph encodable onto the quantum device.

Figure 2: Bayesian optimization of the evolution parameter $t$ using the validation F1-score (80% training, 20% validation) on a 200-sample subset of the MNIST dataset. The optimal value is $t=240.1\ n\text{s}$ (highlighted). For small $t$ , the system does not generate sufficient entanglement, yielding low F1-score. For large $t$ , long excitations cause oscillations between entangled states, leading to a sharp drop.

Figure 3: Comparison of the performances of different distance metrics. Wasserstein achieves the highest accuracy. Shaded regions indicate $\pm 1$ standard deviation over 5 seeds.

Figure 4: Comparison of our quantum kernel against classical baselines. The GCN achieves the highest accuracy, while our quantum kernel performs comparably to the positional WL variant and outperforms both angle-only and featureless WL kernels. Shaded regions indicate $\pm 1$ standard deviation over 5 seeds.

Quantum Kernel Methods

Quantum kernel methods use quantum feature maps and similarity measures to learn patterns, with potential benefits for structured data and quantum systems.

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How Embeddings Shape Graph Neural Networks: Classical vs Quantum-Oriented Node Representations

Nouhaila Innan, Antonello Rosato, Alberto Marchisio, Muhammad Shafique

eBRAIN Lab, Division of Engineering, New York University Abu Dhabi (NYUAD), Abu Dhabi, UAE · Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Rome, Italy · Center for Quantum and Topological Systems (CQTS), NYUAD Research Institute, NYUAD, Abu Dhabi, UAE

Quantum Machine Learning Quantum-Inspired ML Graph Classification Graph Embedding

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Node embeddings act as the information interface for graph neural networks, yet their empirical impact is often reported under mismatched backbones, splits, and training budgets. This paper provides a controlled benchmark of embedding choices for graph classification, comparing classical baselines with quantum-oriented node representations under a unified pipeline. We evaluate two classical baselines alongside quantum-oriented alternatives, including a circuit-defined variational embedding and quantum-inspired embeddings computed via graph operators and linear-algebraic constructions. All variants are trained and tested with the same backbone, stratified splits, identical optimization and early stopping, and consistent metrics. Experiments on five different TU datasets and on QM9 converted to classification via target binning show clear dataset dependence: quantum-oriented embeddings yield the most consistent gains on structure-driven benchmarks, while social graphs with limited node attributes remain well served by classical baselines. The study highlights practical trade-offs between inductive bias, trainability, and stability under a fixed training budget, and offers a reproducible reference point for selecting quantum-oriented embeddings in graph learning.

Abstract

Quantum Kernel Methods

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