Hybrid Quantum or Purely Classical? Assessing the Utility of Quantum Feature Embeddings

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Background As graph datasets—including social networks, supply chains, and bioinformatics data—grow in size and complexity, researchers are driven to search for solutions enhancing model efficiency and speed. One avenue that may provide a solution is Quantum Graph Learning (QGL), a subfield of Quantum Machine Learning (QML) that applies machine learning inspired or powered by quantum computing to graph learning tasks. Methods We reevaluate Quantum Feature Embeddings (QFE), a QGL methodology published by Xu et al. earlier this year. QFE uses Variational Quantum Circuits to preprocess node features and then sends them to a classical Graph Neural Network (GNN), with the goal of increasing performance and/or decreasing total model size. Xu et al. evaluated this methodology by comparing its performance with the performance of variously-sized classical models on the benchmark datasets PROTEINS and ENZYMES, and they report success. Our core methodology and learning task remain unchanged. However, we have made several changes to the experimental design that enhance the rigor of the study: 1) we include the testing of models with no embedder; 2) we conduct a thorough hyperparameter search using a state-of-the-art optimization algorithm; and 3) we conduct stratified five-fold cross-validation, which mitigates the bias produced by our small datasets and provides multiple test statistics from which we can calculate a confidence interval. Results We produce classical models that perform comparably to QFE and significantly outperform the small classical models used in Xu et al.’s comparison. Notably, many of our classical models achieve this using fewer parameters than the QFE models we trained. Xu et al. do not report their total model sizes. Conclusion Our study sheds doubt on the efficacy of QFE by demonstrating that small, well-tuned classical models can perform just as well as QFE, highlighting the importance of hyperparameter tuning and rigorous experimental design.