Quantum Machine Learning Models for High-Dimensional Data Classification

Abstract

High-dimensional data classification -- where feature dimensionality p exceeds or approaches sample size n -- is ubiquitous in genomics, medical imaging, spectroscopy, and financial risk modelling. Quantum machine learning (QML) offers potential advantages for high-dimensional classification through quantum feature maps that implicitly operate in exponentially large Hilbert spaces, potentially capturing feature correlations inaccessible to polynomial-complexity classical kernel methods. However, identifying when and why QML provides genuine classification advantage over classical methods for high-dimensional data remains an open question, complicated by the QCCB finding (Popescu and Petrov, 2024) that quantum kernel advantages are dataset-specific. This paper proposes the Quantum High-Dimensional Classification (QHDC) framework, investigating QML advantage for five high-dimensional classification problems across three quantum model families: quantum kernel SVM (QKSVM) using parameterised ZZFeatureMap and IQPFeatureMap; quantum neural network classifier (QNNC) using LSAD-structured ansatz (Silva et al., 2024); and quantum-classical transfer learning (QCTL) using a quantum feature extractor with classical fine-tuning head. QHDC is evaluated on five datasets: genomic variant classification (p=8,442, n=284), hyperspectral remote sensing (p=200, n=10,249), drug-protein binding prediction (p=1,024, n=4,284), financial credit risk (p=84, n=28,400), and quantum chemistry energy prediction (p=48, n=2,840). QKSVM achieves the highest QML performance: AUC improvement over classical RBF-SVM of 2.4-8.4pp across five datasets, with largest gains on quantum chemistry (8.4pp) and drug- protein (6.4pp) datasets. QNNC underperforms classical baselines on three of five datasets due to barren plateau limitations at high dimensionality. QCTL achieves 4.4pp improvement on genomic classification.