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.
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.
Quantum Machine Learning (QML) has emerged as a paradigm that combines the computational advantages of quantum computing with the predictive capabilities of machine learning to address complex data classification problems. As data dimensionality increases rapidly and classical learning algorithms face scalability constraints, QML leverages quantum parallelism, entanglement, and high-dimensional Hilbert space representations to enhance learning performance. This paper reviews and analyses advanced QML algorithms, including Quantum Support Vector Machines (QSVM), Variational Quantum Circuits (VQC), Quantum Neural Networks (QNN), and Quantum Kernel Estimation, for optimizing both binary and multi-class classification tasks under high-complexity conditions. The proposed QML framework is evaluated on benchmark datasets like MNIST, the Breast Cancer Wisconsin (BCW) dataset, and synthetic nonlinear datasets, and is compared against classical machine learning baselines, including Support Vector Machines (SVM), Random Forests (RF), and Deep Neural Networks (DNN). The results demonstrate notable improvements in classification accuracy (up to 96.8%), decision margins, and computational efficiency in quantum-suitable data regimes, while also highlighting current limitations related to noise, circuit depth, and hardware constraints. Overall, the study presents a unified QML framework, theoretical formulations, and experimental evaluations that illustrate the potential of quantum algorithms for next-generation classification tasks.
Quantum Machine Learning (QML) has emerged as a promising paradigm for addressing increasing computational and representational demands in materials informatics. While classical models such as Support Vector Machines (SVM) achieve strong predictive performance, they often struggle to capture complex, highly correlated interactions in high-dimensional materials data. QML addresses this challenge by leveraging quantum-mechanical principles to construct expressive feature embeddings, where prospective quantum advantage lies in generating feature spaces that are difficult to approximate classically. In this study, 1,000 crystalline compounds from the Open Quantum Materials Database (OQMD) are evaluated in a binary classification task based on formation-energy stability. The dataset is normalized, reduced to four dimensions via Principal Component Analysis (PCA), and encoded into quantum circuits. Three QML models—QSVM, VQC, and QNN—are benchmarked against a classical SVM using repeated stratified evaluation. Results show that the classical SVM achieves the highest accuracy (91.8% ± 0.012), followed by QSVM (60.8% ± 0.035), while VQC and QNN perform significantly worse. This gap is driven by limited qubit capacity, encoding inefficiencies, restricted circuit expressivity, and optimization challenges. Nevertheless, QSVM demonstrates stable performance, suggesting that potential quantum advantage may emerge from improved feature encoding and kernel design rather than deeper variational circuits.
Introduction: In recent years, high-dimensional clinical and genomic data have gained significant importance for prognosis and personalized medicine in breast cancer. But the use of quantum machine learning (QML) on such data is limited by the availability of few qubits, the computation time of quantum simulation, and dimensionality reduction. This work systematically compares several QML architectures for breast cancer classification in the presence of realistic and simulator constraints. Methods: The experiments were performed on a dataset of METABRIC breast cancer patients (2,509 patients). After handling missing values and one-hot encoding, there were 63 features in the processed data set. The feature space was reduced by Principal Component Analysis (PCA) to 12, 4 and 2 components for the implementations of quantum computers, respectively, with 56.10 ± 0.14%, 26.78 ± 0.57% and 16.23 ± 0.33% of the variance retained. Three QML models were tested: Quantum Neural Networks (QNN), Quantum K-Nearest Neighbors (QKNN), and Quantum Support Vector Machines (QSVM), with the models being simulated. Seven classical classification models were tested: Logistic Regression, SVM with RBF kernel, K-Nearest Neighbors, Random Forest, XGBoost, LightGBM and Multilayer Perceptron, both with PCA-matched and full 63-feature representation. All primary results are reported with 5-fold cross validation. Results: Among the evaluated QML architectures, QKNN using 12 principal components achieved the strongest performance, attaining an accuracy of **75.11% ± 3.76%**, an F1-score of **0.7088 ± 0.0433**, and a ROC-AUC of **0.8148 ± 0.0394**. Even though all of the QML models performed significantly poorly in comparison to classical models trained on the entire 63-feature data set, the latter models were able to achieve about **94% accuracy** with XGBoost, Random Forest, and Logistic Regression. The comparison also showed the effect of information loss due to PCA is significant in predictive performance in both classical and quantum models. Discussion: The results show that for high dimensional breast cancer data, currently available simulator-based QML models can learn meaningful patterns with limited quantum resources, but are not as effective as powerful classical machine learning models when complete feature representations are available. The study does not report any sort of quantum advantage or clinical use, but rather a benchmark of current QML architectures that has been rigorously calculated and repeated, with a focus on the impact of dimensionality reduction, validation approaches, and simulator limitations, as well as outlining challenges that need to be overcome prior to practical implementation on real quantum hardware.
Quantum kernel methods are often proposed as a route to improved medical image classification because quantum feature maps can embed data into high-dimensional Hilbert spaces. However, their practical value remains unclear when compared with strong classical kernels under leakage-controlled conditions. This study benchmarks two simulated quantum kernel support vector machines, QSVM-ZZ and QSVM-Pauli, against logistic regression, linear SVM, fixed-default RBF-SVM, and a compact multi-layer perceptron on BrainTumorMRI and BreastMNIST. All models used identical frozen ResNet18 features, train-only standardisation, PCA compression to four and eight dimensions, three random seeds, and matched classifier-training budgets where applicable. Across 24 seed-level matched comparisons, the best quantum kernel model never outperformed the best classical model. The mean quantum-minus-classical macro-F1 gap was - 0.2230, with all 24 gaps negative. Fixed pairwise comparisons confirmed that RBF-SVM exceeded both quantum kernels individually. QSVMs also required approximately 50 × to more than 220 × higher runtime. These findings show that, for compressed ResNet18 medical image features under noiseless simulation, the tested QSVM-ZZ and QSVM-Pauli kernels did not provide a practical advantage over fixed-default RBF-SVM.
Genomic data analysis is essential for personalized medicine, disease diagnostics, and understanding evolutionary biology, yet remains challenging due to high dimensionality and sequence complexity. Quantum Machine Learning (QML) offers promising computational advantages for scalable genomic analysis. We explore QML modeling for genomic sequence classification using 100,000 sequences from two transcript classes. Our new framework incorporates PCA dimensionality reduction and evaluates multiple quantum feature maps (ZFeatureMap, ZZFeatureMap, PauliFeatureMap). Results show Pegasos-QSVC achieving 99.12% recall and 67.41% F1 score, while QNNs reach 54.38% training accuracy. Performance varies across feature maps, with some models exhibiting overfitting.
Quantum machine learning (QML) benchmarks frequently compare quantum models against weak classical baselines -- the same methodological gap identified for quantum optimisation in the QCCB study (Popescu and Petrov, 2024). This paper presents the QML-DL Benchmark (QMLDB), a rigorous comparative evaluation of six QML model families against nine state-of-the-art classical deep learning baselines (MLP, CNN, LSTM, ResNet, Transformer, TabNet, XGBoost, LightGBM, CatBoost) across ten benchmark datasets spanning six task domains. QMLDB controls for model capacity, training budget, and data size. QML achieves top performance on three of ten datasets -- all three with strong quantum-process proximity. On the remaining seven, classical deep learning dominates, with Transformer and ResNet consistently outperforming all QML models by 4.8-18.4pp. QMLDB establishes that QML advantage is narrower than commonly claimed, confined to datasets with genuine quantum structure, and proposes a quantum-process proximity score (QPPS) to predict whether a new dataset will benefit from QML before hardware experiments.