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A Correlation Aware Quantum Feature Map for Variational Quantum Classification

Murat Kurt

Published Jun 23, 2026• 0 citations
Publisher

Abstract

Abstract Quantum Machine Learning (QML) has emerged as a promising research area for learning complex data patterns. However, most existing quantum feature maps employ fixed encoding strategies that do not explicitly consider the relationships among features within a dataset. In this study, we propose a Correlation Aware Quantum Feature Map (CAQFM) which integrates feature dependencies into the quantum encoding process. The proposed approach utilizes Pearson, Spearman, Kendall Tau, Mutual Information, and Distance Correlation measures to identify relationships among features. Dependencies exceeding a predefined threshold are incorporated into the quantum circuit through controlled quantum gates, enabling the construction of richer quantum representations that better reflect the underlying structure of the data. The proposed method is evaluated using a VQC on three benchmark datasets, namely breast cancer diagnosis, credit default prediction, and student placement classification. Simulation results demonstrate that correlation based quantum encoding can improve classification performance compared to conventional encoding strategies. In particular, the Spearman and Kendall Tau based CAQFM variants achieved the highest predictive performance and consistently outperformed standard quantum feature maps. The findings indicate that incorporating dependency information from classical data into quantum feature maps facilitates the generation of more discriminative quantum representations and enhances the effectiveness of variational quantum classifiers.

DOI
10.21203/rs.3.rs-10102081/v1

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Abstract Quantum Machine Learning (QML) has emerged as a promising research area for learning complex data patterns. However, most existing quantum feature maps employ fixed encoding strategies that do not explicitly consider the relationships among features within a dataset. In this study, we propose a Correlation Aware Quantum Feature Map (CAQFM) which integrates feature dependencies into the quantum encoding process. The proposed approach utilizes Pearson, Spearman, Kendall Tau, Mutual Information, and Distance Correlation measures to identify relationships among features. Dependencies exceeding a predefined threshold are incorporated into the quantum circuit through controlled quantum gates, enabling the construction of richer quantum representations that better reflect the underlying structure of the data. The proposed method is evaluated using a VQC on three benchmark datasets, namely breast cancer diagnosis, credit default prediction, and student placement classification. Simulation results demonstrate that correlation based quantum encoding can improve classification performance compared to conventional encoding strategies. In particular, the Spearman and Kendall Tau based CAQFM variants achieved the highest predictive performance and consistently outperformed standard quantum feature maps. The findings indicate that incorporating dependency information from classical data into quantum feature maps facilitates the generation of more discriminative quantum representations and enhances the effectiveness of variational quantum classifiers.
Quantum machine learning has emerged as a promising research area for learning complex data patterns. However, most existing quantum feature maps employ fixed encoding strategies that do not explicitly consider the relationships among features within a dataset. In this study, we propose a Correlation Aware Quantum Feature Map (CAQFM) which integrates feature dependencies into the quantum encoding process. The proposed approach utilizes Pearson, Spearman, Kendall Tau, Mutual Information, and Distance Correlation measures to identify relationships among features. Dependencies exceeding a predefined threshold are incorporated into the quantum circuit through controlled quantum gates, enabling the construction of richer quantum representations that better reflect the underlying structure of the data. The proposed method is evaluated using a Variational Quantum Classifier (VQC) on three benchmark datasets, namely breast cancer diagnosis, credit default prediction, and student placement classification. Simulation results demonstrate that correlation based quantum encoding can improve classification performance compared to conventional encoding strategies. In particular, the Spearman and Kendall Tau based CAQFM variants achieved the highest predictive performance and consistently outperformed standard quantum feature maps. The findings indicate that incorporating dependency information from classical data into quantum feature maps facilitates the generation of more discriminative quantum representations and enhances the effectiveness of variational quantum classifiers.
The way in which classical data are encoded into quantum states plays a significant role in both classification performance and quantum circuit complexity in Quantum Machine Learning. In this study, the effects of different quantum feature encoding strategies on Quantum Support Vector Machine performance were investigated using five binary classification datasets. In particular, the statistical relationships between features were incorporated into quantum circuits through RY(θ)RY(θ)RY(θ) and controlled-RY(θ)RY(θ)RY(θ) gates, and this approach was compared with conventional quantum feature maps. The results demonstrate that incorporating statistical relationships into the encoding process can influence classification performance. However, more complex and densely entangled circuits do not necessarily yield higher performance. In addition, a composite evaluation metric was employed to jointly assess predictive performance, generalization, and circuit cost. The findings across the five datasets indicate that the choice of quantum feature encoding strategy should account for the underlying structure of the data and that predictive performance should be evaluated together with quantum circuit complexity.
Abstract High-dimensional classification remains challenging for hybrid quantum–classical learning because conventional variational quantum feature learning methods often assign equal importance to all input features and do not explicitly account for feature uncertainty. This paper presents Uncertainty-Aware Variational Quantum Feature Learning (UVQFL) , a hybrid framework that combines adaptive feature weighting, uncertainty estimation, and variational quantum representation learning for reliable classification. The proposed framework incorporates an Adaptive Feature Confidence Module (AFCM) to estimate the contribution of individual input features before quantum encoding and an Uncertainty Estimation Module (UEM) to characterize feature reliability during the learning process. The confidence-weighted features are encoded using a variational quantum circuit and subsequently processed by an enhanced multi-layer classical classifier. Benchmark datasets, including MNIST, Fashion-MNIST, and PathMNIST, are employed during data preprocessing and quantum feature generation to establish the proposed framework. The detailed experimental evaluation, performance analysis, and comparative results presented in this study are conducted on the MNIST benchmark dataset to provide a comprehensive assessment of the proposed architecture. A systematic investigation using 4-, 6-, and 8-qubit hybrid models examines the influence of quantum feature dimensionality on classification performance. The final UVQFL model achieves a best validation accuracy of 84.62% , with 84.60% precision , 84.62% recall , and an 84.59% F1-score . The results indicate that integrating adaptive feature confidence with uncertainty-aware quantum feature learning improves feature representation quality and enhances the reliability of hybrid quantum–classical classification.
Quantum assisted machine learning (QML) have the potential to outperform the classical Machine Learning models by utilizing the quantum feature maps embeddings and variational circuits. In this study, a Hybrid Quantum Support Vector Machine (QSVM) and Quantum Neural Network (QNN) is proposed for supervised classification applied to the Breast Cancer Wisconsin Dataset. The QSVM component employs fidelity quantum kernels with three distinct feature maps—Z, ZZ and Pauli—to transform classical data into quantum states. The QNN is implemented using a variational quantum classifier based on the EstimatorQNN, which enables quantum-trainable parameters for enhanced feature extraction. The proposed hybrid methodology is evaluated using seven principal features, and experiments are conducted on IBM’s state vector Qiskit Aer local simulator. Performance is assessed based on accuracy, recall, precision, F1-score, and confusion matrix. Additionally, statistical significance is evaluated using paired t test and F test to compare the performance of different quantum feature maps and to validate improvements made in the Hybrid Model. The results demonstrate that the hybrid QSVM/QNN approach improves classification performance not only in terms of accuracy by achieving above 90% accuracy but also by reducing computational cost. This work contributes to the advancement of quantum enhanced machine learning (ML) algorithms by demonstrating the hybrid quantum-classical approach in structured data classification.
Background: Classical algorithms often struggle with the high dimensionality of medical data critical for early lung cancer diagnosis. While Quantum Machine Learning (QML) offers enhanced pattern recognition capabilities, the impact of specific quantum feature encoding strategies on diagnostic accuracy remains underexplored.Methods: We evaluated Quantum Support Vector Machines (QSVM) using a dataset of 309 lung cancer patients, divided into six balanced subsets to mitigate class imbalance. Models were implemented on a qasm simulator, comparing three encoding strategies: ZFeatureMap, ZZFeatureMap, and PauliFeatureMap. Performance was assessed using standard classification metrics.Results: The choice of feature map significantly influenced model efficacy. The PauliFeatureMap outperformed other kernels, achieving 100% classification accuracy in three of the six subsets, whereas ZFeatureMap and ZZFeatureMap yielded lower predictive consistency.Conclusion: Quantum feature map selection is a decisive factor in QSVM performance. Specifically, the PauliFeatureMap demonstrates high separability for medical data, highlighting the potential of optimized quantum kernels to improve diagnostic precision.
The exponential growth in volume and complexity found in healthcare datasets has created significant challenges for diagnostic pattern recognition. This paper presents a comparative study of classical support vector classifiers (SVC) and quantum support vector classifiers (QSVC) for medical diagnostic applications using the Breast Cancer Wisconsin (Diagnostic). We evaluate metrics for classical SVC and QSVC implementations in noiseless and some factors of noisy simulation environments. To optimize feature representation, we employ Fisher’s Discriminant Ratio (FDR) for feature selection, followed by Pearson correlation analysis to inform the design of a novel Adaptive Feature Map design. Our proposed feature map is compared against established quantum encoding strategies, including a comparative analysis against a ZZ feature map with linear entanglement, demonstrating competitive performance and enhanced correlation-awareness. Through comprehensive evaluation across multiple performance metrics and training scenarios, we analyze the relative strengths of quantum and classical approaches, providing insights into the potential application of quantum machine learning methods in healthcare diagnostics.