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arXiv:2604.01930

Quantum-Inspired Geometric Classification with Correlation Group Structures and VQC Decision Modeling

Nishikanta Mohanty, Arya Ansuman Priyadarshi, Bikash K. Behera, Badshah Mukherjee

quant-phcs.AISubmitted Apr 2, 2026• Announced Apr 3, 2026• 0 citations• Revised Apr 9, 2026 (v2)
v1 · Apr 2, 2026v2 · Apr 9, 2026
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Abstract

We propose a geometry-driven quantum-inspired classification framework that integrates Correlation Group Structures (CGR), compact SWAP-test-based overlap estimation, and selective variational quantum decision modelling. Rather than directly approximating class posteriors, the method adopts a geometry-first paradigm in which samples are evaluated relative to class medoids using overlap-derived Euclidean-like and angular similarity channels. CGR organizes features into anchor-centered correlation neighbourhoods, generating nonlinear, correlation-weighted representations that enhance robustness in heterogeneous tabular spaces. These geometric signals are fused through a non-probabilistic margin-based fusion score, serving as a lightweight and data-efficient primary classifier for small-to-moderate datasets. On Heart Disease, Breast Cancer, and Wine Quality datasets, the fusion-score classifier achieves 0.8478, 0.8881, and 0.9556 test accuracy respectively, with macro-F1 scores of 0.8463, 0.8703, and 0.9522, demonstrating competitive and stable performance relative to classical baselines. For large-scale and highly imbalanced regimes, we construct compact Delta-distance contrastive features and train a variational quantum classifier (VQC) as a nonlinear refinement layer. On the Credit Card Fraud dataset (0.17% prevalence), the Delta + VQC pipeline achieves approximately 0.85 minority recall at an alert rate of approximately 1.31%, with ROC-AUC 0.9249 and PR-AUC 0.3251 under full-dataset evaluation. These results highlight the importance of operating-point-aware assessment in rare-event detection and demonstrate that the proposed hybrid geometric-variational framework provides interpretable, scalable, and regime-adaptive classification across heterogeneous data settings.

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34 Pages, 19 Algorithms , 8 Tables

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We propose a geometry-driven quantum-inspired classification framework that integrates Correlation Group Structures (CGR), compact SWAP-test-based overlap estimation, and selective variational quantum decision modelling. Rather than directly approximating class posteriors, the method adopts a geometry-first paradigm in which samples are evaluated relative to class medoids using overlap-derived Euclidean-like and angular similarity channels. CGR organizes features into anchor-centered correlation neighbourhoods, generating nonlinear, correlation-weighted representations that enhance robustness in heterogeneous tabular spaces. These geometric signals are fused through a non-probabilistic margin-based fusion score, serving as a lightweight and data-efficient primary classifier for small-to-moderate datasets. On Heart Disease, Breast Cancer, and Wine Quality datasets, the fusion-score classifier achieves 0.8478, 0.8881, and 0.9556 test accuracy respectively, with macro-F1 scores of 0.8463, 0.8703, and 0.9522, demonstrating competitive and stable performance relative to classical baselines. For large-scale and highly imbalanced regimes, we construct compact Delta-distance contrastive features and train a variational quantum classifier (VQC) as a nonlinear refinement layer. On the Credit Card Fraud dataset (0.17% prevalence), the Delta + VQC pipeline achieves approximately 0.85 minority recall at an alert rate of approximately 1.31%, with ROC-AUC 0.9249 and PR-AUC 0.3251 under full-dataset evaluation. These results highlight the importance of operating-point-aware assessment in rare-event detection and demonstrate that the proposed hybrid geometric-variational framework provides interpretable, scalable, and regime-adaptive classification across heterogeneous data settings.
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Credit card fraud detection remains a challenging binary classification problem because fraudulent transactions are rare, transaction patterns are complex, and false negatives may have important operational consequences. This study presents a Hybrid Classical–Quantum-Inspired Neural Network (HCQNN) with a simulated variational quantum circuit for credit card fraud detection. The proposed framework combines classical preprocessing, SMOTE-based class balancing, neural network-based feature learning, and quantum-inspired variational feature transformation. The model was evaluated using the Credit Card Fraud Detection dataset after applying SMOTE to the training data and was compared with three classical baseline classifiers: Logistic Regression, Decision Tree, and Linear Support Vector Machine. The experimental results show that the proposed HCQNN achieved an AUC of 97.85%, precision of 91.20%, recall of 90.10%, and an F1-score of 90.64%. These values indicate improved classification balance, particularly in the detection of minority-class fraud cases, compared with the selected baseline models. Training and validation behaviour also showed stable convergence, with training and validation accuracies exceeding 96% and 95%, respectively. Since the variational quantum circuit was simulated on classical hardware, the findings should be interpreted as evidence of the value of hybrid feature learning and quantum-inspired transformations rather than as proof of quantum computational advantage. The study provides a basis for further evaluation using broader datasets, additional baseline models, and real quantum hardware.
Credit card fraud detection is still one of the significant challenges in the digital economy, and most traditional machine learning methods appear to be inadequate fordealing with highly imbalanced datasets and intricate non-linear fraud patterns. This paper introduces and tests Q-fusion enhanced hybrid models, which exploit Quantum-Inspired FeatureMaps to embed classical transaction data in high-dimensional Hilbert spaces with the aim of increasing class distinguishability and performance. Five quantum-boosting classifiers were performed includingand described: Quantum Support Vector Machine (QSVM), Quantum Logistic Regression (QLR), Quantum K-Nearest Neighbors (QKNN), Quantum Gaussian Naive Bayes (QGNB) and Quantum Multi-Layer Perceptron (QMLP). The results show that the Quantum MLP model provided the best performance and reached an accuracy of 99.35%, precision of 0.96, recall of0.92, F1-score of 0.94 and ROC-AUC score of 0.97 which outperformed all quantum-enhanced models as well as classical ANN model.. Quantum feature mapping greatly improved feature separability, especially for minority class fraudulent transactionsand remained compatible with classical infrastructure. These results identify quantum-inspired machine learning as a promising route for enhancing fraud detection in severely imbalanced data sets and can berealized without deploying full-scale quantum hardware. implementation faces hardware limitations ( 27), algorithmic complexity (28), and infrastructure integration challenges (29). Quantum-inspired approaches provide a pragmatic pathway, offering quantum-like advantages through classical simulation (30; 31). Research Problem and Contribution Credit card fraud detection faces interconnected challenges: (1) extreme class imbalance creates severe classifier bias where models achieve high accuracy by predicting all transactions as legitimate while missing fraud (32; 33); (2) feature engineering requires domain expertise to identify transaction attributes, temporal patterns, and behavioral anomalies (14; 34); (3) real-world systems require millisecond classification (35); (4) regulatory compliance demands transparent, explainable systems (36; 37). Despite growing QML interest, empirical evaluations for fraud detection remain limited. Most studies focus either on purely classical methods (8; 32) or theoretical quantum algorithms requiring full hardware (30; 38), creating a gap in practical quantum-inspired implementations. Recent surveys identify this as a critical frontier (26; 39; 40). This research contributions: (1) Implementation and evaluation of five quantum-enhanced hybrid models (QSVM, QLR, QKNN, QGNB, QMLP); (2) Demonstration that quantum-inspired transformations project data into higher-dimensional Hilbert spaces, improving fraud class separability; (3) Empirical evidence of substantial gains (99.35% accuracy, 0.97 ROC-AUC) on classical hardware; (4) Rigorous comparative evaluation with consistent preprocessing and comprehensive metrics; (5) Identification that Quantum MLP achieves synergistic performance combining quantum features with deep learning. Research Objectives This research aims to: (1) develop quantum-inspired feature mapping transforming transaction data into Hilbert space representations; (2) design and evaluate five quantum-enhanced classifiers; (3) conduct comprehensive performance evaluation using imbalanced classification metrics; (4) quantify performance improvements from quantum-inspired transformations; (5) assess computational feasibility for production deployment; (6) provide theoretical explanations based on Hilbert space geometry. Paper Organization Section 2 reviews related work in machine learning fraud detection, quantum computing, and quantum machine learning. Section 3 describes methodology including preprocessing, quantum feature mapping, classifier architectures, and evaluation metrics. Section 4 presents experimental results with performance analysis. Section 5 concludes with key findings and future directions. 2 Related Work 2.1 Classical Machine Learning for Fraud Detection Credit card fraud detection has been extensively studied using classical approaches. Early work established cost-sensitive learning to address class imbalance (41). Logistic Regression provides interpretability and probabilistic outputs (3) but struggles with nonlinear patterns (7). Support Vector Machines identify maximum-margin hyperplanes (5) but face computational challenges (O(n 2 )-O(n 3 )) (42) and performance degradation on imbalanced data (8). Ensemble methods including Random Forest (4) and Gradient Boosting (43; 44) achieve improved stability. Deep learning approaches-Multi-Layer Perceptrons with modern optimization (ReLU (45), batch normalization (46), dropout (47), Adam (48))-achieve state-of-the-art performance with preprocessing (49). Recurrent architectures (LSTM (50), GRU (51)) capture temporal patterns (52), while Autoencoders frame fraud as anomaly detection (53; 54). Imbalance Handling Techniques Class imbalance (¡0.2% fraud) (13) necessitates specialized techniques. SMOTE generates synthetic minority samples through interpolation (6), while SMOTEENN combines SMOTE with Edited Nearest Neighbors for noise reduction (55; 56). Cost-sensitive learning assigns different misclassification penalties (33; 57). Ensemble methods train multiple classifiers on balanced subsets (58; 59).
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Early and accurate prediction of cardiovascular disease is essential to improve patient outcomes and reduce healthcare costs. This research presents a hybrid classical–quantum machine learning framework for heart disease prediction using the Cleveland dataset. The proposed pipeline integrates advanced feature engineering, bio-inspired optimization, and quantum-inspired learning to improve classification performance and interpretability. The system applies multiple feature selection techniques followed by a hybrid feature fusion strategy. Orthogonal Component Analysis is then used for dimensionality transformation, while quantum-inspired feature mapping simulates quantum state coding. A feature selection mechanism based on a Genetic Algorithm optimizes the subset of features. Classical and quantum machine learning models are evaluated, including Random Forest, Gradient Boosting, K-Nearest Neighbors, Logistic Regression, Quantum Support Vector Classifier, Variational Quantum Classifier, Quantum KNN, and Quantum Neural Networks. Model performance is evaluated using accuracy metrics. To ensure transparency and trustworthiness, explainable AI techniques such as SHAP, LIME and DiCE are integrated to provide local and global interpretability of predictions. Experimental results demonstrate that the proposed hybrid framework improves predictive performance by achieving 90% accuracy compared to traditional machine learning approaches, while maintaining model explainability. The model achieved an overall accuracy of 90%, indicating strong predictive capability in cardiovascular disease risk classification. A detailed analysis of class-wise performance shows that for Class 0, the model obtained a precision of 0.85, a recall of 0.97, and an F1-score of 0.90, demonstrating excellent ability to correctly identify negative cases with minimal false negatives. For Class 1, the model achieved a precision of 0.96, a recall of 0.84, and an F1-score of 0.90, indicating high confidence in positive predictions, though with slightly lower recall compared to Class 0. This study highlights the potential of combining classical feature engineering, evolutionary optimization and quantum-inspired learning for next-generation medical decision support systems. The integration of quantum-inspired techniques also provides a promising direction for improving computational efficiency and model robustness in healthcare analytics. The findings suggest that hybrid classical–quantum learning approaches can support clinicians in making faster and more reliable diagnostic decisions.