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Quantum-Inspired Exponential Hilbert Space Feature Embedding with Layered Encoding-Entangling Circuit Architectures for Superior Quantum-Classical Hybrid Performance in Severely Imbalanced Credit Card Fraud Classification

Orbe, Nabil, Kowsar, Jia, Mohammad, Masum, Islam, Md, Mohaiminul, Ángel Rodríguez Sánchez, Miguel, Professor

Published Nov 28, 2025• 0 citations
OpenAlex

Abstract

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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quant-pharXiv:2603.06473•Mar 9, 2026•0 citations
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).
The increasing dependence on digital and card-based payment systems has heightened the risk of financial fraud. This situation creates an urgent need for models that can identify rare fraudulent events in uneven transaction data. Traditional machine learning models often sacrifice recall for precision when the minority class is very small. Quantum classifiers are theoretically appealing for capturing complex feature relationships, but current hardware limitations on qubit count and circuit depth restrict their effectiveness. This work introduces a hybrid quantum-classical framework for credit card fraud detection. It combines an Extreme Gradient Boosting (XGBoost) classifier with a Quantum Support Vector Machine (QSVM) that uses a ZZ feature map and a fidelity-based quantum kernel. To handle class imbalance, we apply the Synthetic Minority Oversampling Technique (SMOTE) and adjust decision thresholds. The quantum element is trained on a reduced, class-balanced data subset, ensuring it stays within the feasible limits of the simulator. We merge predictions from the classical and quantum models using a weighted probability fusion approach, optimizing the final threshold to maximize the F1-score. Using the Kaggle Credit Card Fraud Detection dataset, the hybrid model achieves a precision of 0.9783, recall of 0.9000, F1-score of 0.9375, and ROC-AUC of 0.9805. It surpasses the standalone XGBoost baseline, XGBoost with SMOTE, and the standalone QSVM regarding F1 and ROC-AUC metrics. These results show that blending classical gradient boosting with quantum kernel-based classification, along with imbalance-aware techniques, can significantly enhance fraud detection quality despite current quantum hardware limitations. This offers a practical path for future work in quantum-assisted financial security.
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.
With the rapid growth of digital financial transactions, credit card fraud detection has become a critical challenge in the banking and finance sector. Traditional rule-based systems and classical machine learning (ML) models often struggle to detect complex and evolving fraud patterns, especially in highly imbalanced datasets. This paper proposes a novel hybrid approach to credit card fraud detection using Quantum Machine Learning (QML) techniques combined with classical methods. The system applies Principal Component Analysis (PCA) for dimensionality reduction and Synthetic Minority Oversampling Technique (SMOTE) to handle class imbalance. A classical Random Forest model is implemented as a baseline, while a QML model based on Variational Quantum Circuits (VQC) is developed using PennyLane. A hybrid decision engine combining predictions of both models is designed for improved performance. Experimental results demonstrate that the hybrid model achieves 96.9% accuracy, outperforming individual models by achieving better detection rates and reducing false predictions. The system is deployed via an interactive Streamlit-based dashboard. This work highlights the potential of Quantum Machine Learning in enhancing fraud detection systems in financial security applications.
Credit Card Fraud Detection (CCFD) is a major concern for the financial industry, requiring rapid and accurate identification of fraudulent transactions amidst vast datasets. The rapid evolution of quantum computing presents transformative opportunities for enhancing Machine Learning (ML) applications, particularly in the domain of financial security. This paper explores the implementation of Quantum Machine Learning (QML) techniques for CCFD, a critical challenge in the financial industry characterized by imbalanced datasets. Traditional ML models, while effective, often struggle with scalability and computational efficiency when processing large-scale transactional data. QML leverages quantum phenomenon namely entanglement and superposition to potentially outperform classical algorithms in feature extraction and pattern recognition. Our study proposes a hybrid quantumclassical framework, integrating Variational Quantum Circuits (VQC) with classical Neural Networks (NN) to classify fraudulent transactions. Using a simulated quantum environment, we preprocess a publicly available credit card transaction dataset, encoding features into quantum states for processing through a parameterized quantum circuit. The model is trained to improves its ability to detect fraud accurately with fewer false positives, addressing the critical issue of customer inconvenience.
Abstract The exponential growth of digital financial transactions has increased the demand for intelligent and accurate fraud detection systems. This study proposes a Quantum-Enhanced Fraud Detection Framework that integrates classical feature engineering with advanced quantum machine learning techniques. The framework begins with comprehensive data preprocessing, including Mean, Median, and Mode Imputation to handle missing values and Z-Score Standardization along with Min–Max Scaling to normalize the data. The processed features are then transformed into quantum states using the ZZFeatureMap, enabling the representation of complex, non-linear correlations through quantum entanglement and superposition. The Quantum Kernel evaluates the pairwise similarity of quantum-encoded samples, capturing intricate relationships in high-dimensional feature spaces. Finally, a Quantum Support Vector Machine (QSVM) classifier is trained using the quantum kernel matrix to differentiate between fraudulent and legitimate transactions. The proposed method achieved an accuracy of 91%, demonstrating superior performance over conventional approaches by efficiently identifying subtle fraud patterns. The results validate the potential of Quantum Machine Learning (QML) as a powerful paradigm for financial fraud detection, combining classical data preprocessing with quantum computational advantages to achieve higher generalization and robustness.
This paper investigates whether hybrid quantum-classical machine learning can deliver practical improvements in financial fraud detection performance for card-based and other payment transactions. Building on a Guided Quantum Compressor architecture, the approach integrates an autoencoder, a variational quantum circuit, and a classical neural head, and then embeds this hybrid model into a mixture-of-experts framework including a state-of-the-art gradient-boosted tree classifier. Using a European credit card dataset with severe class imbalance, the routed hybrid architecture with 0.6 threshold achieves average precision scores of 0.793±0.0850.793\pm0.0850.793±0.085 compared to 0.770±0.0960.770\pm0.0960.770±0.096 of XGBoost on 3 repeated 5-fold cross-validation benchmarks. Precision and recall comparisons reveals a possible trade-off of fraud and nominal detections with a reduction in false positives at the cost of a small reduction in fraud detections. The improvements are achieved while adding only 7 to 21 minutes of extra inference time depending on the choice of hyperparameters. These results indicate that selectively routing transactions to quantum-classical models can enhance fraud detection while remaining compatible with the latency and operational constraints of modern financial institutions.