Banks predict credit default with Logistic Regression because regulators can read its coefficients—but it cannot express interactions. We add the missing non-linearity with a quantum-inspired feature map: 8 of the data's 23 columns become rotation angles of 8 qubits in an IQP circuit simulated in PennyLane, and 2 × 8 = 16 outputs are appended to the 23. On the UCI Default of Credit Card Clients data (30,000 clients, 5-fold CV) this lifts it from F1 = 0.462 to 0.517, while Kernel PCA, the strongest classical alternative at the same budget, reaches only 0.493; the gap survives FDR correction over 12 tests (p = 0.00007). The gain is specific to linear models: Random Forest, SVM, XGBoost, and k-NN, already non-linear, do not benefit. What caps n is the simulator, holding 2n amplitudes; on hardware the depth is independent of n.
Banks predict credit default with Logistic Regression because regulators can read its coefficients—but it cannot express interactions. We add the missing non-linearity with a quantum-inspired feature map: 8 of the data's 23 columns become rotation angles of 8 qubits in an IQP circuit simulated in PennyLane, and 2 × 8 = 16 outputs are appended to the 23. On the UCI Default of Credit Card Clients data (30,000 clients, 5-fold CV) this lifts it from F1 = 0.462 to 0.517, while Kernel PCA, the strongest classical alternative at the same budget, reaches only 0.493; the gap survives FDR correction over 12 tests (p = 0.00007). The gain is specific to linear models: Random Forest, SVM, XGBoost, and k-NN, already non-linear, do not benefit. What caps n is the simulator, holding 2n amplitudes; on hardware the depth is independent of n.
Credit default prediction is a tabular classification problem in which modest gains in F1 translate directly into reduced financial exposure. We ask whether Instantaneous Quantum Polynomial-time (IQP) circuits can produce features that improve a classifier over both its raw classical baseline and Kernel PCA - the strongest unsupervised classical non-linear alternative - at an equal feature budget. The dataset provides 23 financial attributes per client; for an n-qubit circuit we select n of them, encode each as a rotation angle, and read 2n expectation values back out as new features. The motivation for using a quantum circuit is computational: an n-qubit IQP circuit runs in constant depth and encodes feature correlations in a 2^n-dimensional Hilbert space, whereas classical simulation of its exact output statistics scales exponentially in n. Using the UCI Default of Credit Card Clients dataset and five-fold cross-validation, we find that appending 16 IQP features (n = 8 qubits) to a Logistic Regression model raises F1 from 0.462 to 0.517 (+0.055, p < 0.0001). Kernel PCA, the next-best method, reaches only 0.493 at the same feature count; the gap survives Benjamini-Hochberg correction across 12 tests (p = 0.00007). No other classifier - Random Forest, SVM, XGBoost, or k-NN - benefits, which points to a linear-expressivity mechanism rather than a generic improvement. We also show that how the 8 input features are chosen matters: Random Forest importance-guided selection reaches F1 = 0.523, while encoding maximally uncorrelated features drops it to 0.496, demonstrating that the circuit amplifies informative structure rather than creating it from scratch.
Financial fraud detection remains difficult due to extreme class imbalance and subtle, nonlinear patterns in transactional data. We investigate a hybrid quantum–classical approach that couples a fidelity-based quantum kernel with a logistic regression classifier (QEKLR). A custom ZZ-inspired feature map comprising Hadamards, mixed-axis Ry/Rzencodings, tunable Ising-ZZ cross terms, and data re-uploading, embeds PCA-reduced, Min–Max scaled features into quantum states. The resulting fidelity kernel is evaluated and used within kernel logistic regression. Experiments on two benchmarks: BankSim (synthetic) and the European Credit Card Fraud dataset, use balanced subsets created via Random Under-Sampling. The proposed model attains the best performance on BankSim (AUC = 0.96; strongest F1), and is competitive on the credit-card dataset (AUC = 0.94), closely tracking XGBoost (AUC = 0.96) while outperforming logistic regression and a variational quantum classifier baseline. These results indicate that quantum kernel methods can provide practical gains on tabular fraud tasks while remaining aligned with current NISQ constraints. We also discuss the quadratic cost of exact kernel evaluation and outline scalable approximations for future deployment on larger, highly imbalanced datasets.
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).
Detecting credit card fraud is notoriously difficult because fraudulent charges make up less than 0.2% of total transactions. Quantum Machine Learning (QML), particularly Quantum Kernel Support Vector Machines (QSVM), promises richer feature representations by embedding classical data into high-dimensional Hilbert spaces. However, whether this theoretical advantage holds up when managing real-world financial data bottlenecks remains unclear. We designed a controlled benchmark comparing three quantum encodings, Angle, ZZFeatureMap, and IQP against classical models while keeping sample sizes, feature counts, and scaling strictly matched. To handle class skew without corrupting quantum state overlaps, we embedded synthetic minority oversampling (SMOTE) directly into the quantum Gram matrix workflow, raising PR-AUC scores by roughly +0.04 across feature maps. When trained on the full European credit card dataset with 30 features, classical baselines reached a top PR-AUC of 0.983. However, restricting classical models to match QSVM hardware constraints (500 samples, 4 PCA features) dropped their PR-AUC to 0.750. This puts our best quantum result 0.730 PR-AUC using IQP encoding on 150 samples into realistic context. Testing on physical quantum hardware reduced performance further to 0.62 due to CNOT gate errors and thermal noise. Overall, our findings pinpoint two main operational bottlenecks for near-term quantum kernels: the scaling of Gram matrix evaluation and heavy information loss from squeezing features onto small qubit registers.
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.
Accurate prediction of future loan defaults is a critical capability for financial institutions that provide lines of credit. For institutions that issue and manage extensive loan volumes, even a slight improvement in default prediction precision can significantly enhance financial stability and regulatory adherence, resulting in better customer experience and satisfaction. Datasets associated with credit default prediction often exhibit temporal correlations and high dimensionality. These attributes can lead to accuracy degradation and performance issues when scaling classical predictive algorithms tailored for these datasets. Given these limitations, quantum algorithms, leveraging their innate ability to handle high-dimensionality problems, emerge as a promising new avenue alongside classical approaches. To assess the viability and effectiveness of quantum methodologies, we investigate a hybrid quantum-classical algorithm, utilizing a publicly available "Default Prediction Dataset" released as part of a third-party data science competition. Specifically, we employ hybrid quantum-classical machine learning models based on projected quantum feature maps and their ensemble integration with classical models to examine the problem of credit card default prediction. Our results indicate that the ensemble models based on the projected quantum features were capable of slightly improving the purely classical results expressed via a "Composite Default Risk" (CDR) metric. Furthermore, we discuss the practical applicability of the studied quantum-classical machine learning techniques and address open questions concerning their implementation.