Comparative Performance Analysis of Quantum Machine Learning Architectures for Credit Card Fraud Detection

1. Problem Statement

Credit card fraud is a pervasive global threat causing billions in losses annually. Traditional Machine Learning (ML) approaches face significant challenges due to:

• The increasing volume and complexity of transactional data.
• Highly imbalanced datasets (fraud cases are rare compared to legitimate transactions).
• The need for real-time decision-making.

Quantum Machine Learning (QML) is proposed as a potential solution to overcome these limitations by leveraging quantum properties like superposition and entanglement to process high-dimensional data more efficiently. However, there is a lack of systematic research comparing different QML architectures, feature maps, and ansatz configurations specifically for financial fraud detection, particularly on non-standardized, real-world datasets.

2. Methodology

The study employs a rigorous experimental framework to evaluate three distinct QML architectures across two datasets.

Datasets

Two datasets were utilized, both preprocessed to address class imbalance (using Random Under Sampling to create a 50/50 ratio) and normalized:

1. BankSim: A synthetic dataset from a Spanish bank simulator containing ~594k records with features like customer ID, merchant, age, gender, category, and amount.
2. European Credit Card Dataset: A real-world dataset with 284k transactions. Features were reduced via Principal Component Analysis (PCA) to 7 components (V1–V7) plus Time and Amount.

Quantum Architectures Evaluated

The study compares three hybrid quantum-classical models:

1. Variational Quantum Classifier (VQC): A standard parameterized quantum circuit optimized via a classical optimizer.
2. Sampler Quantum Neural Network (SQNN): A hybrid model using a quantum sampler to extract samples from a probability distribution, followed by classical optimization.
3. Estimator Quantum Neural Network (EQNN): A hybrid model where quantum measurements (expectation values) are fed into a classical neural network for final classification.

Configuration Variables

To determine optimal configurations, the authors tested:

• Feature Maps (Encoding): Pauli, ZZ (pairwise entanglement), and Z (entanglement-free).
• Ansatz (Variational Layers): Real Amplitudes, Efficient SU2, Two Local, and Pauli Two Design.
• Optimizer: COBYLA (chosen for efficiency).
• Simulation: Qiskit Aer (QasmSimulator) with 80/20 train/test splits.

Evaluation Metrics & Validation

• Performance: Accuracy, Precision, Recall, F1-score, and Loss.
• Statistical Validation: One-way ANOVA was used to test the significance of Model type, Feature Map, Ansatz, and Dataset on F1-scores.
• Robustness: The best-performing models were tested under five quantum noise channels (Amplitude Damping, Bit Flip, Depolarizing, Phase Damping, Phase Flip) to simulate NISQ (Noisy Intermediate-Scale Quantum) conditions.

3. Key Contributions

1. Comprehensive Comparative Analysis: A systematic evaluation of VQC, SQNN, and EQNN on real-world fraud data, revealing that model architecture significantly impacts performance.
2. Configuration Sensitivity: Detailed mapping of how specific Feature Map and Ansatz combinations influence detection capabilities, highlighting that entanglement-enhanced maps (ZZ, Pauli) generally outperform non-entangled maps (Z) in complex models, though Z maps can be superior in specific low-depth scenarios.
3. Statistical Rigor: The use of ANOVA confirms that the observed performance differences are statistically significant (p < 0.05) and not due to random chance, with the Model Type being the most significant factor.
4. Noise Resilience Assessment: Evaluation of top models under realistic quantum noise, providing insights into the practical deployability of these architectures on current NISQ hardware.

4. Key Results

Performance Comparison

• VQC (Variational Quantum Classifier): Demonstrated the strongest overall performance.
  • Achieved the highest F1-score of 0.88 on the European dataset (Z Feature Map + Pauli Two Design).
  • Consistently high precision and stable convergence.
• SQNN (Sampler QNN): Showed promising and robust results, particularly on the BankSim dataset.
  • Achieved an F1-score of 0.85 on BankSim (Z Feature Map + Real Amplitudes).
  • Demonstrated strong adaptability across different configurations.
• EQNN (Estimator QNN): Significantly underperformed compared to VQC and SQNN.
  • Struggled to produce robust results (F1-scores often < 0.60), even with optimal configurations.
  • The authors attribute this to structural limitations in mapping expectation values to class labels and lower circuit expressiveness.

Feature Map & Ansatz Insights

• Entanglement Matters: Feature maps incorporating entanglement (ZZ, Pauli) generally improved performance for VQC and SQNN by capturing complex correlations.
• Ansatz Selection: "Two Local" and "Efficient SU2" were the most versatile ansatzes. "Real Amplitudes" performed well in SQNN but struggled in EQNN.
• Dataset Independence: ANOVA results showed the Dataset factor was not statistically significant, suggesting the models' relative performance trends are consistent across different data distributions.

Robustness to Noise

• SQNN (BankSim): Highly sensitive to noise. Performance dropped significantly (accuracy ~0.45–0.55) under depolarizing and phase damping noise.
• VQC (European): More robust than SQNN. While accuracy declined under noise, it maintained better stability, likely due to its optimized ansatz structure and effective classical post-processing.
• Noise Types: Depolarizing and Phase Damping had the most detrimental effects; Phase Flip noise showed a unique "regularization-like" effect in some cases.

5. Significance and Conclusion

This paper provides critical guidance for researchers and practitioners aiming to deploy QML in financial security.

• Architectural Choice is Critical: The choice of QML model (VQC vs. SQNN vs. EQNN) is the single most important factor in performance, outweighing dataset variations.
• Configuration Strategy: Successful fraud detection requires careful alignment of feature maps and ansatz. While entanglement is beneficial, simpler, shallow circuits (like Z feature maps) can be effective in specific contexts, offering a trade-off between complexity and noise resilience.
• NISQ Viability: The study confirms that VQC and SQNN can maintain competitive performance under simulated quantum noise, making them viable candidates for near-term deployment on NISQ hardware, whereas EQNN requires further architectural refinement.
• Future Directions: The authors suggest exploring deeper circuits, more expressive ansatzes, and task-specific loss functions to further improve the performance of underperforming models like EQNN.

In summary, the study validates that VQC is currently the most effective architecture for credit card fraud detection among the tested models, provided it is paired with an appropriate feature map and ansatz configuration.