We benchmarked quantum kernel $k$-means against classical clustering for credit-card fraud detection on real transaction data, at up to \MaxQubits{} qubits, under a protocol with separated selection and reporting data and matched search budgets. We find no robust quantum advantage: the sign of the difference depends on register size, all effect sizes are below $0.013$ ARI, and the single significant advantage we observe is fully explained by the number of configurations searched. We further show that ordinary hyperparameter choices move performance by considerably more than the quantum kernel does, that additional qubits degrade rather than improve performance through kernel concentration, and that the clustering framing itself fails at realistic class imbalance though kernel-based anomaly scoring does not. We regard the methodological contribution as the more durable one. The search-budget ablation in particular is inexpensive and, in our case, decisive: it converted a statistically significant advantage into a procedural artefact. We would encourage its routine use.
We benchmarked quantum kernel k-means against classical clustering for credit-card fraud detection on real transaction data, at up to \MaxQubits{} qubits, under a protocol with separated selection and reporting data and matched search budgets. We find no robust quantum advantage: the sign of the difference depends on register size, all effect sizes are below 0.013 ARI, and the single significant advantage we observe is fully explained by the number of configurations searched. We further show that ordinary hyperparameter choices move performance by considerably more than the quantum kernel does, that additional qubits degrade rather than improve performance through kernel concentration, and that the clustering framing itself fails at realistic class imbalance though kernel-based anomaly scoring does not. We regard the methodological contribution as the more durable one. The search-budget ablation in particular is inexpensive and, in our case, decisive: it converted a statistically significant advantage into a procedural artefact. We would encourage its routine use.
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.
We develop quantum protocols for anomaly detection and apply them to the task of credit card fraud detection (FD). First, we establish classical benchmarks based on supervised and unsupervised machine learning methods, where average precision is chosen as a robust metric for detecting anomalous data. We focus on kernel-based approaches for ease of direct comparison, basing our unsupervised modelling on one-class support vector machines (OC-SVM). Next, we employ quantum kernels of different type for performing anomaly detection, and observe that quantum FD can challenge equivalent classical protocols at increasing number of features (equal to the number of qubits for data embedding). Performing simulations with registers up to 20 qubits, we find that quantum kernels with re-uploading demonstrate better average precision, with the advantage increasing with system size. Specifically, at 20 qubits we reach the quantum-classical separation of average precision being equal to 15%. We discuss the prospects of fraud detection with near- and mid-term quantum hardware, and describe possible future improvements.
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±0.085 compared to 0.770±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.
Quantum kernel methods are the most concrete near-term proposal for quantum machine learning on classical data, yet published benchmarks disagree on whether they outperform tuned classical kernels, and the disagreement cannot be resolved from the literature because the comparisons are not protocol-controlled. We argue that the obstacle is one of measurement, not theory: the usual setup fixes the quantum feature map's data scaling while grid-searching the classical kernel's hyperparameters, recomputes nothing per fold, and reports cost in simulator time. We therefore treat the comparison itself as the object of study and impose three controls. The bandwidth is tuned on the same grid budget as the classical γ, the kernel is recomputed inside every fold from fold-fitted preprocessing, and cost is counted in hardware circuit evaluations. On top of these we run a factorial design of 324 cells in which dimensionality, training size, class separability and data structure are explicit covariates, together with four standard datasets, a shots-versus-gate-noise ablation, and a cost sweep. The dominant effect we measure is not quantum: tuning the feature map's bandwidth is worth 0.120 accuracy on synthetic data and 0.339 on real data, exceeding every quantum-classical difference we observe. Tuned quantum kernels are then statistically indistinguishable from a tuned RBF on all four real datasets. The advantage on synthetic data is confined almost entirely to data generated by the feature map itself, and it shrinks with dimensionality (-0.0045 per qubit) while growing with sample size. Finite sampling costs an order of magnitude more accuracy than gate and readout noise, and a fidelity kernel needs 5×107 circuits at n = 10,000. Protocol variance is thus sufficient to explain the field's contradictory conclusions.
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.
Quantum machine learning on near-term noisy quantum devices has generated substantial theoretical interest, but rigorous empirical comparisons under realistic noise on practically relevant data remain scarce. This paper compares two paradigmatic quantum learning models, a Quantum Support Vector Machine (QSVM) built on the ZZFeatureMap quantum kernel and a Variational Quantum Classifier (VQC) with an EfficientSU2/RealAmplitudes ansatz, against tuned classical baselines (SVM with four kernels, Random Forest, XGBoost, LightGBM and CatBoost) on the ULB Credit Card Fraud dataset (284,807 transactions, 0.17% fraud). All models share an identical 4-qubit PCA-reduced feature space, evaluated on the full unbalanced test fold over 15 fits (3 folds × 5 seeds) and reported as mean ± standard deviation with bootstrap confidence intervals, AUPRC as the primary metric. Noise robustness is assessed under depolarizing noise p∈{0,0.001,0.01,0.05}, with ranking preservation measured directly through Spearman ρ and Kendall τ between the noisy and noiseless decision scores rather than read off AUPRC, alongside the per-paradigm computational cost. At four qubits the classical baselines lead (AUPRC 0.60 to 0.74, CatBoost best), above the VQC (0.494) and the QSVM (0.240); the controlled QSVM-versus-RBF–SVM comparison puts the cost of the quantum kernel at about 0.45 AUPRC. Under noise the QSVM keeps its score ranking (ρ=0.998 at p=0.001, 0.906 at p=0.01) and an operational decision threshold (recall 0.87 to 0.89, stable calibration), while the VQC AUPRC peaks non-monotonically at p=0.01 (0.494 rising to 0.654, then easing to 0.569 at p=0.05) even as its ranking decays monotonically (ρ from 0.72 to near zero), so average precision on its own misrepresents how noise affects it. The quantum models do not surpass the tuned classical reference at four qubits; the contribution is methodological: under noise, AUPRC has to be read together with a genuine rank statistic, because the two can move in opposite directions.