Comparative Analysis and Noise Robustness Study of Quantum Kernel Methods and Variational Quantum Classifiers for Financial Fraud Detection

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.