Source-linked AI summary
Benchmarking Quantum Kernel SVMs for Credit Card Fraud Detection: Performance Realities Under NISQ Constraints
Hitanshi Arora, Mohit Swarnkar, Aswani Kumar Cherukuri
TL;DR
Fraud cases make up 0.172% of the dataset, making transaction classification highly imbalanced. The paper benchmarks quantum-kernel and classical models under controlled data constraints. Under matched constraints, the best quantum configuration reaches PR-AUC 0.730, close to the classical subsample baseline, while full-data classical models score 0.983.
Problem
Fraud cases make up roughly 0.172% of the dataset, framing transaction classification as a highly imbalanced binary task.
Source: §3 · p. 4Method
The paper benchmarks QSVM and classical models under matched sample constraints, using PCA to reduce features to four and evaluating Angle, ZZFeatureMap, and IQP encodings.
Source: §4.1 · pp. 6–8, §5 · p. 9Results
0.730 PR-AUC for IQP is close to the sample-restricted classical baseline at 0.750, while full-data classical models reach 0.983.
Source: §5 · p. 10, Conclusions · p. 13Takeaways & Limitations
The study attributes the performance gap chiefly to NISQ-era data limits rather than quantum-kernel expressivity, with IQP closest to the classical subsample baseline.
Source: §5 · p. 11Quantum Gram-matrix evaluation requires O(N^2) overlaps, while classical statevector simulation adds an O(2^d) factor, requiring strict subsampling as N grows.
Source: §6 · p. 11
Abstract
from arXiv · showhide
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.
2. Related Work
Prior work reports strong classical fraud-detection performance with sampling and ensembles, while quantum financial studies have required small samples and often lack sample-size-normalized comparisons.
Classical fraud detection
- >0.98 ROC-AUC is reported for decision-tree ensembles combined with undersampling or SMOTE on real-world transaction logs.Classical kernel algorithms also face runtime challenges on high-dimensional nonlinear interactions across large sample volumes.Source: §2 · p. 2
Quantum kernel methods
- Quantum kernel methods evaluate kernel matrices from quantum-state overlaps, and exploratory financial QSVM studies report severe sample-subsampling requirements.Prior comparisons often place these small QSVM trials against full-dataset classical models without normalizing sample size.Source: §2 · p. 3
Benchmarking gap
- Prior QSVM comparisons lack sample-size normalization, obscuring whether performance gaps reflect data volume or kernel expressivity.Table 1 organizes literature across classical machine learning, class-imbalance strategies, and quantum kernels.Source: §2 · p. 3
3. Problem Formulation
The section frames fraud detection as binary classification on a highly imbalanced transaction dataset, then formalizes classical and quantum kernel representations and their use in an SVM solver.
3. Problem Formulation
- Transaction instances are represented by feature vectors and binary labels, with fraud marked 1 and legitimate charges marked 0.Fraud cases make up roughly 0.172% of the dataset.Source: §3 · p. 4
- Fraud detection is formulated on a financial dataset whose transaction feature vectors are paired with their class labels.The fraud label is 1 and the legitimate-charge label is 0.Source: §3 · p. 4
3.1 Classical SVM
- A classical SVM finds a separating decision boundary by maximizing margins in kernel space.The kernel function calculates vector similarity.Source: §3.1 · p. 4
3.2 Quantum Kernel Formulation
- A parameterized circuit maps each input vector into an n-qubit quantum state.The state is formed by applying U(x) to the all-zero input state.Source: §3.2 · p. 4
- The quantum kernel entry measures the overlap, or fidelity, between encoded states in Hilbert space.The circuit U(x) produces the state representation used for this overlap.Source: §3.2 · p. 4
- The computed quantum Gram matrix is passed directly to a classical C-SVM quadratic solver to find optimal margins.Source: §3.2 · p. 4
4. Methodology
The methodology introduces a unified, controlled benchmarking pipeline for classical and quantum models, including a QSVM workflow with SMOTE resampling.
4. Methodology
- The paper constructs a unified benchmarking pipeline to evaluate classical and quantum models under rigorous data controls.The algorithm is identified as a QSVM pipeline with integrated SMOTE resampling.Source: §4 · p. 4
- The pipeline input consists of transaction feature vectors paired with binary class labels.The feature vector is denoted x and the class label y.Source: §4 · p. 4
- Evaluation uses PR-AUC, ROC-AUC, precision, recall, and F1-score.Source: §4 · p. 4
1. Feature Preprocessing & Dimensionality Reduction
Preprocessing standardizes raw features and then uses PCA to project them into the target qubit space.
2. Stratified Partitioning & SMOTE Resampling
The workflow applies SMOTE to the training split and extracts a balanced subset sized for quantum simulation.
2. Stratified Partitioning & SMOTE Resampling
3. Quantum Gram Matrix (𝐊,) Construction
The quantum register is initialized in the zero state, then parameterized feature and adjoint circuits are constructed.
3. Quantum Gram Matrix (𝐊,) Construction
4. Model Optimization & Classification Inference
The encoding schemes trade circuit structure and expressivity against hardware noise, while physical execution scores below ideal simulation. The workflow also integrates SMOTE into the quantum Gram matrix process under matched sample and feature constraints.
4. Model Optimization & Classification Inference
- SMOTE is integrated into the quantum Gram matrix workflow, boosting PR-AUC by roughly +0.04 without distorting Hilbert space inner products.The benchmark matches sample size at N=150 and feature dimensions at d=4 to isolate quantum kernel expressivity from classical sample-volume advantages.Source: §4 · p. 6
4.1 Quantum Feature Encoding Strategies
- Angle Encoding maps four PCA features to single-qubit rotations and achieves PR-AUC 0.700; its linear CNOT chain has limited expressivity.Source: §4.1 · p. 6
- ZZFeatureMap’s adjacent-pair topology omits non-adjacent PCA feature interactions, limiting PR-AUC to 0.700.Source: §4.1 · p. 7
- IQP achieves the highest quantum simulation PR-AUC at 0.730, while its deeper, higher-CNOT circuit is most susceptible to hardware errors.Source: §4.1 · p. 7
- Table 2 compares circuit depth, gate composition, expressivity, and noise sensitivity, showing denser entanglement trades higher expressivity for greater hardware noise susceptibility.Source: Table 2 · p. 8, §4.1 · p. 8
4.2 Hardware Execution vs. Ideal Statevector Simulation
- PR-AUC falls from 0.70 on ideal statevector simulation to 0.62 on the ibm_kingston processor.Table 3 reports the simulation-to-hardware comparison; thermal relaxation, gate infidelities, and readout errors are identified as degradation factors.Source: Table 3 · p. 8, §4.2 · p. 8
5. Experimental Setup & Results
Under matched data constraints, the best quantum result approaches the sample-restricted classical baseline, while full-data classical models remain strongest.
5. Experimental Setup & Results
- The benchmark uses 284,807 transactions with 492 fraud cases and compares N=150 and N=500 subsets after reducing 30 features to four principal components.Training subsets were compared under identical sample constraints.Source: §5 · p. 9
- 0.983 PR-AUC for unconstrained classical models contrasts with 0.750 for N=500 classical baselines and 0.730 for IQP.Table 4 compares models across dataset scopes, sample sizes, and feature counts.Source: Table 4 · p. 9, §5 · p. 9
- Figure 4 compares PR and ROC curves across unconstrained classical models and restricted QSVM variants; Random Forest reaches 0.983 PR-AUC, versus 0.750 for N=500 classical models and 0.730 for IQP.Source: Figure 4 · p. 10, §5 · p. 10
- Figure 5 indicates that the performance gap stems primarily from NISQ-era data limits rather than quantum kernel expressivity, with IQP closest to the classical subsample baseline.The comparison concerns full classical baselines, N=500 classical subsamples, and QSVM models.Source: Figure 5 · p. 10, §5 · pp. 10–11
6. Analysis
With normalized constraints, QSVM performance approaches the sample-restricted classical baseline, but full-data classical models remain stronger. The analysis also identifies resampling gains and computational, dimensionality, and hardware limits.
6. Analysis
- SMOTE integration increases PR-AUC by roughly +0.03 to +0.04 across evaluated quantum encodings.The resampling is integrated into quantum Gram matrix generation.Source: Table 5 · p. 11, §6 · p. 11
- Figure 6 shows QSVM runtime scaling steeply with sample size; Gram-matrix evaluation requires O(N²) overlaps, and physical hardware noise reduces PR-AUC to 0.62.The hardware degradation is attributed to CNOT gate errors and thermal relaxation.Source: Figure 6 · p. 12, §6 · pp. 12–13
- Compressing 30 transaction features to four principal components reduces classical PR-AUC from 0.983 to 0.965.QSVMs are bound to low qubit counts, requiring aggressive linear projection.Source: §6 · p. 12
Conclusions
- In this empirical benchmark on imbalanced financial fraud data, under normalized sample-size and feature constraints, QSVM classification is competitive with classical baselines (PR-AUC 0.730 vs. 0.750), while full-dataset classical models achieve 0.983.Source: Conclusions · p. 13
- The authors propose fault-tolerant quantum execution, variational quantum feature selection, and hybrid quantum neural networks as future directions.Source: Conclusions · p. 13