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Financial Fraud Detection: A Comparative Study of Quantum Machine Learning Models

Nouhaila Innan, Muhammad Al-Zafar Khan, Mohamed Bennai

arXiv:2308.05237v1quant-phcs.LGq-fin.GN

TL;DR

The paper addresses the need for accurate, quick fraud detection by comparing four QML models on a curated dataset using three feature maps. QSVC achieved the highest reported performance, with F1 scores of 0.98 for both fraud and non-fraud classes.

  • Problem

    The paper identifies the need for accurate and quick fraud detection in the face of high consumer costs.

    Source: §I · p. 4

  • Method

    The study compares QSVC, VQC, EQNN, and SQNN on a curated dataset using ZZFeatureMap, PauliFeatureMap, and ZFeatureMap.

    Source: §V · p. 27

  • Results

    F1 scores of 0.98 for both fraud and non-fraud classes made QSVC the top performer among the evaluated models.

    Source: §V · p. 27

  • Takeaways & Limitations

    The authors conclude that QSVC and VQC performance attests to the potential of quantum algorithms for complex classification problems.

    Source: §V · p. 27

    VQC training may need refinement, while EQNN and SQNN had comparatively lower F1 scores, with encoding circuits suggested as a possible influence on accuracy.

    Source: §V · p. 27

Abstract

from arXiv · show

In this research, a comparative study of four Quantum Machine Learning (QML) models was conducted for fraud detection in finance. We proved that the Quantum Support Vector Classifier model achieved the highest performance, with F1 scores of 0.98 for fraud and non-fraud classes. Other models like the Variational Quantum Classifier, Estimator Quantum Neural Network (QNN), and Sampler QNN demonstrate promising results, propelling the potential of QML classification for financial applications. While they exhibit certain limitations, the insights attained pave the way for future enhancements and optimisation strategies. However, challenges exist, including the need for more efficient Quantum algorithms and larger and more complex datasets. The article provides solutions to overcome current limitations and contributes new insights to the field of Quantum Machine Learning in fraud detection, with important implications for its future development.

I. INTRODUCTION

The introduction motivates rapid financial-fraud detection and situates quantum machine learning as an emerging approach alongside established classical methods. It then presents the paper’s comparison of four QML models on BankSim.

I. INTRODUCTION

  • Fraud’s high consumer costs motivate an accurate, quick detection system, with the paper focusing on credit fraud.The introduction cites losses in the UK and US and notes that 80% of app fraud originates from online solicitations.Source: §I · pp. 3–4
  • Classical fraud-detection models are already widely deployed, and prior classical and deep-learning approaches report high fidelity, robustness, and ease of implementation.Source: §I · p. 4
  • QML seeks computational advantage over analogous classical approaches, but remains in an early stage of development.The introduction links broader adoption to advances in hardware, computing power, quantum cloud technologies, and QC approaches.Source: §I · pp. 4–5
  • The authors argue for exploring quantum approaches based on potential real-time analysis, reduced redundant data, parallelisation, and lower algorithmic computational complexity.Source: §I · p. 6
  • The paper applies QSVC, VQC, EQNN, and SQNN to the BankSim dataset.Source: §I · p. 6

II. LITERATURE REVIEW

The literature review surveys QML work in anomaly detection and fraud prediction, spanning theoretical proposals, simulations, and financial applications. It also notes implementation considerations such as detection speed and computing cost.

II. LITERATURE REVIEW

  • The review characterizes QML fraud detection as a fairly new application with relatively few application-based papers, despite growing use of QML methods.Source: §II · pp. 7, 9
  • Prior anomaly-detection work proposed quantum autoencoder methods and density-estimation algorithms, including approaches reported to scale logarithmically with training-data size and quantum-state dimensionality.Source: §II · p. 7
  • Variational Quantum Anomaly Detection was demonstrated in real-noise simulations and on a real quantum computer, with measurement-error mitigation and device-adapted circuits also reported.Source: §II · pp. 7–8
  • Quantum kernels were reported to outperform RBF kernels by over 10% on average precision for supervised fraud detection, while unsupervised use showed a 15% increase in average precision.Source: §II · p. 8
  • A financial-services study reported that a hybrid quantum method outperformed classical methods on accuracy and false-positive rate, and proposed feature selection to reduce dataset dimensionality for a real quantum device.Source: §II · p. 8
  • A QML framework for online transaction data was benchmarked against classical models, with accuracy, detection speed, and computing cost identified as implementation considerations.Source: §II · pp. 8–9

III. THEORY

The theory section introduces the data-encoding methods and QML models used in the paper, providing context for their selection and analysis.

III. THEORY

  • The paper presents ZZFeatureMap, PauliFeatureMap, and ZFeatureMap alongside QSVC, VQC, EQNN, and SQNN.Source: §III · p. 9
  • The authors say the methods’ theory helps establish context and justify their choices.Source: §III · p. 9
  • The theory is presented to guide the analyses and interpretation and enhance the research’s credibility.Source: §III · p. 9

A. Data Encoding Methods

The section describes ZZFeatureMap and PauliFeatureMap as quantum-circuit approaches for encoding classical data, using data-dependent rotations and entanglement.

1. ZZFeatureMap

  • For four features, ZZFeatureMap applies Hadamards, data-dependent rotations using ϕ(x, y, z, w) = (π − x)(π − y)(π − z)(π − w), and CNOT entanglement.Its feature dimension sets the number of qubits, and repetitions specify how often the rotation and entanglement blocks recur.Source: §1 · p. 10, Figure 1 · p. 10

2. PauliFeatureMap

  • PauliFeatureMap represents data as feature-associated Pauli-operator products, then applies Hadamards, data-mapped rotations, and entanglers; repetitions can improve approximation accuracy.The mapping function ϕS(x) maps classical input into the circuit.Source: §2 · pp. 10–11, Figure 2 · p. 11

3. ZFeatureMap

ZFeatureMap is a first-order, non-entangling Pauli-Z encoding circuit, while QSVC adapts the SVM approach using kernels to classify datapoints.

3. ZFeatureMap

  • ZFeatureMap uses fixed Pauli-Z strings in a first-order expansion, omitting entangling gates for applications needing a shallow circuit.Its circuit applies Hadamards followed by configurable repetitions of rotation blocks; its entanglement strategy is null.Source: §3 · pp. 11–12, Figure 3 · p. 12

B. Quantum Support Vector Classifiers

C. Variational Quantum Classifiers

The VQC learns circuit weights through repeated quantum transformations and measurements, while the Estimator QNN combines quantum feature mapping with classical neural-network processing. Both approaches optimize parameters against a loss function.

C. Variational Quantum Classifiers

  • The VQC applies quantum gates to prepared states, measures the result, and repeats the gate and measurement steps until its loss meets an acceptance criterion.Its circuit uses learnable weights optimized by a classical method.Source: C. Variational Quantum Classifiers · pp. 13–14

D. Estimator Quantum Neural Networks

  • The EQNN is hybrid: a quantum feature map encodes classical data into quantum states, and measurement yields features for a fully connected classical neural network to predict values.The process optimizes the VQC parameters and classical network weights and biases to minimize loss.Source: D. Estimator Quantum Neural Networks · pp. 14–15
  • The EQNN searches in parallel for VQC parameters and classical-network weights and biases that minimize the loss.The optimization objective includes θ*, W*, and b*; the passage says their search is carried out in parallel.Source: D. Estimator Quantum Neural Networks · p. 15

E. Sampler Quantum Neural Networks

The Sampler QNN is a hybrid quantum-classical architecture that uses a quantum sampler to draw example states from a probability distribution. Classical methods select solutions, while classical optimization updates circuit parameters.

E. Sampler Quantum Neural Networks

  • The SQNN extends a hybrid quantum-classical architecture with a quantum sampler that extracts example states from complex quantum-state probability distributions.Its feature-map state preparation is the same as the EQNN's.Source: E. Sampler Quantum Neural Networks · pp. 15–16
  • The sampler generates example states under variable configurations, from which samples are chosen and classical methods select the best solutions.The sampler may be the Quantum Approximate Optimisation Algorithm (QAOA).Source: E. Sampler Quantum Neural Networks · p. 16
  • A classical optimization method minimizes the cost function, feeds the resulting parameters back to the VQC, and repeats the process until parameters are optimized.The described optimization uses θ* = arg min J.Source: E. Sampler Quantum Neural Networks · p. 16

IV. RESULTS AND DISCUSSION

The study analyzes BankSim data and identifies transaction amount, demographic patterns, merchant categories, and selected features as informative for fraud detection. Its dataset is a synthetic simulation of bank payments.

A. Dataset and Feature Selection

  • 594,643 BankSim records cover 180 steps, including 587,443 regular payments and 7,200 fraudulent transactions in the simulated six-month period.BankSim is an agent-based simulator based on aggregated transaction data from a Spanish bank.Source: A. Dataset and Feature Selection · p. 17
  • 567.23 mean and 128.47 standard deviation for fraudulent payment amounts contrast with 145.68 mean and 50.32 standard deviation for legitimate payments.The paper reports these differences in its analysis of the payment-amount histogram.Source: Figure 8 · p. 18, A. Dataset and Feature Selection · p. 19
  • 45% of fraudulent transactions involved people aged 26–35 and 56% involved females, compared with 32% aged 36–45 and 34% males.The paper says these demographic trends can guide targeted fraud-detection strategies.Source: A. Dataset and Feature Selection · p. 19, Figure 9 · p. 19
  • “Sports & toys” and “health” accounted for 20% and 15% of fraud cases, respectively, highlighting merchant category as a relevant model feature.Source: A. Dataset and Feature Selection · p. 19, Figure 10 · p. 20
  • PCA ranked amount highest, followed by merchant and category; the study selected age, gender, category, and amount, while amount had a weak negative correlation with fraud.The feature-importance ranking appears in Fig. 11, and the pairwise correlation analysis in Fig. 12.Source: A. Dataset and Feature Selection · pp. 20–21, Figure 11 · p. 21

B. Data Analysis and Experimental Setup

The experimental workflow balances and cleans the data, encodes categorical features, and separates training from testing. Four QML models are trained with COBYLA on a Qasm simulator and evaluated using multiple metrics.

B. Data Analysis and Experimental Setup

  • The analysis uses a balanced 200-record dataset with 100 fraudulent and 100 non-fraudulent transactions, and converts age categories to numeric values.The original dataset was loaded and subsets were extracted before this preprocessing.Source: B. Data Analysis and Experimental Setup · p. 21
  • Category and gender are label-encoded, unused features are removed, and the remaining data is split into training and unseen testing sets.The target labels encode fraud as 1 and non-fraud as 0.Source: B. Data Analysis and Experimental Setup · pp. 22–23
  • All four QML models use Qiskit's COBYLA optimizer with a 200-iteration limit and are trained on the Aer Qasm simulator before evaluation with multiple metrics.Source: B. Data Analysis and Experimental Setup · p. 23

C. Results and Interpretation

Across four QML models evaluated with three feature maps, QSVC with ZFeatureMap achieved the highest performance, while VQC, EQNN, and SQNN showed lower results.

C. Results and Interpretation

V. CONCLUSION

The conclusion compares QSVC, VQC, EQNN, and SQNN across a curated dataset and three feature maps. QSVC leads with F1 scores of 0.98 for both classes, while the other models show potential alongside limitations.

V. CONCLUSION

  • The study evaluated QSVC, VQC, EQNN, and SQNN on a curated dataset using ZZFeatureMap, PauliFeatureMap, and ZFeatureMap.Source: §V · p. 27
  • QSVC achieved F1 scores of 0.98 for both fraud and non-fraud classes, making it the top performer among the evaluated models.Its quantum kernel measures state similarity without conventional loss functions.Source: §V · p. 27
  • VQC achieved an F1 score of 0.90, while EQNN and SQNN had comparatively lower F1 scores.The authors suggest VQC training and the quantum circuits used for data encoding as areas for refinement.Source: §V · p. 27
  • The authors characterize QSVC and VQC performance as evidence of QML algorithms’ potential for complex classification problems.Source: §V · p. 27
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