Quantum-enhanced deep belief networks for financial fraud detection

Department of Computer Science and Engineering Sri Sivasubramaniya Nadar College of Engineering Kalavakkam, Chennai 603110, Tamil Nadu, India

¹ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 23 March 2026

Abstract

A Deep Belief Network (DBN) is a generative model stacking multiple Restricted Boltzmann Machine (RBM) layers to learn hierarchical data representations. While effective for feature extraction, classical DBNs struggle with high-order patterns in complex, imbalanced datasets, such as credit card fraud data. To overcome this, we integrate quantum-inspired RBMs (QRBMs) into the DBN framework.

This study compares four 3-layer DBN configurations on the Credit Card Fraud Detection dataset: (i) classical DBN (all RBM layers), (ii) 1-Quantum DBN (1 QRBM layer), (iii) 2-Quantum DBN (2 QRBM layers), and (iv) full Quantum DBN (all QRBM layers). Models were trained via contrastive divergence and assessed using precision, recall, and F1-score.

Results show the full Quantum DBN outperforming others: precision 0.581, recall 0.637, F1-score 0.602—yielding a 34.4% F1 improvement over classical DBN (precision 0.319, recall 0.755, F1 0.448). Hybrids ranked intermediately. Quantum advantages stem from entanglement and superposition, fostering complex pattern capture and faster convergence (fewer epochs).

These findings highlight quantum-enhanced DBNs’ potential for scalable anomaly detection in financial fraud systems, paving the way for hybrid quantum-classical ML applications.