Quantum Topological Graph Neural Networks for Detecting Complex Fraud Patterns

TL;DR

This paper introduces a quantum graph neural network framework that combines quantum embedding, topological data analysis, and variational graph convolutions to detect complex financial fraud patterns effectively on large-scale networks.

Contribution

It presents a novel hybrid quantum-classical GNN architecture integrating topological analysis, with convergence guarantees and scalability for NISQ devices, advancing quantum machine learning for fraud detection.

Findings

QGTNN outperforms classical baselines in ROC-AUC and precision.

The framework demonstrates robustness to noisy quantum hardware.

Ablation studies highlight the importance of topological features and quantum embeddings.

Abstract

We propose a novel QTGNN framework for detecting fraudulent transactions in large-scale financial networks. By integrating quantum embedding, variational graph convolutions, and topological data analysis, QTGNN captures complex transaction dynamics and structural anomalies indicative of fraud. The methodology includes quantum data embedding with entanglement enhancement, variational quantum graph convolutions with non-linear dynamics, extraction of higher-order topological invariants, hybrid quantum-classical anomaly learning with adaptive optimization, and interpretable decision-making via topological attribution. Rigorous convergence guarantees ensure stable training on noisy intermediate-scale quantum (NISQ) devices, while stability of topological signatures provides robust fraud detection. Optimized for NISQ hardware with circuit simplifications and graph sampling, the framework scales to large transaction networks. Simulations on financial datasets, such as PaySim and Elliptic, benchmark QTGNN against classical and quantum baselines, using metrics like ROC-AUC, precision, and false positive rate. An ablation study evaluates the contributions of quantum embeddings, topological features, non-linear channels, and hybrid learning. QTGNN offers a theoretically sound, interpretable, and practical solution for financial fraud detection, bridging quantum machine learning, graph theory, and topological analysis.