# Quantum Topological Graph Neural Networks for Detecting Complex Fraud Patterns

arXiv: https://arxiv.org/abs/2512.03696 · HTML: https://mlsanity.com/paper/2512.03696/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 53 references that are in the map.
- First posted on arXiv 3 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [Graph-based Anomaly Detection and Description: A Survey](https://mlsanity.com/paper/1404.4679/) (2014)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [Financial Fraud Detection using Quantum Graph Neural Networks](https://mlsanity.com/paper/2309.01127/) (2023)
- [Graph Neural Networks for Financial Fraud Detection: A Review](https://mlsanity.com/paper/2411.05815/) (2024)
- [Dynamic Fraud Detection: Integrating Reinforcement Learning into Graph Neural Networks](https://mlsanity.com/paper/2409.09892/) (2024)
- [Learning Graph Neural Networks with Positive and Unlabeled Nodes](https://mlsanity.com/paper/2103.04683/) (2021)
- [NCoder -- A Quantum Field Theory approach to encoding data](https://mlsanity.com/paper/2402.00944/) (2024)
- [Detecting Credit Card Fraud via Heterogeneous Graph Neural Networks with Graph Attention](https://mlsanity.com/paper/2504.08183/) (2025)
- [Time Series Embedding Methods for Classification Tasks: A Review](https://mlsanity.com/paper/2501.13392/) (2025)
- [Quantum Machine Learning for Anomaly Detection in Consumer Electronics](https://mlsanity.com/paper/2409.00294/) (2024)
- [Graph Neural Networks on Quantum Computers](https://mlsanity.com/paper/2405.17060/) (2024)
- [PhoGAD: Graph-based Anomaly Behavior Detection with Persistent Homology Optimization](https://mlsanity.com/paper/2401.10547/) (2024)
- [Interpretable Machine Learning for Predicting Startup Funding, Patenting, and Exits](https://mlsanity.com/paper/2510.09465/) (2025)
- [Topological Data Analysis for Unsupervised Anomaly Detection and Customer Segmentation on Banking Data](https://mlsanity.com/paper/2508.14136/) (2025)

## Abstract (arXiv)

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.