FiD-QAE: A Fidelity-Driven Quantum Autoencoder for Credit Card Fraud Detection

TL;DR

This work tackles credit card fraud detection under extreme data imbalance by introducing FiD-QAE, a fidelity-driven quantum autoencoder that encodes transactions via amplitude encoding, compresses them with a variational encoder, and uses a SWAP-test fidelity criterion to detect anomalies. The model optimizes a fidelity-based objective and classifies fraud through a threshold on the measured fidelity, demonstrating strong accuracy and robust performance across imbalanced and noisy conditions. Key contributions include a scalable 4-qubit encoder design, extensive simulations and hardware experiments on IBM backends, and a thorough analysis of noise robustness, threshold effects, and cross-dataset generalization. The results show that quantum fidelity provides a powerful, noise-tolerant criterion for anomaly detection, positioning FiD-QAE as a practical near-term quantum solution for financial fraud detection and a stepping stone for future QAEs in finance.

Abstract

Credit card fraud detection is a critical task in financial security, as fraudulent transactions are rare, highly imbalanced, and often resemble legitimate ones. A wide range of classical machine learning methods, as well as more recent quantum machine learning approaches, have been investigated to address this challenge, each providing valuable progress but also leaving open questions regarding scalability, robustness, and adaptability to evolving fraud patterns. In this work, we introduce the Fidelity-based Quantum Autoencoder (FiD-QAE), a quantum architecture that employs fidelity estimation as the decision criterion for anomaly detection. Transactions are encoded into quantum states, compressed through a variational quantum circuit, and evaluated using the SWAP test to distinguish legitimate from fraudulent transactions. We conduct a comprehensive evaluation of FiD-QAE, including statistical analyses, multiple performance metrics, and robustness tests under quantum noise models. The results show that FiD-QAE maintains consistent performance across different imbalance levels and preserves robustness in noisy conditions. Moreover, validation on IBM Quantum hardware backends confirms the feasibility of our approach on real devices, with outcomes consistent with simulation. These findings position quantum fidelity as a powerful criterion for anomaly detection and highlight FiD-QAE as a promising direction that complements existing classical and quantum approaches, offering robustness and generalizability for financial fraud detection in realistic environments.

Figures (18)

• Figure 1: Motivational flow illustrating the reasoning from data imbalance challenges to our proposed FiD-QAE architecture. The process begins with the difficulty of detecting rare and diverse fraud patterns under highly imbalanced datasets, moves through the limitations of existing quantum autoencoders that rely on reconstruction-based detection and exhibit instability, noise sensitivity, and metric imbalance, and culminates in our proposed approach (FiD-QAE), which employs fidelity-driven encoding and SWAP-test evaluation to achieve stable, quantum-consistent anomaly detection and robustness under noise using an efficient 4-qubit design.
• Figure 2: Graphical representation of a classical autoencoder. The encoder compresses the input data into a lower-dimensional latent space, and the decoder reconstructs the input to approximate the original data as closely as possible.
• Figure 3: Block diagram of the QAE. The model processes four input states, encodes them into two compressed latent states and two trash states, and reconstructs the original four states at the output.
• Figure 4: Block diagram of the QAE training process. The objective is to optimize the parameters $\vec{p}$ such that the average fidelity $F\left(\ket{\psi_i}, \rho_i^{\text{out}}\right)$ is maximized.
• Figure 5: SWAP test circuit. The circuit uses a control qubit (qubit 0) initialized with a Hadamard gate, a reference state (qubit 1), a trash state (qubit 2), and a compressed state (qubit 3) to evaluate the fidelity between quantum states.