Quantum Principal Component Analysis for Financial Fraud Detection

Among quantum machine learning applications anomaly detection has garnered significant attention due to its critical role in cybersecurity and financial fraud analysis. While prior research has proposed high-level quantum algorithms, most lack circuit-level implementations suitable for fault-tolerant quantum machines, limiting their practical viability. We present a complete quantum circuit design for an anomaly detection algorithm based on principal component analysis. We derive closed-form expressions for qubits count, circuit depth, gate count, T-depth, and T-count, of each quantum subroutine involved. We apply our implementation to financial fraud detection using a real-world dataset of approximately 10^6 samples with 20 features, and provide asymptotic resource estimates. Our analysis confirms logarithmic scaling in circuit depth with respect to the number of training samples and feature dimensions, achieving an exponential speed-up over the classical anomaly detection algorithm.