Unsupervised Quantum Anomaly Detection on Noisy Quantum Processors

Abstract: Whether in fundamental physics, cybersecurity or finance, the detection of anomalies with machine learning techniques is a highly relevant and active field of research, as it potentially accelerates the discovery of novel physics or criminal activities. We provide a systematic analysis of the generalization properties of the One-Class Support Vector Machine (OCSVM) algorithm, using projected quantum kernels for a realistic dataset of the latter application. These results were both theoretically simulated and experimentally validated on trapped-ion and superconducting quantum processors, by leveraging partial state tomography to obtain precise approximations of the quantum states that are used to estimate the quantum kernels. Moreover, we analyzed both platforms respective hardware-efficient feature maps over a wide range of anomaly ratios and showed that for our financial dataset in all anomaly regimes, the quantum-enhanced OCSVMs lead to better generalization properties compared to the purely classical approach. As such our work bridges the gap between theory and practice in the noisy intermediate scale quantum (NISQ) era and paves the path towards useful quantum applications.