Quantum algorithms for anomaly detection using amplitude estimation

Anomaly detection, as an important branch of machine learning, plays a critical role in fraud detection, health care, intrusion detection, military surveillance, etc. An anomaly detection algorithm based on density estimation (called ADDE algorithm) is one of the widely used algorithms. However, the ADDE algorithm is computationally expensive when processing big data sets. To solve this problem, in this paper, we propose an efficient quantum ADDE algorithm based on amplitude estimation. It is shown that our algorithm achieves exponential speedup on the number of training data points M over its classical counterpart. Besides, the idea of our algorithm can be applied to accelerate the anomaly detection algorithm based on kernel principal component analysis (called ADKPCA algorithm), which also has a wide range of applications. Our algorithm shows exponential speedup on M compared with its classical counterpart.