Quantum machine learning for quantum anomaly detection

TL;DR

This paper develops quantum algorithms for anomaly detection in quantum data, leveraging quantum machine learning techniques like kernel PCA and one-class SVM, with resource efficiency suitable for large-scale quantum datasets.

Contribution

It introduces quantum versions of classical anomaly detection algorithms that operate with logarithmic resources, enabling scalable quantum data analysis.

Findings

Quantum algorithms for anomaly detection can be performed with logarithmic resources.

Resources are logarithmic in the dimension of quantum states and training data size for pure states.

Algorithms are suitable for large quantum datasets due to their efficiency.

Abstract

Anomaly detection is used for identifying data that deviate from `normal' data patterns. Its usage on classical data finds diverse applications in many important areas like fraud detection, medical diagnoses, data cleaning and surveillance. With the advent of quantum technologies, anomaly detection of quantum data, in the form of quantum states, may become an important component of quantum applications. Machine learning algorithms are playing pivotal roles in anomaly detection using classical data. Two widely-used algorithms are kernel principal component analysis and one-class support vector machine. We find corresponding quantum algorithms to detect anomalies in quantum states. We show that these two quantum algorithms can be performed using resources logarithmic in the dimensionality of quantum states. For pure quantum states, these resources can also be logarithmic in the number of quantum states used for training the machine learning algorithm. This makes these algorithms potentially applicable to big quantum data applications.