  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.
