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.

该研究探讨了在量子技术方面，异常探测的重要性并提出了通过机器学习算法（如核主成分分析和一类支持向量机）来实现异常探测。在底层量子逻辑上寻找对应的量子算法，并证明了这两个量子算法的资源需求可以对量子状态的维数以及用于训练机器学习算法的量子状态数量取对数。这使得这些算法可用于处理大规模的量子数据。