Quantum Supervised Learning Method for Outlier Detection

As quantum computers become more viable, there have been significant advancements towards adapting classical machine learning techniques and developing new machine learning techniques to a quantum framework. We present a quantum supervised learning method for outlier detection, in which input states are mapped onto a new Hilbert space through non-identity unitary operators.  The circuit parameters are determined iteratively by minimizing the loss between the input and output states. Outlying data can be subsequently detected by calculating the loss between input and output states. We demonstrate its use for outlier detection in three unique cases: (1) clusters of data points, (2) anomalous images, and (3) irregularities in time series data.