  Quantum machine learning (QML) is a rapidly growing area of research at the
intersection of classical machine learning and quantum information theory. One
area of considerable interest is the use of QML to learn information contained
within quantum states themselves. In this work, we propose a novel approach in
which the extraction of information from quantum states is undertaken in a
classical representational-space, obtained through the training of a hybrid
quantum autoencoder (HQA). Hence, given a set of pure states, this variational
QML algorithm learns to identify, and classically represent, their essential
distinguishing characteristics, subsequently giving rise to a new paradigm for
clustering and semi-supervised classification. The analysis and employment of
the HQA model are presented in the context of amplitude encoded states - which
in principle can be extended to arbitrary states for the analysis of structure
in non-trivial quantum data sets.
