  Generative modeling is an unsupervised machine learning framework, that
exhibits strong performance in various machine learning tasks. Recently we find
several quantum version of generative model, some of which are even proven to
have quantum advantage. However, those methods are not directly applicable to
construct a generative model for learning a set of quantum states, i.e.,
ensemble. In this paper, we propose a quantum generative model that can learn
quantum ensemble, in an unsupervised machine learning framework. The key idea
is to introduce a new loss function calculated based on optimal transport loss,
which have been widely used in classical machine learning due to its several
good properties; e.g., no need to ensure the common support of two ensembles.
We then give in-depth analysis on this measure, such as the scaling property of
the approximation error. We also demonstrate the generative modeling with the
application to quantum anomaly detection problem, that cannot be handled via
existing methods. The proposed model paves the way for a wide application such
as the health check of quantum devices and efficient initialization of quantum
computation.
