  We demonstrate the implementation of a novel machine learning framework for
probability density estimation and classification using quantum circuits. The
framework maps a training data set or a single data sample to the quantum state
of a physical system through quantum feature maps. The quantum state of the
arbitrarily large training data set summarises its probability distribution in
a finite-dimensional quantum wave function. By projecting the quantum state of
a new data sample onto the quantum state of the training data set, one can
derive statistics to classify or estimate the density of the new data sample.
Remarkably, the implementation of our framework on a real quantum device does
not require any optimisation of quantum circuit parameters. Nonetheless, we
discuss a variational quantum circuit approach that could leverage quantum
advantage for our framework.
