  We describe a quantum-assisted machine learning (QAML) method in which
multivariate data is encoded into quantum states in a Hilbert space whose
dimension is exponentially large in the length of the data vector. Learning in
this space occurs through applying a low-depth quantum circuit with a tree
tensor network (TTN) topology, which acts as an unsupervised feature extractor
to identify the most relevant quantum states in a data-driven fashion. This
unsupervised feature extractor then feeds a supervised linear classifier and
encodes the output in a small-dimensional quantum register. In contrast to
previous work on \emph{quantum-inspired} TTN classifiers, in which the
embedding map and class decision weights did not map the data to well-defined
quantum states, we present an approach that can be implemented on gate-based
quantum computing devices. In particular, we identify an embedding map with
accuracy similar to exponential machines (Novikov \emph{et al.},
arXiv:1605.03795), but which produces valid quantum states from classical data
vectors, and utilize manifold-based gradient optimization schemes to produce
isometric operations mapping quantum states to a register of qubits defining a
class decision. We detail methods for efficiently obtaining one- and two-point
correlation functions of the decision boundary vectors of the quantum model,
which can be used for model interpretability, as well as methods for obtaining
classifications from partial data vectors. Further, we show that the use of
isometric tensors can significantly aid in the human interpretability of the
correlation functions extracted from the decision weights, and may produce
models that are less susceptible to adversarial perturbations. We demonstrate
our methodologies in applications utilizing the MNIST handwritten digit dataset
and a multivariate timeseries dataset of human activity recognition.
