  Machine learning (ML) has recently facilitated many advances in solving
problems related to many-body physical systems. Given the intrinsic quantum
nature of these problems, it is natural to speculate that quantum-enhanced
machine learning will enable us to unveil even greater details than we
currently have. With this motivation, this paper examines a quantum machine
learning approach based on shallow variational ansatz inspired by tensor
networks for supervised learning tasks. In particular, we first look at the
standard image classification tasks using the Fashion-MNIST dataset and study
the effect of repeating tensor network layers on ansatz's expressibility and
performance. Finally, we use this strategy to tackle the problem of quantum
phase recognition for the transverse-field Ising and Heisenberg spin models in
one and two dimensions, where we were able to reach $\geq 98\%$ test-set
accuracies with both multi-scale entanglement renormalization ansatz (MERA) and
tree tensor network (TTN) inspired parametrized quantum circuits.
