  Circuit design for quantum machine learning remains a formidable challenge.
Inspired by the applications of tensor networks across different fields and
their novel presence in the classical machine learning context, one proposed
method to design variational circuits is to base the circuit architecture on
tensor networks. Here, we comprehensively describe tensor-network quantum
circuits and how to implement them in simulations. This includes leveraging
circuit cutting, a technique used to evaluate circuits with more qubits than
those available on current quantum devices. We then illustrate the
computational requirements and possible applications by simulating various
tensor-network quantum circuits with PennyLane, an open-source python library
for differential programming of quantum computers. Finally, we demonstrate how
to apply these circuits to increasingly complex image processing tasks,
completing this overview of a flexible method to design circuits that can be
applied to industrially-relevant machine learning tasks.
