  Several variational quantum circuit approaches to machine learning have been
proposed in recent years, with one promising class of variational algorithms
involving tensor networks operating on states resulting from local feature
maps. In contrast, a random feature approach known as quantum kitchen sinks
provides comparable performance, but leverages non-local feature maps. Here we
combine these two approaches by proposing a new circuit ansatz where a tree
tensor network coherently processes the non-local feature maps of quantum
kitchen sinks, and we run numerical experiments to empirically evaluate the
performance of the new ansatz on image classification. From the perspective of
classification performance, we find that simply combining quantum kitchen sinks
with tensor networks yields no qualitative improvements. However, the addition
of feature optimization greatly boosts performance, leading to state-of-the-art
quantum circuits for image classification, requiring only shallow circuits and
a small number of qubits -- both well within reach of near-term quantum
devices.
