  Quantum machine learning (QML) networks promise to have some computational
(or quantum) advantage for classifying supervised datasets (e.g., satellite
images) over some conventional deep learning (DL) techniques due to their
expressive power via their local effective dimension. There are, however, two
main challenges regardless of the promised quantum advantage: 1) Currently
available quantum bits (qubits) are very small in number, while real-world
datasets are characterized by hundreds of high-dimensional elements (i.e.,
features). Additionally, there is not a single unified approach for embedding
real-world high-dimensional datasets in a limited number of qubits. 2) Some
real-world datasets are too small for training intricate QML networks. Hence,
to tackle these two challenges for benchmarking and validating QML networks on
real-world, small, and high-dimensional datasets in one-go, we employ quantum
transfer learning composed of a multi-qubit QML network, and a very deep
convolutional network (a with VGG16 architecture) extracting informative
features from any small, high-dimensional dataset. We use real-amplitude and
strongly-entangling N-layer QML networks with and without data re-uploading
layers as a multi-qubit QML network, and evaluate their expressive power
quantified by using their local effective dimension; the lower the local
effective dimension of a QML network, the better its performance on unseen
data. Our numerical results show that the strongly-entangling N-layer QML
network has a lower local effective dimension than the real-amplitude QML
network and outperforms it on the hard-to-classify three-class labelling
problem. In addition, quantum transfer learning helps tackle the two challenges
mentioned above for benchmarking and validating QML networks on real-world,
small, and high-dimensional datasets.
