Quantum Transfer Learning for Real-World, Small, and High-Dimensional Datasets

—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). Addi- tionally, 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 bench- marking 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. Therefore, we first compute the local effective dimension of these QML networks on Eurosat and synthetic datasets, because we can encode these datasets efficiently in a few qubits, and their local effective dimension should correlate with their classification performance. To validate this correlation, we then benchmarked and trained the QML networks via quantum transfer learning on the real-world, small, and high-dimensional three-class labelling problem (i.e., hard-to-classify images) of a UC Merced Land Use dataset, (a dense residential , medium residential , and sparse residential area image recognition and labelling problem), because this three-class dataset meets the two challenges mentioned above: 1) its data points are characterized by 256 × 256 × 3 elements (i.e., a high-dimensional image), and 2) this dataset consists of only 288 image scenes (i.e., a small dataset). 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.