Quantum Transfer Learning for Real-World, Small, and High-Dimensional Remotely Sensed Datasets
Soronzonbold Otgonbaatar, Gottfried Schwarz, Mihai Datcu, Dieter Kranzlmüller
Abstract
Quantum Machine Learning (QML) models 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 ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> 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 comprising a classical VGG16 layer and a multi-qubit QML layer. We use real-amplitude and strongly-entangling N-layer QML networks with and without data re-uploading layers as a multi-qubit QML layer, 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. As datasets, we utilize Eurosat and synthetic datasets ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> easy-to-classify datasets), and an UC Merced Land Use dataset ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> a hard-to-classify 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 datasets. 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.