Natural Embedding of the Stokes Parameters of Polarimetric Synthetic Aperture Radar Images in a Gate-Based Quantum Computer

Quantum algorithms are designed to process quantum data (quantum bits) in a gate-based quantum computer. They are proven rigorously that they reveal quantum advantages over conventional algorithms when their inputs are certain quantum data or some classical data mapped to quantum data. However, in a practical domain, data are classical in nature, and they are very big in dimension, size, and so on. Hence, there is a challenge to map (embed) classical data to quantum data, and even no quantum advantages of quantum algorithms are demonstrated over conventional ones when one processes the mapped classical data in a gate-based quantum computer. For the practical domain of earth observation (EO), due to the different sensors on remote-sensing platforms, we can map directly some types of EO data to quantum data. In particular, we have polarimetric synthetic aperture radar (PolSAR) images characterized by polarized beams. A polarized state of the polarized beam and a quantum bit are the Doppelganger of a physical state. We map them to each other, and we name this direct mapping a natural embedding, otherwise an artificial embedding. Furthermore, we process our naturally embedded data in a gate-based quantum computer by using a quantum algorithm regardless of its quantum advantages over conventional techniques; namely, we use the QML network as a quantum algorithm to prove that we naturally embedded our data in input qubits of a gate-based quantum computer. Therefore, we employed and directly processed PolSAR images in a QML network. Furthermore, we designed and provided a QML network with an additional layer of a neural network, namely, a hybrid quantum-classical network, and demonstrate how to program (via optimization and backpropagation) this hybrid quantum-classical network when employing and processing PolSAR images. In this work, we used a gate-based quantum computer offered by an IBM Quantum and a classical simulator for a gate-based quantum computer. Our contribution is that we provided very specific EO data with a natural embedding feature, the Doppelganger of quantum bits, and processed them in a hybrid quantum-classical network. More importantly, in the future, these PolSAR data can be processed by future quantum algorithms and future quantum computing platforms to obtain (or demonstrate) some quantum advantages over conventional techniques for EO problems.