Quantum Fourier transform and its application in synthetic aperture radar image processing

Abstract

Synthetic Aperture Radar (SAR) has played an important role in Earth observation, with applications in disaster monitoring, agriculture, forestry, ice surveillance, defense, and planetary exploration. The reconstruction of SAR images is a costly operation that uses Fourier Transform, while quantum computing has some key advantages that potentially enhance the algorithm to make it faster. Therefore, in the first part of the thesis, a major image processing method used in SAR systems is studied, known as the Range Doppler Algorithm (RDA). RDA is implemented on a simulated data set and a real data set from ICEYE Oy. In the second half of the thesis, quantum computing basic is studied and reviewed, including qubits, 1-qubit gate and 2-qubits gates, as well as the Quantum Fourier Transform (QFT) that are specific to replace the classical Fourier Transform. A framework for implementing the Range Doppler Algorithm (RDA) on a quantum computer, referred to as the Quantum Range Doppler Algorithm (QRDA), is proposed. In addition, the required resources under ideal quantum-computing assumptions are analyzed, including time complexity (algorithmic scaling) and space complexity (the number of qubits required). Lastly, the potential applicability of the proposed. QRDA in the context of current quantum device, Noisy Intermediate-Scale Quantum (NISQ) machine, is discussed.