Quantum Meets SAR: An End-to-End Quantum Implementation of the Range-Doppler Algorithm

Synthetic Aperture Radar (SAR) is a critical remote sensing technology widely used for Earth observation, but the processing of high-resolution SAR raw data remains computationally demanding on classical computing architectures. As quantum computing hardware and algorithms continue to advance, they offer a promising paradigm for accelerating computationally intensive signal processing tasks, motivating the development of quantum-native SAR image formation methods.

In our earlier work, we introduced a quantum implementation of Range Cell Migration Correction (RCMC), a critical stage of the Range-Doppler Algorithm (RDA). Building on that foundation, this paper presents a complete quantum realization of the RDA for SAR image formation. We introduce a dedicated quantum circuit architecture based on amplitude encoding, enabling efficient representation of complex SAR raw data within a quantum state space. The proposed framework performs the principal stages of the RDA entirely in the quantum domain, employing Quantum Fourier Transforms (QFTs) for spatial-frequency transformations and specialized diagonal unitary operators for range compression, RCMC, and azimuth compression.

To validate the proposed methodology, the architecture is simulated using the Qiskit Aer statevector simulator on a representative 4×4 SAR raw data matrix. The results demonstrate the successful execution of the complete processing chain, including all quantum phase operations and frequency-domain transformations. The recovered processed state exhibits mathematical consistency with the expected outcome of classical SAR focusing, confirming the correctness and feasibility of the proposed implementation.

By extending a quantum realization of a single RDA component to a complete end-to-end quantum SAR focusing pipeline, this work establishes a rigorous framework for translating classical SAR image formation algorithms into their quantum equivalents. These results provide a foundation for future scalable quantum SAR processing systems and next-generation Earth observation applications.