Magnitude Is All You Need? Rethinking Phase in Quantum Encoding of Complex SAR Data

Synthetic Aperture Radar (SAR) data is inherently complex-valued, while quantum machine learning (QML) models operate in complex Hilbert spaces. This similarity suggests that using both the magnitude and phase of SAR data in quantum encoding should help automatic target recognition in SAR images. In this study, we test this assumption by comparing five encoding strategies for quantum models: magnitude-only encoding, joint magnitude-phase encoding, in-phase and quadrature encoding, preprocessed phase encoding, and a purely quantum architecture. All approaches are evaluated under a unified experimental setup on the MSTAR benchmark dataset. Surprisingly, we find that magnitude-only encoding performs better than phase-inclusive encodings in hybrid quantum-classical models. It achieves 99.57 percent accuracy on the 3-class task and 71.19 percent accuracy on the 8-class task, outperforming complex-valued alternatives under the same framework. Adding phase information provides little or no improvement and can sometimes degrade performance. However, in purely quantum models with only 184 to 224 trainable parameters and no classical neural-network layers, phase information becomes much more important, improving accuracy by up to 21.65 percentage points. These findings show that the usefulness of phase information depends not only on the data, but also on the architecture used to process it. Hybrid models can compensate for missing phase information through their classical components, while pure quantum models rely more strongly on phase information for class discrimination. The results provide practical guidance for encoding complex-valued data in quantum machine learning and highlight the importance of jointly designing encoding strategies and model architectures for current quantum systems.