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

Abstract: Synthetic Aperture Radar (SAR) data is inherently complex-valued, while quantum machine learning (QML) models naturally operate in complex Hilbert spaces. This apparent alignment suggests that incorporating both magnitude and phase information into quantum encoding should improve performance in SAR Automatic Target Recognition (ATR). In this work, we systematically evaluate this assumption by comparing five quantum encoding strategies: magnitude-only, joint complex, I/Q-based, preprocessed phase, and pure quantum, under a unified experimental framework on the MSTAR benchmark dataset. Contrary to expectation, we observe a consistent pattern: in hybrid quantum-classical architectures, magnitude-only encoding outperforms all complex-valued strategies, achieving 99.57% accuracy on a 3-class task and 71.19% on an 8-class task, while phase-aware methods provide negligible (~0%) or negative improvements. In contrast, in purely quantum architectures with only 184-224 trainable parameters and no classical components, phase information becomes essential, contributing up to 21.65% improvement in accuracy. These results reveal that the utility of phase information is not inherent to the data, but depends critically on the model architecture. Hybrid models rely on classical components that compensate for missing phase information, whereas purely quantum models require phase to construct discriminative representations. Our findings provide practical design guidelines for encoding complex-valued data in QML and highlight the importance of encoding-architecture co-design in the NISQ era.