QuSAE: Quantum Structure-aware amplitude encoding with improved fidelity-complexity trade-off

Efficiently loading classical data into quantum states is a prerequisite for translating the potential advantages of quantum computing into practical data-intensive applications. Yet exact amplitude encoding of generic data can require exponentially many gates, which is beyond the reach of current quantum devices. Approximate amplitude encoding alleviates this overhead by trading state fidelity for representation complexity. However, most existing methods treat the target state generically from a quantum perspective, overlooking structural regularities inherent in real-world data that could be exploited to achieve more efficient encoding. To address this gap, we propose a multiscale Quantum Structure-Aware Amplitude Encoding (QuSAE) framework, which exploits the intrinsic multiscale organization of classical data to guide structured sparsification and efficient tensorization for approximate state preparation. This enables explicit control over approximation fidelity while reducing representation complexity. Comprehensive experiments across five benchmark datasets demonstrate that QuSAE exhibits favorable fidelity–complexity trade-off over competing methods, while preserving multiscale information in the resulting compact representations. More broadly, our results highlight structure-aware state construction as a general design principle for efficient quantum data encoding.