QuGeo: An End-to-end Quantum Learning Framework for Geoscience -- A Case Study on Full-Waveform Inversion

The rapid advancement of quantum computing has generated considerable anticipation for its transformative potential. However, harnessing its full potential relies on identifying "killer applications". In this regard, QuGeo emerges as a groundbreaking quantum learning framework, poised to become a key application in geoscience, particularly for Full-Waveform Inversion (FWI). This framework integrates variational quantum circuits with geoscience, representing a novel fusion of quantum computing and geophysical analysis. This synergy unlocks quantum computing's potential within geoscience. It addresses the critical need for physics-guided data scaling, ensuring high-performance geoscientific analyses aligned with core physical principles. Furthermore, QuGeo's introduction of a quantum circuit custom-designed for FWI highlights the critical importance of application-specific circuit design for quantum computing. In the OpenFWI's FlatVelA dataset experiments, the variational quantum circuit from QuGeo, with only 576 parameters, achieved significant improvement in performance. It reached a Structural Similarity Image Metric (SSIM) score of 0.905 between the ground truth and the output velocity map. This is a notable enhancement from the baseline design's SSIM score of 0.800, which was achieved without the incorporation of physics knowledge.