Seismic inversion using hybrid quantum neural networks

Seismic inversion-including post-stack, pre-stack, and full waveform inversion is compute and memory-intensive. Recently, several approaches, including physics-informed machine learning, have been developed to address some of these limitations. Motivated by the potential of quantum computing, we report on our attempt to map one such classical physics-informed algorithm to a quantum framework. The primary goal is to investigate the technical challenges of this mapping, given that quantum algorithms rely on computing principles fundamentally different from those in classical computing. Quantum computers operate using qubits, which exploit superposition and entanglement, offering the potential to solve classically intractable problems. While current quantum hardware is limited, hybrid quantum-classical algorithms-particularly in quantum machine learning (QML)-demonstrate potential for near-term applications and can be readily simulated. We apply QML to subsurface imaging through the development of a hybrid quantum physics-informed neural network (HQ-PINN) for post-stack and pre-stack seismic inversion. The HQ-PINN architecture adopts an encoder-decoder structure: a hybrid quantum neural network encoder estimates P- and S-impedances from seismic data, while the decoder reconstructs seismic responses using geophysical relationships. Training is guided by minimizing the misfit between the input and reconstructed seismic traces. We systematically assess the impact of quantum layer design, differentiation strategies, and simulator backends on inversion performance. We demonstrate the efficacy of our approach through the inversion of both synthetic and the Sleipner field datasets. The HQ-PINN framework consistently yields accurate results, showcasing quantum computing's promise for geosciences and paving the way for future quantum-enhanced geophysical workflows.