Putting machine learning to the test in a quantum many-body system

Abstract Quantum many-body systems pose a formidable computational challenge due to the exponential growth of their Hilbert space. While deep learning (DL) has shown promise as an alternative paradigm, many applications in these systems are still to mature further, beyond the proof-of-concept stages of energy estimation at the lower end of the spectrum. Here, we extend DL beyond this frontier by extensively testing HubbardNet , a deep neural network architecture for the Bose–Hubbard model. Pushing improvements in the optimizer and learning rates, and introducing physics-informed output activations that can resolve extremely small wave-function amplitudes, we achieve ground-state energy errors reduced by orders of magnitude and wave-function fidelities exceeding 99%. We further assess physical relevance by analyzing generalized inverse participation ratios and multifractal dimensions for ground and excited states in one and two dimensions, demonstrating that optimized DL models reproduce localization, delocalization, and multifractality trends across the spectrum. Crucially, these qualitative predictions remain robust across four decades of the interaction strength, e.g. spanning across superfluid, Mott-insulating, as well as quantum chaotic regimes. Together, these results suggest DL as a viable qualitative predictor of many-body structure, complementing the quantitative strengths of exact diagonalization and tensor-network methods.