arXiv2025
A fundamental limitation of probabilistic deep learning is its predominant reliance on Gaussian priors. This simplistic assumption prevents models from accurately capturing the complex, non-Gaussian landscapes of natural data, particularly in demanding domains like complex biological data, severely hindering the fidelity of the model for scientific discovery. The physically-grounded Boltzmann distribution offers a more expressive alternative, but it is computationally intractable on classical computers. To date, quantum approaches have been hampered by the insufficient qubit scale and operational stability required for the iterative demands of deep learning. Here, we bridge this gap by introducing the Quantum Boltzmann Machine-Variational Autoencoder (QBM-VAE), a large-scale and long-time stable hybrid quantum-classical architecture. Our framework leverages a quantum processor for efficient sampling from the Boltzmann distribution, enabling its use as a powerful prior within a deep generative model. Applied to million-scale single-cell datasets from multiple sources, the QBM-VAE generates a latent space that better preserves complex biological structures, consistently outperforming conventional Gaussian-based deep learning models like VAE and SCVI in essential tasks such as omics data integration, cell-type classification, and trajectory inference. It also provides a typical example of introducing a physics priori into deep learning to drive the model to acquire scientific discovery capabilities that breaks through data limitations. This work provides the demonstration of a practical quantum advantage in deep learning on a large-scale scientific problem and offers a transferable blueprint for developing hybrid quantum AI models.