Wavefunction Flows: Efficient Quantum Simulation of Continuous Flow Models

Continuous flow models transform Gaussian noise into samples from a learned distribution that closely approximates a complex data distribution. We present a natural mapping between these models and a Schrödinger equation, the fundamental equation of quantum mechanics, whose solution is a quantum state encoding the learned distribution. Our main result is that this Schrödinger equation is efficiently solvable on a quantum computer, which we prove by precisely bounding the discretization error. Therefore, given a trained flow model, the theoretical analysis we introduce implies that future quantum computers will enable a fundamentally different—and potentially more powerful—type of access to its learned distribution, which could be used to perform downstream tasks (e.g., Monte Carlo estimation) more efficiently. More broadly, our results reveal a rare close connection between state-of-the-art generative modeling techniques, such as flow matching and diffusion models, and one of the main expected capabilities of quantum computers: simulating quantum mechanics.