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 show that these models map naturally to a Schrödinger equation, the fundamental equation of quantum mechanics, whose solution is a quantum state encoding the learned distribution. Moreover, we prove that this Schrödinger equation is efficiently solvable on a quantum computer. Therefore, given a trained flow model, future quantum computers will enable a fundamentally new 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 machine learning techniques, such as flow matching and diffusion models, and one of the main expected capabilities of quantum computers: simulating quantum mechanics. Speaker Bio: David Layden is a Staff Research Scientist at IBM Research in Cambridge, MA. He completed his PhD in Quantum Science and Engineering at MIT in 2020. His research is at the intersection of generative AI and quantum computing, and aims to develop connections between quantum physics and dynamical techniques in AI like diffusion models, Markov chain Monte Carlo etc., to benefit both fields. We plan to record tomorrow's seminar. Please note that if you attend in person or intervene during the talk, we understand that you consent to appearing in the recording. Find seminar details and upcoming talks: https://www.microsoft.com/en-us/research/event/microsoft-research-new-england-generative-modeling-sampling-seminar/