Generative Modeling of Quantum Distribution with Functional Flow Matching
2026-07-01 • Machine Learning
Machine Learning
AI summaryⓘ
The authors introduce Quantum Flow Matching (QFM), a new method to help computers learn and generate complex quantum states. They do this by turning quantum information into a special function called the spin Wigner function and then using flow matching to model it. This approach lets their model accurately capture important quantum properties like purity and entanglement. Their results show that QFM can effectively represent multi-qubit quantum systems.
quantum distributionsspin Wigner functionflow matchingdensity matrixmulti-qubit systemstracepurityentanglement entropydeep generative modelsquantum states
Authors
Jaehoon Hahm, Tak Hur, Joonseok Lee, Daniel K. Park
Abstract
The emergence of powerful deep generative models based on diffusion and flow matching has enabled the learning and modeling of complex distributions. Learning quantum distributions, however, remains challenging due to the inherent difficulty of accurately modeling the meaningful physical properties of quantum states. We propose Quantum Flow Matching (QFM), a novel generative model designed to learn quantum distribution by utilizing spin Wigner function and flow matching. By converting density matrix into the spin Wigner function and leveraging functional flow matching to learn distributions in function space, QFM enables accurate and effective learning of multi-qubit quantum distributions. We demonstrate the effectiveness of our method by evaluating physical quantities such as trace, purity, and entanglement entropy of the generated quantum states, accurately capturing the underlying physics of the given quantum distributions.