Quantum Flow Matching Models Complex Quantum Distributions

The field of deep generative models, particularly those based on diffusion and flow matching, has shown remarkable success in learning and modeling complex data distributions. However, applying these techniques to quantum distributions presents unique challenges due to the intricate physical properties of quantum states. This research addresses this by proposing Quantum Flow Matching (QFM). QFM is a novel generative model specifically designed to learn quantum distributions. Its core innovation lies in converting the density matrix, which describes a quantum state, into a spin Wigner function. This transformation allows the model to then utilize functional flow matching to learn distributions within a function space. The effectiveness of QFM is demonstrated through evaluations of key physical quantities of the generated quantum states, such as trace, purity, and entanglement entropy. The results indicate that QFM accurately captures the underlying physics of the given quantum distributions, making it a promising tool for quantum state engineering and simulation.