Generative Modeling of Quantum Distribution with Functional Flow Matching
This work addresses the challenge of learning quantum distributions for quantum physics and quantum computing, enabling accurate modeling of physical properties.
The paper introduces Quantum Flow Matching (QFM), a generative model that learns quantum distributions by converting density matrices into spin Wigner functions and applying functional flow matching. QFM accurately captures physical properties like trace, purity, and entanglement entropy of multi-qubit quantum states.
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.