Generative Modeling of Quantum Distribution with Functional Flow Matching

2026-06-30

AI Summary

Accurately modeling the quantum distribution of multi-qubit systems and key physical quantities—such as trace, purity, and entanglement entropy—remains challenging. This work introduces functional flow matching into quantum state generation for the first time, representing density matrices via spin Wigner functions and constructing a deep generative model in function space. The proposed approach effectively preserves and learns the intrinsic physical properties of quantum states, yielding generated states whose trace, purity, and entanglement entropy closely match those of the true distribution. These results demonstrate the method’s accuracy and efficacy in capturing essential quantum features.

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.

Problem

• quantum distribution
• generative modeling
• quantum states
• physical properties
• multi-qubit systems

Innovation

• Quantum Flow Matching
• spin Wigner function
• functional flow matching
• quantum state generation
• multi-qubit distribution