用函数流匹配生成量子态，精准还原物理特性。
Generative Modeling of Quantum Distribution with Functional Flow Matching
- 基于自旋威格纳函数与函数流匹配建模量子分布
- 生成态在迹、纯度和纠缠熵上准确复现物理特性
- 适合量子信息研究者用于高维量子态生成
基于扩散与流匹配的深度生成模型已能学习复杂分布。然而，由于难以精确建模量子态的物理性质，学习量子分布仍具挑战。本文提出量子流匹配（QFM），通过将密度矩阵转换为自旋威格纳函数，并利用函数流匹配在函数空间中学习分布，实现对多量子比特量子分布的精准有效建模。我们通过迹、纯度和纠缠熵等物理量评估生成态，验证了方法能准确捕捉给定量子分布的底层物理特性。
原文摘要 · Abstract (English)
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.
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