将经典流匹配拓展到量子领域，实现密度矩阵高效生成与采样。
Quantum Flow Matching
- 用量子电路实现量子流匹配，直接生成目标态密度矩阵。
- 可在不重设计电路下完成磁化、纠缠熵等目标态生成与自由能估算。
- 适合研究量子系统中的生成建模、非平衡统计与超扩散现象。
流匹配已成为经典生成建模的主流范式，能高效地在两个复杂分布间进行插值。本文将其拓展至量子领域，提出量子流匹配（Quantum Flow Matching, QFM），一种基于量子电路的实现方式，可高效地在两个密度矩阵间进行插值。QFM支持密度矩阵的系统性制备和样本生成，用于准确估计可观测量，且可在量子计算机上实现而无需代价高昂的电路重设计。我们在多个应用中验证了其通用性：(i) 生成具有指定磁化和纠缠熵的目标态；(ii) 估算非平衡自由能差以检验量子Jarzynski等式；(iii) 加速超扩散现象的研究。这些结果表明，QFM是跨量子系统生成建模的统一且有前景的框架。
原文摘要 · Abstract (English)
The flow matching has rapidly become a dominant paradigm in classical generative modeling, offering an efficient way to interpolate between two complex distributions. We extend this idea to the quantum realm and introduce the Quantum Flow Matching (QFM), a quantum-circuit realization that offers efficient interpolation between two density matrices. QFM offers systematic preparation of density matrices and generation of samples for accurately estimating observables, and can be realized on quantum computers without the need for costly circuit redesigns. We validate its versatility on a set of applications: (i) generating target states with prescribed magnetization and entanglement entropy, (ii) estimating nonequilibrium free-energy differences to test the quantum Jarzynski equality, and (iii) expediting the study on superdiffusion. These results position QFM as a unifying and promising framework for generative modeling across quantum systems.
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