用张量网络加速连续时间生成模型的量子模拟，大幅降低存储与计算开销。
Scalable quantum simulation of continuous-time generative models via tensor networks
- 将时变势能和态表示为张量网络，实现高效量子模拟
- 在8维空间下存储需求减少约10^7倍，耗时降低超1000倍
- 适合研究量子机器学习与稀有事件采样等前沿领域
连续时间流模型与扩散模型广泛应用于计算机视觉、蛋白质折叠、语言建模、时间序列及量子态模拟等领域。训练后从连续时间模型推断统计特性成本高昂。波函数流通过将学习到的传输过程重构为酉演化，其最终的玻恩分布近似目标分布，从而准备出可被量子算法后处理的相干幅值编码（量子样本），相比蒙特卡洛采样具有二次加速优势。本文首次对这类流模型进行数值研究，将时变势能与状态表示为张量网络。在空间维度d=8时，存储量较N^d密集网格降低约10^7倍，演化墙钟时间比基于d≤5数据外推的基线降低超过10^3倍。通过重现稀有事件采样中O(1/√p_rare)的缩放规律，验证了管道的有效性。
原文摘要 · Abstract (English)
Continuous-time flow and diffusion models are widely used across many application domains, from large-scale deployment in computer vision and protein folding to emerging adoption for modeling language, time series, and quantum states. After training, inferring statistical properties from continuous-time models is costly. Wavefunction flows target this cost by recasting learned transport as unitary evolution, whose final Born distribution approximates the target distribution. This prepares a coherent amplitude encoding (a qsample) that can be post-processed by quantum algorithms offering a quadratic advantage over Monte Carlo sampling. We present the first numerical study of these flows, in which we represent time-dependent potentials and states as tensor networks. At spatial dimension $d=8$, storage falls by $\sim 10^7\times$ relative to the dense grid of $N^d$ points, and evolution wall-clock time falls by $\gtrsim 10^3\times$ against a baseline extrapolated from the measured $d\le 5$ scaling. We validate our pipeline by reproducing the $O(1/\sqrt{p_{\rm rare}})$ scaling of rare-event sampling.
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