基于张量网络的连续时间生成模型的可扩展量子模拟
Scalable quantum simulation of continuous-time generative models via tensor networks
- Sygaldry Technologies, Inc.（西格尔德里技术公司）
- University of Michigan（密歇根大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究将连续时间流模型表示为张量网络，实现了可扩展的量子模拟，大幅降低了存储和演化时间，验证了稀有事件采样的缩放关系，为连续时间生成模型的高效量子模拟提供了新方案。
AI中文摘要：
连续时间流模型和扩散模型广泛应用于计算机视觉、蛋白质折叠等大规模部署场景，也被用于建模语言、时间序列和量子态等新兴领域。训练后，从连续时间模型中推断统计特性成本高昂。波函数流通过将学习到的传输重新表述为幺正演化来降低该成本，其最终玻恩分布近似目标分布，这会制备出相干振幅编码（即量子样本），可由量子算法进行后处理，相比蒙特卡洛采样具有二次优势。我们对这些流开展了首次数值研究，将时变势和态表示为张量网络。在空间维度d=8时，与N^d个点的密集网格相比，存储量降低了约10^7倍；与从测得的d≤5的缩放关系外推得到的基线相比，演化的挂钟时间降低了至少10^3倍。我们通过重现稀有事件采样的O(1/√p_rare)缩放关系验证了我们的流程。
英文摘要：
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.
