用量子模型辅助预测复杂混沌系统，实现更准更省的长期模拟。
Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantage
- 先用量子模型学小尺度规律，再用经典模型生成时空演化。
- 预测精度提升最高17.25%，全频谱保真度提高29.36%。
- 适合需要高效高精度模拟的流体力学与复杂系统研究者。
我们提出一种量子启发机器学习（QIML）框架，用于建模高维混沌系统的长期行为。QIML结合一次性离线训练的量子生成模型与经典自回归预测器，用于时空场生成。量子模型学习量子先验（Q-Prior），引导对小尺度相互作用的表征，提升细粒度动态建模能力。我们在Kuramoto-Sivashinsky方程、二维柯尔莫哥洛夫流动和三维湍流通道流（作为真实入流条件）上评估QIML。在这些系统中，相比经典基线，QIML将预测分布精度提升最多17.25%，全频谱保真度提升最多29.36%。在湍流通道入流场景中，Q-Prior在超导量子处理器上训练，至关重要：无此先验则预测失稳，而QIML能生成物理一致的长期预测，优于主流偏微分方程求解器。除精度外，QIML还具备内存优势：将数兆字节数据压缩至千字节级的Q-Prior，实现量子资源在科学建模中的可扩展集成。
原文摘要 · Abstract (English)
We introduce a quantum-informed machine learning (QIML) framework for modelling the long-term behaviour of high-dimensional chaotic systems. QIML combines a one-time, offline-trained quantum generative model with a classical autoregressive predictor for spatiotemporal field generation. The quantum model learns a quantum prior (Q-Prior) that guides the representation of small-scale interactions and improves the modelling of fine-scale dynamics. We evaluate QIML on the Kuramoto-Sivashinsky equation, two-dimensional Kolmogorov flow, and the three-dimensional turbulent channel flow used as a realistic inflow condition. Across these systems, QIML improves predictive distribution accuracy by up to 17.25% and full-spectrum fidelity by up to 29.36% relative to classical baselines. For turbulent channel inflow, the Q-Prior is trained on a superconducting quantum processor and proves essential: without it, predictions become unstable, whereas QIML produces physically consistent long-term forecasts that outperform leading PDE solvers. Beyond accuracy, QIML offers a memory advantage by compressing multi-megabyte datasets into a kilobyte-scale Q-Prior, enabling scalable integration of quantum resources into scientific modelling.
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