We introduce a quantum-informed machine learning (QIML) framework for the long-term dynamical behavior of high-dimensional chaotic systems. The method 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 modeling of fine-scale dynamics. We evaluate QIML on three representative systems: the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and a cross-section of fully developed three-dimensional turbulent channel flow used as a realistic inflow condition. Compared to the classical baseline, QIML yields up to 17.25% improvement in predictive distribution accuracy and a 29.36% improvement in the fidelity of the predicted full energy spectrum. For turbulent channel inflow, the Q-Prior is essential: without it, the model fails to evolve in time, while QIML produces stable, physically consistent forecasts that surpass leading machine learning models for PDEs, including the Fourier Neural Operator and Markov Neural Operator, whose errors diverge. Beyond accuracy, QIML also achieves a memory advantage, compressing multi-megabyte datasets into a kilobyte-scale Q-Prior that captures only the invariant measure needed to guide the classical model, thus circumventing Holevo's bound by avoiding full data reconstruction. Our findings provide a practical and scalable pathway for integrating the advantages brought by quantum devices into large-scale scientific, engineering modeling and simulation.
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