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arXiv:2507.19861 · Science Advances

Quantum-informed machine learning for predicting spatiotemporal chaos with practical quantum advantage

Maida Wang, Xue Xiao, Mingyang Gao, Peter V. Coveney

Published Apr 17, 2026• 2 citations
arXivHTMLPDF

Abstract

We introduce a quantum-informed machine learning (QIML) framework for modeling the long-term behavior 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 modeling 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 partial differential equation solvers. Beyond accuracy, QIML offers a memory advantage by compressing multimegabyte datasets into a kilobyte-scale Q-Prior, enabling scalable integration of quantum resources into scientific modeling.

DOI
10.1126/sciadv.aec5049

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We introduce a quantum-informed machine learning (QIML) framework for modeling the long-term behavior 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 modeling 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 partial differential equation solvers. Beyond accuracy, QIML offers a memory advantage by compressing multimegabyte datasets into a kilobyte-scale Q-Prior, enabling scalable integration of quantum resources into scientific modeling.
Accurately predicting turbulent flows remains a central challenge in fluid dynamics due to their high dimensionality and intrinsic nonlinearity. Recent developments in quantum algorithms and machine learning offer new opportunities for overcoming the computational barriers inherent in turbulence modeling. Here we present a new hybrid quantum-classical framework that enables faster-than-real-time turbulence prediction by integrating machine learning, quantum computation, and fluid dynamics modeling, in particular, the reduced-order modeling. The novel framework combines quantum proper orthogonal decomposition (QPOD) with a quantum-enhanced deep kernel learning (QDKL) approach. QPOD employs quantum circuits to perform efficient eigenvalue decomposition for low-rank flow reconstruction, while QDKL exploits quantum entanglement and nonlinear mappings to enhance kernel expressivity and dynamic prediction accuracy. The new method is demonstrated on three benchmark turbulent flows, our architecture achieves significantly improved predictive accuracy at reduced model ranks, with training speeds up to 10 times faster and parameter counts reduced by a factor of 1/N compared to classical counterparts, where N is the input dimensionality. Although constrained by current noisy intermediate-scale quantum (NISQ) hardware, our results demonstrate the potential of quantum machine learning to transform turbulence simulation and lay a solid foundation for scalable, real-time quantum fluid modeling in future quantum computers.
Accurate financial volatility forecasting is crucial but challenged by the non-linear, highly correlated nature of market data. Recently, quantum computing has emerged as a promising paradigm for solving complex high-dimensional sampling problems. To harness this, we propose a novel hybrid framework combining the temporal representation power of classical neural networks with the distribution-learning capabilities of quantum models. Specifically, we integrate a Long Short-Term Memory (LSTM) network with a Quantum Circuit Born Machine (QCBM). The LSTM extracts dynamic features, while the QCBM acts as a learnable generative prior modeling complex market distributions to guide forecasting. Evaluated on 5-minute high-frequency data from the SSE Composite and CSI 300 indices, our model significantly outperforms a classical LSTM baseline across MSE, RMSE, and QLIKE metrics. Furthermore, by introducing a stochastic ``Drop-Prior" mechanism during training, the LSTM implicitly distills structured information from the quantum prior. This establishes a pragmatic paradigm of ``quantum-assisted training with classical-efficient inference", whereby the model retains its quantum-enhanced accuracy even when the quantum module is entirely disabled during deployment. This demonstrates a practical pathway for leveraging quantum computing to enhance classical models without real-time quantum inference latency.
Long-horizon prediction of a chaotic system is governed by fidelity to its invariant measure, and which parts of that measure a learned predictor needs is a physical question not known in advance. We establish a quantum statistical memory advantage for interrogating it. A quantum statistical prior (Q-Prior), trained once on classical data, stores an efficiently preparable kkk-point marginal in polynomially many circuit parameters against exponentially many for explicit tabulation. Collective Bell measurements on two copies then estimate any post hoc Pauli-expectation magnitude at a copy cost independent of register size, with a worst-case exponential separation from single-copy protocols. A single Bell dataset supports an entire family of candidate observables at a cost growing only logarithmically in the family size, so an exponentially large candidate space stays open for later analysis. We implement the protocol on IQM superconducting processors with two-copy registers of up to 54 physical-qubit chips. We apply this to turbulent channel flow and ERA5 forecasting, resolving invariant structure by statistical sector and order. Turbulent phase correlations persist through eighth order, while most predictive gains arise from low-order constraints; in ERA5, planetary-wave phase coherence complements covariance regularisation, identifying distinct low-order sectors with predictive value. Quantum statistical memory is therefore both a near-term computational resource and an instrument for identifying which invariant structures matter for prediction.
Machine-learning surrogates of physical systems face a paradox: explainable models facing the challenge of expressivity to capture complex nonlinear flows, whereas expressive deep surrogates match high-fidelity simulations only through massive parameterisations that turn the learned dynamics into a black box. Here, we introduce quantum-compressed machine learning (QCML), which resolves this tension by compressing the latent propagator of a flow surrogate from 524,288524{,}288524,288 trainable parameters to no more than 888. This parameter reduction brings the learned dynamical law to the parameter scale of a physical constitutive relation rather than a black-box neural network, making the surrogate directly interpretable and controllable without sacrificing expressivity. The compression is realised by a structured quantum circuit whose unitary propagator constrains the latent spectrum to the unit circle exactly and by construction, replacing exponential error growth with linear accumulation over autoregressive rollouts. Classical regularisation only approximates this constraint: even a quantum-inspired classical baseline penalised towards unitarity collapses within one Lyapunov time on turbulent channel flow, whereas QCML remains stable over the full rollout. Shared phase and coupling angles parameterising the circuit correspond directly to modal frequencies and inter-mode interactions, giving the learned dynamics a physical interpretation in spectral space. On two patient-specific cardiovascular benchmarks, the structured QCML propagator matches the predictive accuracy of its classical counterpart on surface pressure spectra, pressure drop, and wall shear stress. These results establish QCML as a working component of scientific machine learning and a concrete contribution towards practical quantum advantage in real-world prediction.
Weather forecasting plays a critical role across various sectors, supporting strategic planning and reducing the impact of hazardous climatic conditions. However, the inherently chaotic and nonlinear nature of atmospheric systems limits the performance of conventional forecasting approaches, often resulting in prediction inaccuracies and heightened risk. This study proposes a quantum-driven predictive framework that exploits the computational strengths of Quantum Machine Learning (QML) and hybrid quantum–classical optimization to enhance the accuracy and efficiency of modern forecasting models. The framework employs Quantum Neural Networks (QNNs) combined with Variational Quantum Circuits (VQCs) to learn complex spatial–temporal dynamics embedded within large meteorological datasets. Through quantum feature encoding, key atmospheric indicators—including temperature, humidity, wind velocity, and barometric pressure—are projected into high-dimensional Hilbert spaces, enabling more expressive pattern extraction and robust predictive behavior. Simulation results reveal that the quantum-augmented approach surpasses traditional deep learning architectures in both training convergence and forecast precision when applied to extensive weather records. The hybrid design further supports scalability by intelligently distributing computational workloads between classical processors and quantum hardware. Overall, this research demonstrates the transformative potential of quantum computing in atmospheric modeling, offering a foundation for future real-time forecasting systems capable of managing the increasing complexity of global climate patterns.
Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse grids, while circuit depth limitations prevent accurate long-time integration. These hardware bottlenecks confine quantum PDE solvers to low-fidelity regimes despite their theoretical potential for computational speedup. We introduce a multifidelity learning framework that corrects coarse quantum solutions to high-fidelity accuracy using sparse classical training data, facilitating the path toward practical quantum utility for scientific computing. The approach trains a low-fidelity surrogate on abundant quantum solver outputs, then learns correction mappings through a multifidelity neural architecture that balances linear and nonlinear transformations. Demonstrated on benchmark nonlinear PDEs including viscous Burgers equation and incompressible Navier-Stokes flows via quantum lattice Boltzmann methods, the framework successfully corrects coarse quantum predictions and achieves temporal extrapolation well beyond the classical training window. This strategy illustrates how one can reduce expensive high-fidelity simulation requirements while producing predictions that are competitive with classical accuracy. By bridging the gap between hardware-limited quantum simulations and application requirements, this work establishes a pathway for extracting computational value from current quantum devices in real-world scientific applications, advancing both algorithm development and practical deployment of near-term quantum computing for computational physics.