Quantum-Informed Machine Learning for Chaotic Systems

• URL: http://arxiv.org/abs/2507.19861v2
• Date: Fri, 01 Aug 2025 15:03:13 GMT
• Title: Quantum-Informed Machine Learning for Chaotic Systems
• Authors: Maida Wang, Xiao Xue, Peter V. Coveney,
• Abstract summary: We introduce a quantum-informed machine learning framework for learning partial differential equations.<n>A quantum circuit Born machine is employed to learn the invariant properties of chaotic dynamical systems.<n>The framework is evaluated on three representative systems: the Kuramoto-Sivashinsky equation, two-dimensional Kolmogorov flow and turbulent channel flow.
• Score: 0.8110978727364399
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Learning the behaviour of chaotic systems remains challenging due to instability in long-term predictions and difficulties in accurately capturing invariant statistical properties. While quantum machine learning offers a promising route to efficiently capture physical properties from high-dimensional data, its practical deployment is hindered by current hardware noise and limited scalability. Here, we introduce a quantum-informed machine learning framework for learning partial differential equations, with an application focus on chaotic systems. A quantum circuit Born machine is employed to learn the invariant properties of chaotic dynamical systems, achieving substantial memory efficiency by representing these complex physical statistics with a compact set of trainable circuit parameters. This approach reduces the data storage requirement by over two orders of magnitude compared to the raw simulation data. The resulting statistical quantum-informed prior is then incorporated into a Koopman-based auto-regressive model to address issues such as gradient vanishing or explosion, while maintaining long-term statistical fidelity. The framework is evaluated on three representative systems: the Kuramoto-Sivashinsky equation, two-dimensional Kolmogorov flow and turbulent channel flow. In all cases, the quantum-informed model achieves superior performance compared to its classical counterparts without quantum priors. This hybrid architecture offers a practical route for learning dynamical systems using near-term quantum hardware.

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