Data-driven quantum Koopman method for simulating nonlinear dynamics
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Abstract (arXiv)
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman method (QKM), a data-driven framework that bridges this gap through transforming nonlinear dynamics into linear unitary evolution in higher-dimensional observable spaces. Leveraging the Koopman operator theory to achieve a global linearization, our approach maps system states into a hierarchy of Hilbert spaces using a deep autoencoder. Within the linearized embedding spaces, the state representation is decomposed into modulus and phase components, and the evolution is governed by a set of unitary Koopman operators that act exclusively on the phase. These operators are constructed from diagonal Hamiltonians with coefficients learned from data, a structure designed for efficient implementation on quantum hardware. This architecture enables direct multi-step prediction, and the operator's computational complexity scales logarithmically with the observable space dimension. The QKM is validated across diverse nonlinear systems. Its predictions maintain relative errors below 6% for reaction-diffusion systems and shear flows, and capture key statistics in 2D turbulence. This work establishes a practical pathway for quantum-accelerated simulation of nonlinear phenomena, exploring a framework built on the synergy between deep learning for global linearization and quantum algorithms for unitary dynamics evolution.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 17 of its 94 references that are in the map. First posted on arXiv 29 Jul 2025.
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17 of 94 references.
References · 17
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5 more
- 2023KoopmanLab: machine learning for solving complex physics equationscited by 9
- 2023Disentangling Hype from Practicality: On Realistically Achieving Quantum Advantagecited by 8
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