A learned Koopman embedding plus shallow LCHS circuits simulates moderately nonlinear dynamics on NISQ hardware and marks the noise-to-representation performance boundary.
Data-driven quantum Koopman method for simulating nonlinear dynamics
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abstract
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.
years
2026 4representative citing papers
Quantum Koopman Algorithms define an observable-space quantum framework for simulating linear quantum and nonlinear classical dynamics with polylog gate costs in some cases.
Quantum circuit framework for advection-diffusion PDEs with Robin and periodic boundary conditions via LCHS, including LCU error analysis and gate complexity showing potential quantum advantage in high dimensions.
Quantum algorithm for 1D NLSE via Lax-pair scattering performs time evolution analytically in the scattering domain and reconstructs solutions with QSVT.
citing papers explorer
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Quantum simulation of real-world nonlinear dynamics via Koopman method
A learned Koopman embedding plus shallow LCHS circuits simulates moderately nonlinear dynamics on NISQ hardware and marks the noise-to-representation performance boundary.
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Quantum Koopman Algorithms
Quantum Koopman Algorithms define an observable-space quantum framework for simulating linear quantum and nonlinear classical dynamics with polylog gate costs in some cases.
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Quantum circuits for the advection-diffusion equation with boundary conditions based on LCHS
Quantum circuit framework for advection-diffusion PDEs with Robin and periodic boundary conditions via LCHS, including LCU error analysis and gate complexity showing potential quantum advantage in high dimensions.
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Quantum algorithm for the nonlinear Schr\"odinger equation via the Lax-pair scattering
Quantum algorithm for 1D NLSE via Lax-pair scattering performs time evolution analytically in the scattering domain and reconstructs solutions with QSVT.