Quantum Simulation of Real-World Nonlinear Dynamics via the Koopman Method

The paper proposes a quantum Koopman method for simulating nonlinear dynamics by learning observables from trajectory data, projecting the lifted dynamics into a finite-dimensional linear subspace, and decomposing the resulting non-unitary propagator into parallel spectral channels. On a superconducting processor, the authors simulate reaction-diffusion dynamics, fluid motion on a sphere, and satellite-derived Gulf Stream observations using up to 32 parallel circuits with 10 qubits. The reported simulations reproduce dominant multiscale patterns and statistical signatures, while exposing a shift from hardware-noise limits to finite-dimensional representation limits as nonlinear interactions become stronger.