Quantum simulation of real-world nonlinear dynamics via Koopman method

2026-07-08

AI Summary

Quantum computers, constrained by unitary evolution, struggle to directly simulate nonlinear dynamical systems. This work proposes a quantum Koopman approach that leverages data-driven learning of Koopman observables to embed nonlinear dynamics into a linear space, enabling their evolution via shallow, parallelized quantum circuits. The method is experimentally demonstrated on a superconducting quantum processor, achieving the first successful quantum simulations of reaction–diffusion systems, spherical fluid flows, and observational Gulf Stream data, accurately reproducing multiscale patterns and statistical properties. Validation across 32 parallel circuits, each comprising 10 qubits, confirms the efficacy of the approach while revealing fundamental limitations imposed by hardware noise and Koopman embedding dimensionality on simulation fidelity.

Abstract

Nonlinear dynamics is ubiquitous in nature, ranging from chemical pattern formation to ocean circulation, yet its simulation on quantum computers is fundamentally limited by the unitary nature of quantum evolution. We propose the quantum Koopman method, a data-driven framework that embeds nonlinear dynamics into a learned linear representation and implements the resulting evolution using shallow quantum circuits. This method learns Koopman observables from trajectory data, projects the lifted dynamics onto a finite-dimensional subspace, and decomposes the corresponding non-unitary propagator into parallel spectral channels. We utilize the Koopman method on a superconducting processor to simulate three distinct nonlinear systems, comprising reaction-diffusion dynamics, fluid motion on a sphere, and satellite-derived observations of Gulf Stream currents, employing up to 32 parallel circuits of 10 qubits. These quantum simulations capture the dominant multiscale patterns and statistical signatures of the underlying dynamics, and reveal a transition from performance limited by hardware noise in weakly nonlinear systems to performance limited by finite-dimensional Koopman representations as nonlinear scale interactions increase. This transition identifies a practical boundary for quantum-amenable nonlinear dynamics, establishing a hardware-validated route for simulating moderately nonlinear dynamics on near-term quantum hardware.

Problem

• nonlinear dynamics
• quantum simulation
• Koopman method
• quantum computing
• unitary evolution

Innovation

• quantum Koopman method
• nonlinear dynamics
• shallow quantum circuits
• data-driven simulation
• non-unitary propagator