Quantum simulation of real-world nonlinear dynamics via Koopman method

• URL: http://arxiv.org/abs/2607.07338v1
• Date: Wed, 08 Jul 2026 12:27:12 GMT
• Title: Quantum simulation of real-world nonlinear dynamics via Koopman method
• Abstract summary: We propose the quantum Koopman method, a data-driven framework that embeds nonlinear dynamics into a learned linear representation.<n>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.<n>We utilize the Koopman method on a superconducting processor to simulate three distinct nonlinear systems.
• Score: 8.214716873336412
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Time evolution of nonlinear dynamics on a quantum processor [0.0]
  We experimentally realize the time evolution of nonlinear fluid dynamics on a quantum processor.<n>Our results constitute to our knowledge the first experimental realization of nonlinear time propagation on a quantum processor.
  arXiv  Detail & Related papers  (2026-08-13T10:07:19Z)
• Variational quantum simulation of many-body dissipative dynamics on a superconducting quantum processor [10.739803066812476]
  We show a variational quantum algorithm capable of scalable simulation of non-unitary many-body dissipative dynamics.<n>Our work underlines the capability of noisy intermediate-scale quantum devices in simulating dissipative many-body dynamics.
  arXiv  Detail & Related papers  (2025-10-23T01:43:53Z)
• Data-driven quantum Koopman method for simulating nonlinear dynamics [10.895862740181151]
  We propose a data-driven framework that transforms nonlinear dynamics into linear unitary evolution in higher-dimensional observable spaces.<n>The quantum Koopman method (QKM) is validated across diverse nonlinear systems.<n>This work establishes a practical pathway for quantum-accelerated simulation of nonlinear phenomena.
  arXiv  Detail & Related papers  (2025-07-29T15:00:56Z)
• Generative System Dynamics in Recurrent Neural Networks [56.958984970518564]
  We investigate the continuous time dynamics of Recurrent Neural Networks (RNNs)<n>We show that skew-symmetric weight matrices are fundamental to enable stable limit cycles in both linear and nonlinear configurations.<n> Numerical simulations showcase how nonlinear activation functions not only maintain limit cycles, but also enhance the numerical stability of the system integration process.
  arXiv  Detail & Related papers  (2025-04-16T10:39:43Z)
• Quantum lattice Boltzmann method for simulating nonlinear fluid dynamics [12.270811823319576]
  We introduce a novel ensemble description of lattice gas for simulating nonlinear fluid dynamics on a quantum computer.<n>We propose a quantum lattice Boltzmann method that relies on linear operations with medium dimensionality.
  arXiv  Detail & Related papers  (2025-02-23T13:25:35Z)
• Hybrid Stabilizer Matrix Product Operator [44.99833362998488]
  We introduce a novel hybrid approach combining tensor network methods with the stabilizer formalism to address the challenges of simulating many-body quantum systems. We demonstrate the effectiveness of our method through applications to random Clifford T-doped circuits and Random Clifford Floquet Dynamics.
  arXiv  Detail & Related papers  (2024-05-09T18:32:10Z)
• Linear-scale simulations of quench dynamics [2.7615495205203318]
  We develop a linear-scale computational simulation technique for the non-equilibrium dynamics of quantum quench systems. An expansion-based method allows us to efficiently compute the Loschmidt echo for infinitely large systems. We observe wave vector-independent dynamical phase transitions in self-dual localization models.
  arXiv  Detail & Related papers  (2023-11-16T04:18:32Z)
• Variational quantum simulation using non-Gaussian continuous-variable systems [39.58317527488534]
  We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology. The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space.
  arXiv  Detail & Related papers  (2023-10-24T15:20:07Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops [68.8204255655161]
  static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. Results show that a cubic interaction allows to increase the effective rates of both linear and nonlinear operations.
  arXiv  Detail & Related papers  (2021-07-14T15:11:05Z)
• Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms [74.17312533172291]
  We describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) We then explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation)
  arXiv  Detail & Related papers  (2020-12-12T00:01:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.