QKoopman

Authors: Baoyang Zhang, Zhen Lu, Yaomin Zhao, Yue Yang
Paper: arXiv:2507.21890

QKoopman is an experimental research project exploring the potential of quantum-accelerated nonlinear dynamics simulation through a novel data-driven quantum Koopman method that combines deep learning for global linearization with quantum algorithms for unitary evolution.

Installation

To set up the QKoopman environment:

# Create and activate a conda environment
conda create -n qk python=3.10.12
conda activate qk

# Install required dependencies
pip install -r requirements.txt

Project organization

This repository contains implementations for three fundamental nonlinear dynamics cases:

• Reaction-diffusion system (gray/)

• 2D turbulence (kol/)

• Shear flow (shear/)

Post-processing tools are available in kpo/.

Getting Started

Training with DeepSpeed

We utilize DeepSpeed for distributed data-parallel training.

The training process can be launched using the following shell script:

NUM_GPUS=$(nvidia-smi -L 2>/dev/null | wc -l)

deepspeed --num_gpus ${NUM_GPUS} \
          gd_h4.py  \
          --deepspeed \
          --deepspeed_config ds_config.json \
          > run.log 2>&1

Testing & Reproduction

To evaluate the models and reproduce results from our paper:

1. Download the dataset
   The data for this project is hosted on Hugging Face Datasets:
   

2. Run visualization notebook
   Execute our Jupyter notebook for generating figures:

   jupyter notebook ./kpo/draw.ipynb

Citation

If you use our code, please cite:

@misc{Zhang2025quantumKoopman,
      title={Data-driven quantum {Koopman} method for simulating nonlinear dynamics}, 
      author={Zhang, Baoyang and Lu, Zhen and Zhao, Yaomin and Yang, Yue},
      year={2025},
      eprint={2507.21890},
      archivePrefix={arXiv},
      primaryClass={quant-ph},
      url={https://arxiv.org/abs/2507.21890}, 
}