QHDOPT: A Quantum Software for Nonlinear Optimization

QHDOPT (QHD-based OPTimizer) is an open-source, end-to-end software package (Github) for solving nonlinear and nonconvex optimization problems using quantum computers. QHDOPT implements the Quantum Hamiltonian Descent (QHD) algorithm, a quantum-upgraded version of gradient descent that demonstrates significant advantages in solving nonlinear/nonconvex optimization problems.

Recently, QHDOPT also incorporated Quantum-Inspired Hamiltonian Descent (QIHD) on a GPU-based backend, which provides a stepping stone for large scale empirical study of quantum optimization in solving real-world problems.

Key Features

Accessible interface for the optimization community with no prior quantum computing knowledge
Automatic mapping to various quantum backends (D-Wave, IonQ, etc.) as well as GPU-based backends for QIHD
Built-in compiler powered by SimuQ
Automatic post-processing and fine-tuning of results
Support for both gate-based and analog quantum computers

Tutorials & Related Talks

TUT 25 @ IEEE Quantum Week, September 2025.
- Notebooks available at Colab Notebook
- Session 1 (slides)(video).
- Session 2 (slides)(video).
Exponential Quantum Speedup in Optimization: Theory and Practice.
- May 2025 @ UCLA. (slides)
Hamiltonian-oriented Quantum Algorithm Design and Programming.
- September 2023 @ Columbia. (slides)
Quantum Hamiltonian Decent.
- Jiaqi Leng's talk at BGM 2024, October 2024.
- AWS-IQIM seminar, Caltech, October 2023. (slides)
- Xiaodi Wu's talk at the Fields Institute, October 2022.

Related Publications

Quantum Hamiltonian Descent
- Quantum Hamiltonian Descent. (website)
- A Quantum-Classical Performance Separation in Nonconvex Optimization. arXiv:2311.00811
- A quantum central path algorithm for linear optimization. QIP 2025. arXiv:2311.03977
- Quantum Hamiltonian Descent for Non-smooth Optimization. arXiv:2503.15878
- (Sub)Exponential Quantum Speedup for Optimization. arXiv:2504.14841
Quantum-Inspired Hamiltonian Descent
- Quantum-Inspired Hamiltonian Descent for Mixed-Integer Quadratic Programming. Extended abstract to appear in ScaleOPT workshop @ NeurIPS 2025. A GPU-based implementation, called OpenPhiSolve, is available at Github.
- A progress report on applications in healthcare, communication, and machine learning will appear in INFORMS 2025.

Citation

If you use QHDOPT in your work, please cite our paper:

Publication

QHDOPT: A Software for Nonlinear Optimization with Quantum Hamiltonian Descent
Samuel Kushnir, Jiaqi Leng, Yuxiang Peng, Lei Fan, Xiaodi Wu
INFORMS Journal on Computing, 2024
DOI: 10.1287/ijoc.2024.0587.cd, Github: QHDOPT

@misc{kushnir2024qhdopt,
  author = {Kushnir, Sam and Leng, Jiaqi and Peng, Yuxiang and Fan, Lei and Wu, Xiaodi},
  publisher = {{INFORMS Journal on Computing}},
  title = {{QHDOPT}: A Software for Nonlinear Optimization with {Q}uantum {H}amiltonian {D}escent},
  year = {2024},
  doi = {10.1287/ijoc.2024.0587.cd},
  url = {https://github.com/INFORMSJoC/2024.0587}
}

Acknowledgments

QHDOPT's development is partially supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, Accelerated Research in Quantum Computing under Award Number DE-SC0020273, the Air Force Office of Scientific Research under Grant No. FA95502110051, the U.S. National Science Foundation grant CCF-1816695, CCF-1942837 (CAREER), ECCS-2045978, a Sloan research fellowship, the Simons Quantum Postdoctoral Fellowship, a Simons Investigator award through Grant No. 825053, as well as an open-source quantum software grant from the Unitary Fund.