QHDOPT

QHDOPT (QHD-based OPTimizer) is a software package for nonlinear optimization.

QHDOPT implements a quantum optimization algorithm named Quantum Hamiltonian Descent (QHD) on available quantum computers (such as the D-Wave systems). QHD is a quantum-upgraded version of gradient descent (GD). Unlike the classical GD, QHD demonstrates a significant advantage in solving nonconvex and nonlinear optimization problems.

Why QHDOPT?

QHDOPT is for everyone!

QHDOPT aims to eliminate the technical barrier of using QHD for the broader operations research (OR) community. We do not assume users to have prior knowledge of quantum computing, while we allow expert users to specify advanced solver parameters for customized experience. Our target users include:

• Professionals pursuing an off-the-shelf nonconvex optimization solver to tackle problems in operations research (e.g., power systems, supply chains, manufacturing, health care, etc.),
• Researchers who hope to advance the theory and algorithms of optimization via quantum technologies,
• Experts in quantum computation who want to experiment with hyperparameters and/or encodings in QHD to achieve even better practical performance.

Fast compilation empowered by SimuQ

QHDOPT has a built-in compiler powered by SimuQ, a framework for programming and compiling quantum Hamiltonian systems.

Automatic post-processing

QHDOPT automatically post-processes the results returned by the quantum machines. The post-processing includes decoding the raw measurement results and improving their precision (i.e., fine-tuning) via a classical local solver. Users may disable the fine-tuning if needed.

Installation

QHDOPT has a dependency on Ipopt. You may install Ipopt in your conda environment by

conda install -c conda-forge cyipopt==1.3.0

To install QHDOPT, you can directly install with pip by

pip install qhdopt

If you prefer to install from sources, clone this repo and install by

git clone https://github.com/jiaqileng/QHDOPT.git
cd QHDOPT/
pip install ".[all]"

Usage

Two example notebooks for a jump start are examples/1_quadratic_programming.ipynb and examples/2_nonlinear_programming.ipynb. The following illustrates the basic building blocks of QHDOPT and their functionalities briefly.

Import QHDOPT by running

from qhdopt import QHD

You can create a problem instance by directly constructing the function via SymPy.

from sympy import symbols, exp

x, y = symbols("x y")
f = y**1.5 - exp(4*x) * (y-0.75)
model = QHD.SymPy(f, [x, y], bounds=(0,1))

Then you need to setup the solver and the backend device (D-Wave in this example).

model.dwave_setup(resolution=8, api_key="API_key")

Here resolution represents the resolution of the QHD algorithm, and api_key represents the API key of the D-Wave account obtained at D-Wave Leap.

Now you can solve the target problem.

minimum = model.optimize()

The minimal value of $f$ found by QHDOPT is then stored in minimum. To print more details in the process, you can run model.optimize(verbose=1).

Contact

Jiaqi Leng [email protected]

Yuxiang Peng [email protected]

Contributors

Samuel Kushnir, Jiaqi Leng, Yuxiang Peng, Lei Fan, Xiaodi Wu

Citation

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

@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},
  note      = {Available for download at https://github.com/INFORMSJoC/2024.0587},
}