QMCPy: Quasi-Monte Carlo Community Software in Python

Quasi-Monte Carlo (QMC) methods are used to approximate multivariate integrals. They have four main components: a discrete distribution, a true measure of randomness, an integrand, and a stopping criterion. Information about the integrand is obtained as a sequence of values of the function sampled at the data-sites of the discrete distribution. The stopping criterion tells the algorithm when the user-specified error tolerance has been satisfied. We are developing a framework that allows collaborators in the QMC community to develop plug-and-play modules in an effort to produce more efficient and portable QMC software. Each of the above four components is an abstract class. Abstract classes specify the common properties and methods of all subclasses. The ways in which the four kinds of classes interact with each other are also specified. Subclasses then flesh out different integrands, sampling schemes, and stopping criteria. Besides providing developers a way to link their new ideas with those implemented by the rest of the QMC community, we also aim to provide practitioners with state-of-the-art QMC software for their applications.

Resources

The QMCPy documentation contains a detailed package reference documenting functions and classes including thorough doctests. A number of example notebook demos are also rendered into the documentation from QMCSoftware/demos/. We recommend the following resources to start learning more about QMCPy

• mathematical description of QMCPy software and components.
• Aleksei Sorokin's 2023 PyData Chicago video tutorial and corresponding notebook
• Fred Hickernell's 2020 MCQMC video tutorial and corresponding notebook
• The QMCPy introduction notebook and quickstart notebook

Installation

pip install qmcpy

To install from source, please see the contributing guidelines.

Citation

If you find QMCPy helpful in your work, please support us by citing the JOSS paper and QMCPy software below, which are also available as BibTex citations:

Aleksei G. Sorokin, Fred J. Hickernell, Sou-Cheng T. Choi, Jagadeeswaran Rathinavel, Pieterjan Robbe, and Aadit Jain,
QMCPy: A Python Framework for (Quasi-)Monte Carlo Algorithms.
Journal of Open Source Software, 11(117), 9705, 2026.
https://doi.org/10.21105/joss.09705

Sou-Cheng T. Choi, Fred J. Hickernell, Aadit Jain, Jagadeeswaran Rathinavel, Pieterjan Robbe, and Aleksei G. Sorokin,
QMCPy: A Quasi-Monte Carlo Python Library. 2026.
https://qmcsoftware.github.io/QMCSoftware/

We maintain a list of publications on the development and use of QMCPy as well as a list of select references upon which QMCPy was built.

Package usage stats

PyPI download statistics are tracked automatically in stats/pypi_downloads.md (in the pypi-stats branch).

Other quasi-Monte Carlo software

A page listing other QMC software is available in this branch at docs/qmc-software.md.

The page content is generated automatically from data/qmc-software.yml.

Development

Want to contribute to QMCPy? Please see our guidelines for contributors which includes instructions on installation for developers, running tests, and compiling documentation.

This software would not be possible without the efforts of the QMCPy community including our steering council, collaborators, contributors, and sponsors.

QMCPy is distributed under an Apache 2.0 license from the Illinois Institute of Technology.