A library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling. For more information, please see the documentation.
- Fast calculation of hafnians, loop hafnians, and torontonians of general and certain structured matrices.
- An easy to use interface to use the loop hafnian for Gaussian quantum state calculations.
- Sampling algorithms for hafnian and torontonians of graphs.
- Efficient classical methods for approximating the hafnian of non-negative matrices.
- Easy to use implementations of the multidimensional Hermite polynomials, which can also be used to calculate hafnians of all reductions of a given matrix.
Pre-built binary wheels are available for the following platforms:
|macOS 10.6+||manylinux x86_64||Windows 64bit|
To install, simply run
pip install thewalrus
Compiling from source
The Walrus depends on the following Python packages:
In addition, to compile the C++ extension, the following dependencies are required:
- A C++11 compiler, such as
- Eigen3 - a C++ header library for linear algebra.
On Debian-based systems, these can be installed via
$ sudo apt install g++ libeigen3-dev
or using Homebrew on MacOS:
$ brew install gcc eigen
Alternatively, you can download the Eigen headers manually:
$ mkdir ~/.local/eigen3 && cd ~/.local/eigen3 $ wget http://bitbucket.org/eigen/eigen/get/3.3.7.tar.gz -O eigen3.tar.gz $ tar xzf eigen3.tar.gz eigen-eigen-323c052e1731/Eigen --strip-components 1 $ export EIGEN_INCLUDE_DIR=$HOME/.local/eigen3
Note that we export the environment variable
EIGEN_INCLUDE_DIR so that The Walrus can find the Eigen3 header files (if not provided, The Walrus will by default look in
Once all dependencies are installed, you can compile the latest stable version of the The Walrus library as follows:
$ python -m pip install thewalrus --no-binary :all:
Alternatively, you can compile the latest development version by cloning the git repository, and installing using pip in development mode.
$ git clone https://github.com/XanaduAI/thewalrus.git $ cd thewalrus && python -m pip install -e .
libwalrus uses OpenMP to parallelize both the permanent and the hafnian calculation. At the moment, this is only supported on Linux using the GNU g++ compiler, due to insufficient support using Windows/MSCV and MacOS/Clang.
Using LAPACK, OpenBLAS, or MKL
If you would like to take advantage of the highly optimized matrix routines of LAPACK, OpenBLAS, or MKL, you can optionally compile the
libwalrus such that Eigen uses these frameworks as backends. As a result, all calls in the
libwalrus library to Eigen functions are silently substituted with calls to LAPACK/OpenBLAS/MKL.
For example, for LAPACK integration, make sure you have the
lapacke C++ LAPACK bindings installed (
sudo apt install liblapacke-dev in Ubuntu-based Linux distributions), and then compile with the environment variable
$ USE_LAPACK=1 python -m pip install thewalrus --no-binary :all:
Alternatively, you may pass
USE_OPENBLAS=1 to use the OpenBLAS library.
To ensure that The Walrus library is working correctly after installation, the test suite can be run by navigating to the source code folder and running
$ make test
To run the low-level C++ test suite, Googletest will need to be installed. In Ubuntu-based distributions, this can be done as follows:
sudo apt-get install cmake libgtest-dev cd /usr/src/googletest/googletest sudo cmake sudo make sudo cp libgtest* /usr/lib/ sudo mkdir /usr/local/lib/googletest sudo ln -s /usr/lib/libgtest.a /usr/local/lib/googletest/libgtest.a sudo ln -s /usr/lib/libgtest_main.a /usr/local/lib/googletest/libgtest_main.a
Alternatively, the latest Googletest release can be installed from source:
sudo apt install cmake wget -qO - https://github.com/google/googletest/archive/release-1.8.1.tar.gz | tar -xz cmake -D CMAKE_INSTALL_PREFIX:PATH=$HOME/googletest -D CMAKE_BUILD_TYPE=Release googletest-release-1.8.1 make install
If installing Googletest from source, make sure that the included headers and libraries are available on your include/library paths.
The Walrus documentation is available online on Read the Docs.
To build it locally, you need to have the following packages installed:
They can be installed via a combination of
apt if on a Debian-based system:
$ sudo apt install pandoc doxygen $ pip3 install sphinx sphinxcontrib-bibtex nbsphinx breathe exhale
To build the HTML documentation, go to the top-level directory and run the command
$ make doc
The documentation can then be found in the
Contributing to The Walrus
We welcome contributions - simply fork The Walrus repository, and then make a pull request containing your contribution. All contributors to The Walrus will be listed as authors on the releases.
We also encourage bug reports, suggestions for new features and enhancements, and even links to projects, applications or scientific publications that use The Walrus.
Brajesh Gupt, Josh Izaac and Nicolás Quesada.
All contributions are acknowledged in the acknowledgments page.
If you are doing research using The Walrus, please cite our paper:
Brajesh Gupt, Josh Izaac and Nicolás Quesada. The Walrus: a library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling. Journal of Open Source Software, 4(44), 1705 (2019)
- Source Code: https://github.com/XanaduAI/thewalrus
- Issue Tracker: https://github.com/XanaduAI/thewalrus/issues
If you are having issues, please let us know by posting the issue on our Github issue tracker.
The Walrus is free and open source, released under the Apache License, Version 2.0.