ACE:

Code for numerically-exact simulations of open quantum systems.

Original author: Moritz Cygorek

Contributors: Thomas Bracht

Scope and Methods

Its name derives from the Automated Compression of Environments (ACE) algorithm [1] based on real-time path integrals and tensor networks. Over the years a number of other methods have been implemented so that it grew to a quite versatile and general open quantum systems simulator. These methods include:

	Authors	Title	Journal
[1]	M. Cygorek, M. Cosacchi, A. Vagov, V.M. Axt, B.W. Lovett, J.Keeling & E.M. Gauger	Simulation of open quantum systems by automated compression of arbitrary environments	Nat. Phys. 18, 662–668 (2022).
[2]	M.R. Jørgensen, F.A. Pollock	Exploiting the Causal Tensor Network Structure of Quantum Processes to Efficiently Simulate Non-Markovian Path Integrals	Phys. Rev. Lett. 123, 240602 (2019).
[3]	M. Cygorek, J. Keeling, B.W. Lovett, E.M. Gauger	Sublinear Scaling in Non-Markovian Open Quantum Systems Simulations	Phys. Rev. X 14, 011010 (2024).
[4]	M. Cygorek, B.W. Lovett, J. Keeling, E.M. Gauger	Treelike process tensor contraction for automated compression of environments	Phys. Rev. Research 6, 043203 (2024).
[5]	V. Link, H.-H. Tu, W.T. Strunz	Open Quantum System Dynamics from Infinite Tensor Network Contraction	Phys. Rev. Lett. 132, 200403 (2024)

The code is written in C/C++ but offers extensive Python bindings. Usage of the C/C++-Code based on Parameter files is described in:

	Authors	Title	Journal
[6]	M. Cygorek, E.M. Gauger	ACE: A general-purpose non-Markovian open quantum systems simulation toolkit based on process tensors	J. Chem. Phys. 161, 074111 (2024).

More about the concept of process tensors can be found in

	Authors	Title	Journal
[7]	M. Cygorek, E.M. Gauger	Understanding and utilizing the inner bonds of process tensors	SciPost Phys. 18, 024 (2025).

Installation:

The ACE code can be used in two ways:

The C/C++ binaries simulate open quantum systems based on parameter files.
Python bindings access the same internal C/C++ functions but allow easy integration into common Python-based data processing frameworks

The binaries can be directly downloaded from the releases. Simulation are then started from the command line by providing a parameter file as, e.g.,

ACE.exe example.param

Note that the binary must be chosen according to the operating system, and it must be placed in a PATH that can be resolved by the terminal.

The standalone Python package can be straightforwardly installed via

pip install ACE-OQS

Once installed, methods can be called after import ACE in Python scripts (see examples in the pybind/examples/ subdirectory).

It should be noted that these binaries are not linked against BLAS/LAPACK functions, e.g., provided by the Intel MKL. Linking against BLAS/LAPACK may lead to a sizable speed-up. To this end we recommend to download the source using git clone https://github.com/mcygorek/ACE and compile it. This process is described for different operating systems below.

Compilation from source in Linux:

Go to ACE directory and type "make"

The Eigen library has to available. The Makefile tries "/usr/include/eigen3/". If it's located elsewhere, please set the environment variable "EIGEN_HOME" during compilation.

The Intel MKL is automatically used if set up correctly on the system.

Successful compilation produces a binary "ACE" in the "bin" subdirectory

If "pybind11" is installed (if not, run python3 -m pip install build pybind11 first), Python bindings can be generated with "make pybind". This creates a .whl file in the pybind/ subdirectory that can be installed using pip install pybind/*.whl.

Compilation from source in Windows:

WSL2:

First, install WSL2 with Ubuntu and update the repository. To this end, open the PowerShell and type:

wsl --install Ubuntu

sudo apt-get update

sudo apt-get upgrade

Next, install C++ and Python compilers as well as required libraries

sudo apt install g++ make libeigen3-dev

sudo apt install python3-dev python3-matplotlib

Then, clone the github repository and compile (including python bindings)

cd

git clone https://github.com/mcygorek/ACE

cd ACE

make

Now, there should be a binary file "ACE" in the "bin" subdirectory. Ideally, set the path to this directory by appending to your local .bashrc

export PATH=$PATH:/PATH_TO/ACE/bin where PATH_TO is to be replaced by the path to the ACE directory, typically /home/USERNAME/ with the name of the user USERNAME

Try running examples, e.g.

ACE ACE/examples/JCP2024/Fig5/phonon_assisted.param

Python bindings

The ACE library provides Python bindings via pybind11. To install this, run

sudo apt install python3-pybind11

and in the ACE directory

make pybind

You can check out the python examples in the ACE/pybind subdirectory, e.g.,

python3 /PATH_TO/ACE/pybind/06_cQED.py but be sure to edit the second line and replace the /.../ by /PATH_TO/

Jupyter notebooks

If you want to use .ipynb notebooks, you can install jupyter on WSL, then access the notebooks via your regular browser (outside of WSL):

sudo apt install python3-notebook

If you run

jupyter-notebook

you will see a link (starting with "localhost:8888/"). Copy this long URL into your browser and go there. To try out the examples in the ACE/pybind subdirectory, make sure to copy the content of the .py files into newly created .ipynb notebook files. Note: the ".../ACE/pybind" in the second line in the examples should be replaced by "/home/WSLUSER/ACE/pybind", where WSLUSER is the username provided when installing WSL.

VS Code with WSL extension

There is an extension to VS Code that lets you access WSL. Just make sure you have

sudo apt install python3-ipython

installed on WSL and you should be able to access .ipynb notebooks on WSL using VS Code.

MSYS2:

A precompiled ACE.exe is included for easy usage, which however comes with limited functionality and suboptimal performance, and it may be outdated. A new Windows executable can be created with MSYS2:

First, install and run MSYS2. Then, in the UCRT version of MSYS2, run

pacman -S mingw-w64-ucrt-x86_64-toolchain

pacman -S mingw-w64-ucrt-x86_64-eigen3

pacman -S git

pacman -S make

git clone https://github.com/mcygorek/ACE

export EIGEN_HOME=/ucrt64/include/eigen3

cd ACE; make -f Makefile_static

Successful compilation produces a binary "ACE.exe" in the "bin" subdirectory

Python bindings on MSYS2 have not been tested yet.

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ACE-OQS 1.3.2

ACE:

Scope and Methods

Installation:

Compilation from source in Linux:

Compilation from source in Windows:

WSL2:

Python bindings

Jupyter notebooks

VS Code with WSL extension

MSYS2:

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