This is the code repository for the paper: Bergh, Parentin: Permutation Invariant Optimization Problems in Quantum Information Theory: A Framework for Channel Fidelity and Beyond. arXiv:<will be added once published>
It provides a python package with tools for efficiently computing values of high-dimensional permutation-invariant optimization problems as they appear in quantum information theory. In particular, it allows phrasing many typical operations used in quantum information theory (partial traces, (partial) channel applications) wholly within the permutation-invariant subspace and without ever constructing exponentially large matrices.
Note that this package is still in its early stages. While the code is fully functional and can be used for various problems, we currently don't guarantee any form of API stability, in particular we might still refactor the structure of the package and change the call signature of certain functions. Once the API has matured we will release a published version on pypi.
This package requires Python version >= 3.12. Clone the repository and make sure you have uv installed. Then run uv sync, this will install all dependencies into a local venv. If you would like GPU acceleration you need a CUDA compatible GPU. If you have CUDA installed locally, you can install with the necessary cupy dependencies by running uv sync --extra cuda12 or uv sync --extra cuda13 depending on your CUDA version. If you don't already have CUDA installed you can run uv sync --extra cuda12standalone or uv sync --extra cuda13standalone to install the full CUDA toolchain into the python venv.
Unfortunately, on MacOS Intel (x86-64) Python 3.14 is not supported due to some dependencies not being available.
- Most of the representation theoretic constructions from Section III of the paper are in
representation/, in particular the block-diagonalizing *-isomorphisms, as well as the constructions for channel composition and partial traces - The
SDP/folder contains an implementation of the symmetric seesaw method for channel fidelity using SDP solvers from Section IV of the paper - The
power_method/folder contains an implementation of the power-method for channel fidelity from Section IV of the paper. This code is also GPU accelerated if a GPU is available. - the
algebra/folder contains many classes used throughout the code, in particular all constructions involving orbit-basis matrices and their properties.
Under examples/simulations you can find code reproducing the examples that are included in the paper, in particular non-asymptotic
superactivation using (a pre- and postprocessed version of) the original Smith-Yard channel pair,
as well calculating the channel fidelity of the qubit amplitude damping and depolarizing channel.
Many expensive sections of the code (in particular creating the *-isomorphisms and channel link product relations) use a caching system based on python weak references. That means that if any of these classes have been created and are still referenced somewhere, any subsequent creation with the same parameters will reuse the previous instance and not create a new one. This is implemented in utilities.caching.WeakRefMemoize. The functions of this package will hold such references as long as such objects are used within the function (and thus avoid recomputation within the function), but do not create eternal objects by themselves to not clog up the available memory. If you would like any of these objects to be cached for a longer period of time, just create and store them yourself. Creation of such expensive objects is usually logged to stdout.