[Application] Investigate resource-state protocols

[mgarnier59]

On the one hand, graph state are ubiquitous in quantum information science and technology. Indeed, they play a role in quantum computation (resource state engineering), quantum error correction and quantum communications (entanglement distribution) among others. This is due to the fact that they have a clear entanglement structure are suitable to theoretical processing either in their graph form or using their relationship with stabiliser states. On the other hand, their manipulation is natural in Graphix.

For example, here are some recent papers on these topics

• Freund, Pirker, Vandré and Dür, Graph state extraction from two-dimensional cluster states (2025) preprint.
• Claudet and Perdix, Local equivalence of stabilizer states: a graphical characterisation (2024) preprint.
• Claudet, Mhalla and Perdrix, Small k-pairable states (2023) preprint.

The idea would be to

• [ ] choose one of the above examples (or propose something along the same lines)
• [ ] add an example, to examples/resource-state.py for graphix. Please leave the implementation of the algorithm in the examples/resource-state.py directory and not in main graphix package.
• [ ] Confirm the scalability of such a protocol by increasing the number of nodes associated and checking the scaling of the computing time vs problem size.
• [ ] Make sure the docs render correctly.
• [ ] Suggest what could be improved that could led to upgrades/new features in graphix.

[harshqec]

Hello Team, I am working on the this issue with the implementation of this paper: Freund, Pirker, Vandré and Dür, Graph state extraction from two-dimensional cluster states (2025) preprint. Kindly assign me this pull request.