Code accompanying Automated discovery of high-dimensional multipartite entanglement with photons that never interacted (Arlt, Krenn, Gu), arXiv:2510.10707.

For every path-identity setup in the paper, this repo computes the post-selected quantum state directly from the PyTheus solution graph and reports its fidelity against the ideal target. Pure Python 3, no dependencies.

Run

python run_all.py

The script walks every figure panel and prints:

• the ideal target state, e.g. 1/√2 · (|00⟩ + |11⟩),
• the state actually produced by the graph (numerical coefficients),
• the fidelity between them.

A summary table is printed at the end.

Mapping to the paper

Figure	Setup	Graph directory
Fig. 2	GHZ_n (n=2,4,6,8) across A, B	graphs/fig2/
Fig. 3	W_n (n=2,4,6,8) across 2/3/4 nodes	graphs/fig3/
Fig. 4	SRV(4,2,2), 3 parties	graphs/fig4/
Fig. 5	[[4,1,2]] logical Bell	graphs/fig5/
Appendix	[[3,1,2]]_3 and [[4,1]]_3 Bell pairs	graphs/appendix/

Each panel has a solution_*.json (the graph) and a matching config_*.json (target basis kets and ancilla count).

Formalism

A solution is a weighted colored multigraph. An edge keyed "(u, v, c_u, c_v)" with real weight w represents a photon-pair source emitting one photon at vertex u in mode c_u and one at vertex v in mode c_v. Vertices are detector locations.

Under post-selection on one photon per detector (no number resolving), the state prepared at the system vertices is

|ψ⟩  =  Σ_{M ∈ PM(G)}  (∏_{e ∈ M} w_e)  ⊗_v |c_v(M)⟩

restricted to matchings whose ancilla vertices all land in mode 0. graph_to_state in graph_state.py implements this in ~30 lines on top of a small perfect-matching enumerator. See the PyTheus paper (Krenn et al., Phys. Rev. X 11, 031044 (2021)) for the underlying graph-to-state correspondence.

File layout

companion_repo/
├── README.md
├── graph_state.py        # graph→state engine (load, enumerate PMs, fold into ket)
├── run_all.py            # walks every figure panel, prints state + fidelity
└── graphs/
    ├── fig2/             # GHZ panels (a–d)
    ├── fig3/             # W panels   (a–d)
    ├── fig4/             # SRV(4,2,2)
    ├── fig5/             # [[4,1,2]] logical Bell
    └── appendix/         # qutrit logical Bell pairs