Meta-solutions for quantum-state experiment families

The problem asks whether a human-readable program can automatically generate correct quantum-optical experiments throughout a state family, including families without a previously known construction rule. The available work gives successful examples, not a theorem covering every family and size.

Known results

• Known rules for GHZ, W, two-dimensional Bell, and three-dimensional Bell families were rediscovered.
• A sequence-to-sequence transformer reported new rules for the general spin-$\frac{1}{2}$ family and Majumdar–Ghosh states.
• Six of twenty tested families succeeded; other outputs failed on larger sizes or produced invalid states.
• A six-particle GHZ three-dimensional product family was reported impossible with the supplied resources without ancillary photons.

2024–2026 meta-design results

The generated Python programs matched larger tested instances for selected families and were computationally checked, but the study explicitly notes that finite data underdetermines an infinite sequence. No formal proof of correctness for every size, universal existence theorem, laboratory realization, or subsequent verification was found.

Current status (as of September 2026): Several families have claimed computationally validated construction rules, including two previously unknown cases, but universal automatic discovery and correctness for every family and size remain open.