AI Proof WatchKeep up with AI contributions

Diagonal cases of the Krenn–Gu perfect-matching quantum-graph problem

The Krenn–Gu perfect-matching model asks which colored quantum graphs can represent the required multiparticle states in linear optics. The diagonal cases set the number N of particles equal to the local dimension d, here N=d=4, 6 or 10. Existence or impossibility must be stated for a specified coefficient domain.

Why it matters and what counts as progress

Why it matters: These graph constructions encode possibilities and obstructions for producing high-dimensional Greenberger–Horne–Zeilinger (GHZ) states using linear optics.

What counts as progress: Construct a graph satisfying the perfect-matching requirements, or prove impossibility in a new case with its coefficient domain specified. A theorem for real, complex or restricted coefficients must not be silently transferred to the other settings.

How the problem developed

  1. 2017 · Problem formulation [1]

    Mario Krenn, Xuemei Gu, and Anton Zeilinger Introduced quantum experiments represented by coherent superpositions of perfect matchings in graphs.

  2. 2019 · Open problem [2]

    Mario Krenn, Xuemei Gu, and Matthias Soltész Developed structural questions about perfect matchings inspired by the quantum-graph model.

  3. 28 May 2026 · Reported claim [3]

    Google DeepMind AlphaProof Nexus The paper reports resolving several monochromatic quantum-graph conjectures for N=d in {4,6,10}; it does not specify that every complex-weighted diagonal case is covered.

AI contribution

Advancing Mathematics Research with AI-Driven Formal Proof Search

George Tsoukalas, Anton Kovsharov, Sergey Shirobokov, Anja Surina, Moritz Firsching, Gergely Bérczi, Francisco J. R. Ruiz, Arun Suggala, Adam Zsolt Wagner, Eric Wieser, Lei Yu, Aja Huang, Miklós Z. Horváth, Andrew Ferraiuolo, Henryk Michalewski, Edward Lockhart, Codrut Grosu, Thomas Hubert, Matej Balog, Pushmeet Kohli, Swarat Chaudhuri

The AlphaProof Nexus report says its agent ruled out monochromatic quantum graphs for the diagonal four-, six- and ten-particle cases N=d=4, 6 and 10 in the Krenn–Gu perfect-matching model.

AI involvementAI-led
ImportanceNotable
Technical verificationReported
Human understandingFew
Paper date:

Read the contribution and its assessment →

Sources

  1. Krenn, Gu, and Zeilinger, Quantum experiments and graphs: multiparty states as coherent superpositions of perfect matchings
  2. Krenn, Gu, and Soltész, Questions on the Structure of Perfect Matchings inspired by Quantum Physics
  3. AlphaProof Nexus quantum-optics results
  4. Krenn, monochromatic quantum-graph cases
  5. Later separate quantum-graph Lean result
Website timeline

Publication dates and editorial changes.