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arXiv · 2609.20678

Schrijver-Delsarte rigidity in association schemes and undecidability of quantum graph homomorphism

Lorenzo Ciardo·Iris Hebbeker·Gideo Joubert·Jana Kreiß·Antoine Mottet
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Abstract

We prove RE-completeness of the quantum homomorphism problem parameterised by families of graphs derived from the classic metric association schemes. These include Kneser graphs, $q$-Kneser graphs, and the complements of Johnson, Grassmann, and Hamming graphs. Our proof develops a spectral method for establishing non-contextuality of quantum polymorphisms. It combines an equality analysis of Roberson's bound on the projective packing number in terms of Schrijver's theta with a structural argument inspired by Erdős-Ko-Rado theory.

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Lorenzo Ciardo, Iris Hebbeker, Gideo Joubert, Jana Kreiß, Antoine Mottet. 2026-09-17. Schrijver-Delsarte rigidity in association schemes and undecidability of quantum graph homomorphism. https://arxiv.org/abs/2609.20678

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