Problem
Research questions and friction points this paper is trying to address.
quantum homomorphism
association schemes
RE-completeness
Kneser graphs
q-Kneser graphs
Schrijver-Delsarte rigidity in association schemes and undecidability of quantum graph homomorphism
🤖 AI Summary
本文证明了基于经典度量关联方案的图族参数化量子同态问题的RE-完全性，通过结合谱方法和结构论证解决了该问题。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
quantum homomorphism
spectral method
non-contextuality
Schrijver's theta
RE-completeness
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