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Quantum Machine Learning
Quantum Polymorphisms and Commutativity Gadgets
arXiv
Authors: Lorenzo Ciardo, Gideo Joubert, Antoine Mottet
Year
2025
Paper ID
16478
Status
Preprint
Abstract Read
~2 min
Abstract Words
98
Citations
N/A
Abstract
We introduce the concept of quantum polymorphisms to the complexity theory of non-local games. We use this notion to give a full characterisation of the existence of commutativity gadgets for relational structures, introduced by Ji as a method for achieving quantum soundness of classical CSP reductions. Prior to our work, a classification was only known in the Boolean case [Culf--Mastel, STOC'25]. As an application of our framework, we prove that the entangled CSP parameterised by odd cycles is undecidable. Furthermore, we establish a quantum version of Galois connection for entangled CSPs in the case of non-oracular quantum homomorphisms.
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- This paper contributes to the Quantum Machine Learning research area in the Quantum Articles archive.
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- We introduce the concept of quantum polymorphisms to the complexity theory of non-local games.
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