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"Abelian Hypergroups and Quantum Computation", Juani Bermejo-Vega and Kevin C. Zatloukal, 2015

Reviewed August 17, 2023

Citation: Bermejo-Vega, Juan, and Kevin C. Zatloukal. "Abelian hypergroups and quantum computation." arXiv preprint arXiv:1509.05806 (2015).

Web: https://arxiv.org/abs/1509.05806

Tags: Abelian-anyons, Computer-scientific

This paper generalizes earlier work on simulation of normalizer circuits on abelian groups to "abelian hypergroups", objects resembling fusion rings. The theory of these hypergroups is presented in high detail, and it is shown how they can be used to solve the "hidden normal subgroup problem".

This work approaches the computational theory in a very different way than is standard in TQC literature, but its results seem readily applicable to the TQC setting.