Shor's algorithm is said to solve the hidden subgroup problem for finite Abelian groups, at least according to the Wikipedia article I read. This means that it can be used to solve factoring or discrete logarithm problems for integers. Can Shor's algorithm be used to factor non-commutative or non-associative unique factorization domains such as Hurwitz quaternions or 'Cayley integers' described by Conway and Smith over octonions? Does the hidden subgroup problem for finite Abelian groups not apply to these algebras because they aren't finite Abelian groups?
2026-03-25 15:39:24.1774453164
Does Shor's algorithm work for noncommutitive or nonassociative algebras?
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