A quantum polylog algorithm for non-normal maximal cyclic hidden subgroups in the affine group of a finite field

We give an algorithm to solve the quantum hidden subgroup problem for maximal cyclic non-normal subgroups of the affine group of a finite field (if the field has order $q$ then the group has order $q(q-1)$) with probability $1-\varepsilon$ with (polylog) complexity $O(\log(q)^{R}\log(\varepsilon)^{2})$ where $R<\infty.$

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