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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 $R<infty.$
Let $pi_1(C)$ be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic $p>0$ of countable cardinality. Let $N$ be a normal (resp. characteristic) subgroup of $pi_1(C)$. Under
We characterize the algebraic structure of semi-direct product of cyclic groups, $Z_{N}rtimesZ_{p}$, where $p$ is an odd prime number which does not divide $q-1$ for any prime factor $q$ of $N$, and provide a polynomial-time quantum computational alg
We report on the existence of the phenomenon of sudden birth of maximal hidden quantum correlations in open quantum systems. Specifically, we consider the CHSH-inequality for Bell-nonlocality, the $rm F_3$-inequality for EPR-steering, and usefulness
The orbifold group of the Borromean rings with singular angle 90 degrees, $U$, is a universal group, because every closed oriented 3--manifold $M^{3}$ occurs as a quotient space $M^{3} = H^{3}/G$, where $G$ is a finite index subgroup of $U$. Therefor
Recent results of Qu and Tuarnauceanu describe explicitly the finite p-groups which are not elementary abelian and have the property that the number of their subgroups is maximal among p-groups of a given order. We complement these results from the b