An Efficient Quantum Algorithm for the Hidden Subgroup Problem over a Class of Semi-direct Product Groups
نویسندگان
چکیده
In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups Zn ⋊ Zq. The definition of the semi-direct product depending on the choice of an homomorphism, we first analyze the different possibilities for this homomorphism in function of n and q. Then, we present a polynomial-time quantum algorithm solving the HSP over the groups of the form Zpr ⋊ Zp, where p is an odd prime, and finally extend it to the class of groups Zpr ⋊ Zp.
منابع مشابه
An Efficient Algorithm for the Hidden Subgroup Problem over a Class of Semi-direct Product Groups
In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups Zn⋊Zq. The definition of the semi-direct product depending on the choice of an homomorphism, we first analyze the different possibilities for this homomorphism in function of n and q. Then, we present a polynomial-time quantum algorithm for the case Zpr ⋊ Zp when p is an odd prime.
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