An Efficient Quantum Algorithm for the Hidden Subgroup Problem over some Non-Abelian Groups
نویسندگان
چکیده
منابع مشابه
An Efficient Quantum Algorithm for the Hidden Subgroup Problem over Weyl-Heisenberg Groups
Many exponential speedups that have been achieved in quantum computing are obtained via hidden subgroup problems (HSPs). We show that the HSP over Weyl-Heisenberg groups can be solved efficiently on a quantum computer. These groups are well-known in physics and play an important role in the theory of quantum error-correcting codes. Our algorithm is based on noncommutative Fourier analysis of co...
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متن کاملAn Efficient Quantum 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 solving the HSP over the groups of the form Zpr ⋊ Zp...
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In this paper, we consider the hidden subgroup problem (HSP) over the class of semi-direct product groups Zpr ⋊ Zq, for p and q prime. We first present a classification of these groups in five classes. Then, we describe a polynomial-time quantum algorithm solving the HSP over all the groups of one of these classes: the groups of the form Zpr ⋊ Zp, where p is an odd prime. Our algorithm works ev...
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ژورنال
عنوان ژورنال: TEMA (São Carlos)
سال: 2017
ISSN: 2179-8451,1677-1966
DOI: 10.5540/tema.2017.018.02.0215