An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Nil-2 Groups
نویسندگان
چکیده
منابع مشابه
An Efficient Quantum Algorithm for the Hidden Subgroup Problem in Extraspecial Groups
Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of ...
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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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ژورنال
عنوان ژورنال: Algorithmica
سال: 2010
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-010-9467-0