An Efficient Quantum Algorithm for the Hidden Subgroup Problem over some Non-Abelian Groups

Demerson Nunes Gonçalves, Tharso D Fernandes, C M M Cosme

Abstract


The hidden subgroup problem (HSP) plays an important role in quantum computation, because many quantum algorithms that are exponentially faster than classical algorithms are special cases of the HSP. In this paper we show that there exist a new efficient quantum algorithm for the HSP on groups $\Z_{N}\rtimes\Z_{q^s}$ where $N$ is an integer with a special prime factorization, $q$ prime number and $s$ any positive integer.


Keywords


Quantum Algorithms, Hidden Subgroup Problem, Quantum Computational Group Theory

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References


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DOI: http://dx.doi.org/10.5540/tema.2017.018.02.0215

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TEMA - Trends in Applied and Computational Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)
ISSN: 1677-1966  (print version),  2179-8451  (online version)

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