Imran, Muhammad and Ivanyos, Gábor (2024) Zero sum subsequences and hidden subgroups. QUANTUM INFORMATION PROCESSING, 23 (1). ISSN 1570-0755 10.1007/s11128-023-04228-2

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Abstract

We propose a method for solving the hidden subgroup problem in nilpotent groups. The main idea is iteratively transforming the hidden subgroup to its images in the quotient groups by the members of a central series, eventually to its image in the commutative quotient of the original group, and then using an abelian hidden subgroup algorithm to determine this image. Knowing this image allows one to descend to a proper subgroup unless the hidden subgroup is the full group. The transformation relies on finding zero sum subsequences of sufficiently large sequences of vectors over finite prime fields. We present a new deterministic polynomial time algorithm for the latter problem in the case when the size of the field is constant. The consequence is a polynomial time exact quantum algorithm for the hidden subgroup problem in nilpotent groups having constant nilpotency class and whose order only have prime factors also bounded by a constant.

Item Type:	Article
Subjects:	Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Divisions:	Informatics Laboratory
SWORD Depositor:	MTMT Injector
Depositing User:	MTMT Injector
Date Deposited:	24 Feb 2024 16:50
Last Modified:	24 Feb 2024 16:50
URI:	https://eprints.sztaki.hu/id/eprint/10704

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