Revisiting finite Abelian hidden subgroup problem and its distributed exact quantum algorithm

• URL: http://arxiv.org/abs/2512.22959v1
• Date: Sun, 28 Dec 2025 15:00:50 GMT
• Title: Revisiting finite Abelian hidden subgroup problem and its distributed exact quantum algorithm
• Authors: Ziyuan Dong, Xiang Fan, Tengxun Zhong, Daowen Qiu,
• Abstract summary: We revisit the finite Abelian hidden subgroup problem (AHSP) from a mathematical perspective.<n>We present an exact quantum algorithm for the finite AHSP, which is more concise than the previous exact algorithm.<n>We propose a distributed exact quantum algorithm for finite AHSP, which requires fewer qudits, lower quantum query complexity, and no quantum communication.
• Score: 4.250782756734906
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We revisit the finite Abelian hidden subgroup problem (AHSP) from a mathematical perspective and make the following contributions. First, by employing amplitude amplification, we present an exact quantum algorithm for the finite AHSP, our algorithm is more concise than the previous exact algorithm and applies to any finite Abelian group. Second, utilizing the Chinese Remainder Theorem, we propose a distributed exact quantum algorithm for finite AHSP, which requires fewer qudits, lower quantum query complexity, and no quantum communication. We further show that our distributed approach can be extended to certain classes of non-Abelian groups. Finally, we develop a parallel exact classical algorithm for finite AHSP with reduced query complexity; even without parallel execution, the total number of queries across all nodes does not exceed that of the original centralized algorithm under mild conditions.

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