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<p>In the field of quantum computing, the hidden subgroup problem (HSP) for finitely generated Abelian groups has been effectively solved, while research on non-Abelian groups continues to explore quantum computational capabilities. The dihedral hidden subgroup problem (DHSP), critical for cryptographic security, has attracted significant attention. This paper presents a quantum–classical hybrid scheme that replaces the iterative step in DHSP algorithms. The method generalizes the semiclassical quantum Fourier transform (QFT) to the DHSP context, which avoids serial processing limitations and reduces the complexity of modifying sampling circuits. By decoupling sampling from iteration, the proposed scheme enhances overall algorithmic efficiency.</p>

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Improvements to the DHSP quantum solving algorithm

  • 期刊论文

  • 发表日期：

    2026年4月4日

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  • Cui Fuxin,
  • Wang Bei,
  • Dou Menghan,
  • Li Ye

摘要

In the field of quantum computing, the hidden subgroup problem (HSP) for finitely generated Abelian groups has been effectively solved, while research on non-Abelian groups continues to explore quantum computational capabilities. The dihedral hidden subgroup problem (DHSP), critical for cryptographic security, has attracted significant attention. This paper presents a quantum–classical hybrid scheme that replaces the iterative step in DHSP algorithms. The method generalizes the semiclassical quantum Fourier transform (QFT) to the DHSP context, which avoids serial processing limitations and reduces the complexity of modifying sampling circuits. By decoupling sampling from iteration, the proposed scheme enhances overall algorithmic efficiency.