2017/12/01 by Changpeng Shao, Shao, Changpeng
Computer Science · Physics and Astronomy · #46N50 #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1712.01350
openalex publication_date 2017/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantum Fourier transformation is important in many quantum algorithms. In this paper, we generalize quantum Fourier transformation over the Abelian group ℤN from two different points to get more efficient unitary transformations. The obtained unitary transformations are given in concise and explicit formula which can be used directly. A relationship between the generalized quantum Fourier transformation and the dihedral hidden subgroup problem are discussed in this paper. This may lead a way to solve the dihedral hidden subgroup problem. The second goal of this paper is to give an explicit formula of quantum Haar transformation.