Abstract
This paper proposes an O(n4) quantum Fourier transform (QFT) algorithm over symmetric group Sn, the fastest QFT algorithm of its kind. We propose a fast Fourier transform algorithm over symmetric group Sn, which consists of O(n3) multiplications of unitary matrices, and then transform it into a quantum circuit form. The QFT algorithm can be applied to constructing the standard algorithm of the hidden subgroup problem.
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