Quantum Fourier transform over symmetric groups — improved result. (July 2016) - Kawano, Yasuhito; Sekigawa, Hiroshi
Abstract: This paper describes the fastest quantum algorithm at this moment for the quantum Fourier transform (QFT) over symmetric groups. We provide a new FFT (classical) algorithm over symmetric groups and then transform it to a quantum algorithm. The complexity of our QFT algorithm is O ( n 3 log ⁡ n ), faster than the existing O ( n 4 log ⁡ n ) QFT algorithm. In addition, we show that the algorithm can be performed in O ( n 3 ) if the use of threshold gates is allowed.