Realization of quantum Fourier transform over ZN

doi:10.1088/1674-1056/23/2/020306

Abstract Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over Z_N based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z_N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z_N. According to probability amplitude, we prove that the transform can be used to realize QFT over Z_N and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z_N.

Keywords: quantum Fourier transform semiclassical quantum Fourier transform quantum algorithm

Received: 21 April 2013
Revised: 04 July 2013
Accepted manuscript online:

PACS:	03.67.Lx	(Quantum computation architectures and implementations)
	03.65.Sq	(Semiclassical theories and applications)
	03.65.Ta	(Foundations of quantum mechanics; measurement theory)
	03.67.-a	(Quantum information)

Fund: Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).

Corresponding Authors: Bao Wan-Su
E-mail: 2010thzz@sina.com

About author: 03.67.Lx; 03.65.Sq; 03.65.Ta; 03.67.-a

Cite this article:

Fu Xiang-Qun (付向群), Bao Wan-Su (鲍皖苏), Li Fa-Da (李发达), Zhang Yu-Chao (张宇超) Realization of quantum Fourier transform over Z_N 2014 Chin. Phys. B 23 020306

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Realization of quantum Fourier transform over Z_N