Research On Quantum Fourier Transformation And It's Applications

Quantum Fourier transform(QFT) is an important algorithm in quantum computation. Quantum computer can solve the problem using QFT and Quantum Searching Algorithm, which problem need too much resource in classical computer. In this paper, we translate the potent circuitry of QFT and the first moment of phase estimation again. This paper is organized as follows.In Chapter 1, first we introduce some definitions in quantum computation and quantum information, e. g. quantum, quantum bit. Then we expound some principle in quantum mechanics. And we explain the quantum state can not be cloned. At last, we discuss a few of quantum bit gates.In Chapter 2, first we introduce the definition of QFT. To understand the potent circuitry of QFT more, we study the factorization of QFT and we give an example. By similar way, we get the factorization of the first moment of phase estimation.