摘要
Because of the difficulty of building a high-dimensional quantum register,this paper presents an implementation of the high-dimensional quantum Fourier transform(QFT)based on a low-dimensional quantum register.First,we define the t-bit semi- classical quantum Fourier transform.In terms of probability amplitude,we prove that the transform can realize quantum Fourier transformation,illustrate that the requirement for the two-qubit gate reduces obviously,and further design a quantum circuit of the transform.Combining the classical fixed-window method and the implementation of Shor's quantum factorization algorithm,we then redesign a circuit for Shor's algorithm,whose required computation resource is approximately equal to that of Parker's.The requirement for elementary quantum gates for Parker's algorithm is 3 O (logN),and the quantum register for our circuit re- quires t-1 more dimensions than Parker's.However,our circuit is t2 times as fast as Parker's,where t is the width of the window.
Because of the difficulty of building a high-dimensional quantum register, this paper presents an implementation of the high-dimensional quantum Fourier transform （QFT） based on a low-dimensional quantum register. First, we define the t-bit semiclassical quantum Fourier transform. In terms of probability amplitude, we prove that the transform can realize quantum Fourier transformation, illustrate that the requirement for the two-qubit gate reduces obviously, and further design a quantum circuit of the transform. Combining the classical fixed-window method and the implementation of Shor＇s quantum factorization algorithm, we then redesign a circuit for Shor＇s algorithm, whose required computation resource is approximately equal to that of Parker＇s. The requirement for elementary quantum gates for Parker＇s algorithm is O（log N]3）, and the quantum register for our circuit requires t-1 more dimensions than Parker＇s. However, our circuit is t2 times as fast as Parker＇s, where t is the width of the window.
作者简介
Corresponding author:BAO WanSu,email:2010thzz@sina.com.
