摘要
文中通过多次量子Fourier变换和变量代换,给出了一个ZN上离散对数量子计算算法,刻画了元素的阶r与算法成功率的关系,当r为素数时,算法成功的概率接近于1,新算法所需基本量子门数的规模为O(L3),且不需要执行函数|f(x1,x2)〉的量子Fourier变换的反演变换,优于已有的ZN上离散对数量子计算算法,其中L=[log N]+1.
By applying multiple Fourier transform and variable transform,a quantum algorithmfor discrete logarithm problem over ZN is presented.The relationship between order r and successprobability is quantitatively characterized,where r is the order of the selective element.Particularly,when r is a prime number,the success probability is close to 1 and the scale of elementary quantumgates is O（L3）,where L=[logN]＋1.The new algorithm doesn’t need to perform inverse quantumFourier transform on｜f（X1,X2）〉,which is superior to the existing algorithm.
出处
《计算机学报》
EI
CSCD
北大核心
2014年第5期1058-1062,共5页
Chinese Journal of Computers
基金
国家"九七三"重点基础研究发展规划项目基金(2013CB338002)资助
