shor大数分解算法 Classical part[edit] Pick a random number a < N.Compute gcd(a, N). This may be done using the Euclidean algorithm.If gcd(a, N) ≠ 1, then this number is a nontrivial factor of N, so we are done.Otherwise, use the period-finding subrouti…
quantum Fourier transform
DFT 输入:复向量 x 0 , x 1 , x 2 , . . . , x N − 1 x_0,x_1,x_2,...,x_{N-1} x0,x1,x2,...,xN−1输出:复向量 y 0 , y 1 , y 2 , . . . , y N − 1 y_0,y_1,y_2,...,y_{N-1} y0,y1,y2,...,yN−1 y k 1 N…
周期函数: f ( x ) = a x m o d N f(x) = a^x \bmod{N} f(x)=axmodN 问题:如何找到一个周期函数的周期r?
Shor’s algorithm
Shor’s solution中函数U: U ∣ y ⟩ ≡ ∣ a y m o d N ⟩ U|y\rangle \equiv |ay \bmod N \rangle U∣y⟩≡∣aymodN⟩
接下来…