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December 25, 2015 04:53
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Simulation of Shor's Algorithm
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import numpy as np | |
import matplotlib.pyplot as plt | |
def Hadamard(n): | |
def Hn(H=np.array([[1, 1], [1, -1]], dtype=np.complex64), n=n): | |
if n > 1: | |
return Hn(H=np.kron(np.array([[1, 1], [1, -1]], dtype=np.complex64), H), n=n-1) | |
return H | |
return Hn(n=n) | |
def QFT(t): | |
Q = np.zeros(shape=(2 ** t, 2 ** t), dtype=np.complex64) | |
N = 2 ** t | |
for i in range(N): | |
for j in range(N): | |
Q[i][j] = np.exp(np.pi * 2j * ((i * j) % N) / N) | |
return Q | |
N = 21 | |
t = 9 | |
H = Hadamard(t) | |
reg1 = np.zeros(shape=(2 ** t), dtype=np.complex64) | |
reg2 = np.ones(shape=(2 ** t), dtype=np.complex64) | |
reg1[0] = 1 | |
reg1 = H.dot(reg1) | |
for i in range(2 ** t): | |
reg2[i] = 2 ** i % N | |
r = reg2[0] | |
for i in range(2 ** t): | |
if reg2[i] != r: | |
reg1[i] = 0 | |
Q = QFT(9) | |
reg1 = np.linalg.inv(Q).dot(reg1) | |
print abs(reg1) | |
print abs(reg1[0]) | |
print abs(reg1[85]) | |
print abs(reg1[86]) | |
fig, ax = plt.subplots( nrows=1, ncols=1 ) | |
ax.plot(abs(reg1)) | |
fig.savefig('plot.png') | |
plt.close(fig) |
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