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import math as mth
import cmath as cmt
import numpy as npy
import scipy.linalg as sla
#import matplotlib.pyplot as plt
alpha = 1 / npy.sqrt(2)
beta = 1 / npy.sqrt(2)
state = npy.array([alpha, beta])
dt = 0.2
iterations = 20
H = npy.array([[2,-2j],[2j,3]])
def time_evolution(state, dt = dt):
return npy.dot(state, sla.expm(-1j * dt * H))
def bloch_map(state):
temp = npy.conj(state[0] / state[1])
phi = 2 * npy.arctan(1 / abs(temp))
theta = npy.arctan(temp.imag / temp.real)
return npy.array([phi, theta])
def sphere2cart(phi, theta):
return [
mth.sin(theta) * mth.cos(phi),
mth.sin(theta) * mth.sin(phi),
mth.cos(theta)
]
historie = npy.array([bloch_map(state)])
for i in range(iterations):
state = time_evolution(state)
h = npy.dot(state, state)
historie = npy.vstack([historie,bloch_map(state)])
coords = bloch_map(state)
coords = sphere2cart(coords[0], coords[1])
print(f"{coords[0]}; {coords[1]}; {coords[2]}")
import plotting
plotting.phi(historie[:,0])
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