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%matplotlib inline
import matplotlib.pyplot as plt
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import numpy as np
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import matplotlib.animation as animation
from mpl_toolkits.mplot3d import Axes3D
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from qutip import *
from qutip.ipynbtools import plot_animation
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def qubit_integrate(w, theta, gamma1, gamma2, psi0, tlist):
# operators and the hamiltonian
sx = sigmax(); sy = sigmay(); sz = sigmaz(); sm = sigmam()
H = w * (np.cos(theta) * sz + np.sin(theta) * sx)
# collapse operators
c_op_list = []
n_th = 0.5 # temperature
rate = gamma1 * (n_th + 1)
if rate > 0.0: c_op_list.append(np.sqrt(rate) * sm)
rate = gamma1 * n_th
if rate > 0.0: c_op_list.append(np.sqrt(rate) * sm.dag())
rate = gamma2
if rate > 0.0: c_op_list.append(np.sqrt(rate) * sz)
# evolve and calculate expectation values
output = mesolve(H, psi0, tlist, c_op_list, [sx, sy, sz])
return output
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w = 1.0 * 2 * np.pi # qubit angular frequency
theta = 0.2 * np.pi # qubit angle from sigma_z axis (toward sigma_x axis)
gamma1 = 0.5 # qubit relaxation rate
gamma2 = 0.2 # qubit dephasing rate
# initial state
a = 1.0
psi0 = (a* basis(2,0) + (1-a)*basis(2,1))/(np.sqrt(a**2 + (1-a)**2))
tlist = np.linspace(0, 4, 150)
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result = qubit_integrate(w, theta, gamma1, gamma2, psi0, tlist)
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def plot_setup(result):
fig = plt.figure(figsize=(8,8))
axes = Axes3D(fig, azim=-40,elev=30)
return fig, axes
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sphere = None
def plot_result(result, n, fig=None, axes=None):
global sphere
if fig is None or axes is None:
fig, axes = plot_setup(result)
if not sphere:
sphere = Bloch(axes=axes)
sphere.vector_color = ['r']
sphere.clear()
sphere.add_vectors([np.sin(theta), 0, np.cos(theta)])
sphere.add_points([result.expect[0][:n+1], result.expect[1][:n+1], result.expect[2][:n+1]], meth='l')
sphere.make_sphere()
return fig, axes
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plot_animation(plot_setup, plot_result, result)
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from qutip.ipynbtools import version_table
version_table()
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