import numpy as np
import qutip
from matplotlib import pyplot, animation
from mpl_toolkits.mplot3d import Axes3D

def qubit_integrate(w, theta, gamma1, gamma2, psi0, tlist):
    # operators and the hamiltonian
    sx = qutip.sigmax()
    sy = qutip.sigmay()
    sz = qutip.sigmaz()
    sm = qutip.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 = qutip.mesolve(H, psi0, tlist, c_op_list, [sx, sy, sz])
    return output.expect[0], output.expect[1], output.expect[2]

## calculate the dynamics
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*qutip.basis(2, 0) + (1-a)*qutip.basis(2, 1))/np.sqrt(a**2 + (1-a)**2)
tlist = np.linspace(0, 4, 250)
#expectation values for ploting
sx, sy, sz = qubit_integrate(w, theta, gamma1, gamma2, psi0, tlist)

fig = pyplot.figure()
ax = Axes3D(fig, azim=-40, elev=30)
sphere = qutip.Bloch(axes=ax)

def animate(i):
   sphere.clear()
   sphere.add_vectors([np.sin(theta), 0, np.cos(theta)])
   sphere.add_points([sx[:i+1], sy[:i+1], sz[:i+1]])
   sphere.make_sphere()
   return ax

def init():
   sphere.vector_color = ['r']
   return ax

ani = animation.FuncAnimation(fig, animate, np.arange(len(sx)),
                              init_func=init, blit=False, repeat=False)
ani.save('bloch_sphere.mp4', fps=20)

QuTiP Version:      4.7.1
Numpy Version:      1.23.5
Scipy Version:      1.10.1
Cython Version:     None
Matplotlib Version: 3.7.1
Python Version:     3.11.2
Number of CPUs:     12
BLAS Info:          INTEL MKL
OPENMP Installed:   False
INTEL MKL Ext:      True
Platform Info:      Linux (x86_64)