# QuTiP example: Bloch sphere animation¶

J.R. Johansson and P.D. Nation

Animation with qutip and matplotlib: decaying qubit visualized in a Bloch sphere. (Animation with matplotlib does not work yet in python3)

In [1]:
%matplotlib inline
import matplotlib.pyplot as plt

In [2]:
import numpy as np

In [3]:
import matplotlib.animation as animation
from mpl_toolkits.mplot3d import Axes3D

In [4]:
from qutip import *
from qutip.ipynbtools import plot_animation

In [5]:
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

In [6]:
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)

In [7]:
result = qubit_integrate(w, theta, gamma1, gamma2, psi0, tlist)

In [8]:
def plot_setup(result):

fig = plt.figure(figsize=(8,8))
axes = Axes3D(fig, azim=-40,elev=30)

return fig, axes

In [9]:
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.make_sphere()

return fig, axes

In [10]:
plot_animation(plot_setup, plot_result, result)

Out[10]:
<matplotlib.figure.Figure at 0x7fcf87c94950>

## Versions¶

In [11]:
from qutip.ipynbtools import version_table

version_table()

Out[11]:
SoftwareVersion
Cython0.21.1
SciPy0.14.0
QuTiP3.1.0
Python2.7.8 (default, Oct 20 2014, 15:05:19) [GCC 4.9.1]
IPython2.3.0
OSposix [linux2]
Numpy1.9.0
matplotlib1.4.2
Tue Jan 13 11:57:02 2015 JST