class BlochPlot():
'''
Dynamic plot context, intended for displaying geometries.
like removing axes, equal axis, dynamically tune your figure and save it.
Args:
figsize (tuple, default=(6,4)): figure size.
filename (filename, str): filename to store generated figure, if None, it will not save a figure.
Attributes:
figsize (tuple, default=(6,4)): figure size.
filename (filename, str): filename to store generated figure, if None, it will not save a figure.
ax (Axes): matplotlib Axes instance.
Examples:
with BlochPlot() as bp:
bp.ball.add_vectors([0.4, 0.6, 0.8])
'''
def __init__(self, figsize=(6, 4), filename=None, dpi=300):
self.figsize = figsize
self.filename = filename
self.ax = None
def __enter__(self):
from qutip import Bloch3d, Bloch
plt.ion()
self.fig = plt.figure(figsize=self.figsize)
self.ax = Axes3D(self.fig, azim=-30, elev=15)
self.ball = Bloch(axes=self.ax)
self.ball.zlabel = [r'$|N\rangle$', r'$|S\rangle$']
return self
def __exit__(self, *args):
self.ax.axis('off')
self.ax.set_aspect("equal")
#self.ball.make_sphere()
self.ball.make_sphere()
plt.close()
if self.filename is not None:
print('Press `c` to save figure to "%s", `Ctrl+d` to break >>' %
self.filename)
pdb.set_trace()
plt.savefig(self.filename, dpi=300)
else:
pdb.set_trace()
def add_polar(self, theta, phi, color=None):
self.ball.add_vectors(polar2vec([1, theta, phi]))
self.ball.vector_color.append(color)
def text(self, vec, txt, fontsize=14):
if len(vec) == 2:
vec = polar2vec(*vec)
self.ax.text(vec[0],
vec[1],
vec[2],
txt,
fontsize=fontsize,
va='center',
ha='center')
def bloch_from_dataframe(df, fig, axes):
"""
Plot Bloch sphere
:param df: pd.DataFrame
:param axes:
:return:
"""
bloch = Bloch(fig=fig, axes=axes)
bloch.vector_color = plt.get_cmap('viridis')(np.linspace(0, 1, len(df)))
bloch.add_states([
Qobj([[row.Jxx, row.beta + 1j * row.gamma],
[row.beta - 1j * row.gamma, row.Jyy]])
for _, row in df.iterrows()
])
bloch.make_sphere()
class CVisualizeAnim(object):
"""
Class for drawing animation
"""
def __init__(self, fig):
#################################################################
#
# Initialize plotting exact plots tools
#
#################################################################
# p = np.linspace(-20., 20., 1000)[:, np.newaxis]
# q = np.linspace(-20., 20., 1000)[np.newaxis, :]
#
# self.hybrid = CAnalyticQCHybrid(p, q, kT=0.5)
#
# img_params = dict(
# extent=[q.min(), q.max(), p.min(), p.max()],
# origin='lower',
# cmap='seismic',
# # norm=WignerNormalize(vmin=-0.1, vmax=0.1)
# norm=WignerSymLogNorm(linthresh=1e-10, vmin=-0.01, vmax=0.1)
# )
p = np.linspace(-25, 25, 600)[:, np.newaxis]
q = np.linspace(-25, 25, 600)[np.newaxis, :]
self.hybrid = CAnalyticQCHybrid(p=p,
q=q,
omega=1.,
beta=2.,
alpha=0.95)
img_params = dict(
extent=[q.min(), q.max(), p.min(),
p.max()],
origin='lower',
cmap='seismic',
# norm=WignerNormalize(vmin=-0.1, vmax=0.1)
norm=WignerSymLogNorm(linthresh=1e-10, vmin=-0.01, vmax=0.1))
#################################################################
#
# Initialize Pauli propagator
#
#################################################################
self.pauli = SplitOpPauliLike1D(
X_amplitude=2. * q.max(),
X_gridDIM=512,
dt=0.0001,
K0="0.5 * P ** 2",
V0="0.5 * X ** 2",
V1="0.5 * 0.95 * X ** 2",
# kT=self.hybrid.kT, # parameters controlling the width of the initial wavepacket
).set_wavefunction("exp(-0.5 * X ** 2)")
#################################################################
#
# Initialize plotting facility
#
#################################################################
self.fig = fig
self.fig.suptitle(
"Quantum-classical hybrid $m=1$, $\omega=1$, $\\alpha=0.95$, $\\beta={:.1e}$ (a.u.) (a.u.)"
.format(self.hybrid.beta))
self.ax = fig.add_subplot(221)
self.ax.set_title('Classical density')
# generate empty plots
self.img_classical_density = self.ax.imshow([[0]], **img_params)
self.ax.set_xlabel('$q$ (a.u.)')
self.ax.set_ylabel('$p$ (a.u.)')
ax = fig.add_subplot(222)
ax.set_title('Quantum purity')
self.quantum_purity_plot, = ax.plot([0., 40], [1, 0.5],
label='hybrid')
self.pauli_quantum_purity_plot, = ax.plot([0., 40], [1, 0.5],
label='Pauli')
ax.set_xlabel('time (a.u.)')
ax.set_ylabel("quantum purity")
ax.legend()
self.time = []
self.qpurity = []
self.pauli_qpurity = []
ax = fig.add_subplot(223)
ax.set_title("Coordinate distribution")
self.c_coordinate_distribution, = ax.semilogy(
[self.hybrid.q.min(), self.hybrid.q.max()], [1e-11, 1e0],
label="hybrid")
self.pauli_coordinate_distribution, = ax.semilogy(
[self.hybrid.q.min(), self.hybrid.q.max()], [1e-11, 1e0],
label="Pauli")
ax.legend()
ax.set_xlabel('$q$ (a.u.)')
ax.set_ylabel('Probability density')
ax = fig.add_subplot(224, projection='3d', azim=90, elev=0)
self.bloch = Bloch(axes=ax)
self.bloch.make_sphere()
def __call__(self, frame_num):
"""
Draw a new frame
:param frame_num: current frame number
:return: image objects
"""
# convert the frame number to time
#t = 0.05 * frame_num
t = self.pauli.t
# calculate the hybrid density matrix
self.hybrid.calculate_D(t)
# plot the classical density
c_rho = self.hybrid.classical_density()
self.img_classical_density.set_array(c_rho)
self.ax.set_title(
'Classical density \n $t = {:.1f}$ (a.u.)'.format(t))
# plot the coordinate distribution for the classical density
coordinate_marginal = c_rho.sum(axis=0)
# coordinate_marginal *= self.hybrid.dp
coordinate_marginal /= coordinate_marginal.max()
self.c_coordinate_distribution.set_data(self.hybrid.q.reshape(-1),
coordinate_marginal)
coordinate_density = self.pauli.coordinate_density
coordinate_density /= coordinate_density.max()
self.pauli_coordinate_distribution.set_data(
self.pauli.X, coordinate_density)
# plot quantum purity
self.time.append(t)
self.qpurity.append(self.hybrid.quantum_purity())
self.quantum_purity_plot.set_data(self.time, self.qpurity)
# Get the Pauli density matrix
rho12 = np.sum(self.pauli.psi1 * self.pauli.psi2.conjugate())
rho_pauli = np.array(
[[np.sum(np.abs(self.pauli.psi1)**2), rho12],
[rho12.conjugate(),
np.sum(np.abs(self.pauli.psi2)**2)]])
rho_pauli *= self.pauli.dX
# plot Pauli purity
self.pauli_qpurity.append(rho_pauli.dot(rho_pauli).trace().real)
self.pauli_quantum_purity_plot.set_data(self.time,
self.pauli_qpurity)
# plot Bloch vector
self.bloch.clear()
self.bloch.add_states(
[Qobj(self.hybrid.quantum_density()),
Qobj(rho_pauli)])
self.bloch.make_sphere()
#
self.pauli.propagate(1000)
return self.img_classical_density, self.quantum_purity_plot, self.pauli_quantum_purity_plot,\
self.bloch, self.pauli_coordinate_distribution
class CVisualizeAnim(object):
"""
Class for drawing animation
"""
def __init__(self, fig):
#################################################################
#
# Initialize plotting exact plots tools
#
#################################################################
# p = np.linspace(-20., 20., 1000)[:, np.newaxis]
# q = np.linspace(-20., 20., 1000)[np.newaxis, :]
#
# self.hybrid = CAnalyticQCHybrid(p, q, kT=0.5)
#
# img_params = dict(
# extent=[q.min(), q.max(), p.min(), p.max()],
# origin='lower',
# cmap='seismic',
# # norm=WignerNormalize(vmin=-0.1, vmax=0.1)
# norm=WignerSymLogNorm(linthresh=1e-10, vmin=-0.01, vmax=0.1)
# )
p = np.linspace(-0.1, 0.1, 500)[:, np.newaxis]
q = np.linspace(-0.1, 0.1, 500)[np.newaxis, :]
self.hybrid = SolAGKEq(p=p, q=q, omega=1., beta=1e5, alpha=0.95)
img_params = dict(
extent=[q.min(), q.max(), p.min(),
p.max()],
origin='lower',
cmap='seismic',
#norm=WignerNormalize(vmin=-0.1, vmax=0.1)
norm=WignerSymLogNorm(linthresh=1e-10, vmin=-0.01, vmax=0.1))
# List to save the total hybrid energy for testing (it must be a conserved quantity)
self.total_energy = []
# List to save the x component of the Bloch vector
self.sigma_1 = []
#################################################################
#
# Initialize plotting facility
#
#################################################################
self.fig = fig
self.fig.suptitle(
"Quantum-classical hybrid $m=1$, $\omega=1$, $\\alpha=0.95$, $\\beta={:.1e}$ (a.u.) (a.u.)"
.format(self.hybrid.beta))
self.ax = fig.add_subplot(221)
self.ax.set_title('Classical density')
# generate empty plots
self.img_classical_density = self.ax.imshow([[0]], **img_params)
self.ax.set_xlabel('$q$ (a.u.)')
self.ax.set_ylabel('$p$ (a.u.)')
ax = fig.add_subplot(222)
ax.set_title('Quantum purity')
self.quantum_purity_plot, = ax.plot([0., 1000000], [1, 0.5])
ax.set_xlabel('time (a.u.)')
ax.set_ylabel("quantum purity")
self.time = []
self.qpurity = []
ax = fig.add_subplot(223)
ax.set_title("Coordinate distribution")
self.c_coordinate_distribution, = ax.semilogy(
[self.hybrid.q.min(), self.hybrid.q.max()], [1e-11, 1e0],
label="hybrid")
ax.legend()
ax.set_xlabel('$q$ (a.u.)')
ax.set_ylabel('Probability density')
ax = fig.add_subplot(224, projection='3d', azim=0, elev=0)
self.bloch = Bloch(axes=ax)
self.bloch.make_sphere()
def __call__(self, frame_num):
"""
Draw a new frame
:param frame_num: current frame number
:return: image objects
"""
# convert the frame number to time
t = 4000. * frame_num
# calculate the hybrid density matrix
self.hybrid.calculate_D(t)
# Save total energy
self.total_energy.append(self.hybrid.energy())
# Save <sigma_1>
self.sigma_1.append(self.hybrid.average_sigma_1())
# plot the classical density
c_rho = self.hybrid.classical_density()
self.img_classical_density.set_array(c_rho)
self.ax.set_title(
'Classical density \n $t = {:.1f}$ (a.u.)'.format(t))
# plot the coordinate distribution for the classical density
coordinate_marginal = c_rho.sum(axis=0)
# coordinate_marginal *= self.hybrid.dp
coordinate_marginal /= coordinate_marginal.max()
self.c_coordinate_distribution.set_data(self.hybrid.q.reshape(-1),
coordinate_marginal)
# plot quantum purity
self.time.append(t)
self.qpurity.append(self.hybrid.quantum_purity())
self.quantum_purity_plot.set_data(self.time, self.qpurity)
# plot Bloch vector
self.bloch.clear()
self.bloch.add_states(Qobj(self.hybrid.quantum_density()))
self.bloch.make_sphere()
#
# self.pauli.propagate(100)
return self.img_classical_density, self.quantum_purity_plot, self.bloch,
@author: wittek
"""
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from qutip import Bloch
from graphics_utils import initialize_graphics
colors = initialize_graphics()
fig = plt.figure()
axes = Axes3D(fig)
axes.grid = True
axes.axis("off")
axes.set_axis_off()
b=Bloch()
b.fig = fig
b.axes = axes
#b.fig = fig
#b.frame_width=1
b.sphere_color = 'white'
b.sphere_alpha = 0.1
#b.size = [10, 10]
b.make_sphere()
plt.savefig('./bloch_sphere.svg',bbox_inches='tight')
#b.show()
#b.save('bloch_sphere.pdf',format='pdf')