# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2018.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
# pylint: disable=invalid-name,ungrouped-imports,import-error
# pylint: disable=inconsistent-return-statements,unsubscriptable-object
# pylint: disable=missing-param-doc,missing-type-doc,unused-argument
"""
Visualization functions for quantum states.
"""
from functools import reduce
import colorsys
import numpy as np
from scipy import linalg
from qiskit.quantum_info.states import DensityMatrix
from qiskit.util import deprecate_arguments
from .matplotlib import HAS_MATPLOTLIB
if HAS_MATPLOTLIB:
from matplotlib import get_backend
from matplotlib import pyplot as plt
from matplotlib.patches import FancyArrowPatch
from matplotlib.patches import Circle
import matplotlib.colors as mcolors
from matplotlib.colors import Normalize, LightSource
import matplotlib.gridspec as gridspec
from mpl_toolkits.mplot3d import proj3d
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from qiskit.visualization.exceptions import VisualizationError
from qiskit.visualization.bloch import Bloch
from qiskit.visualization.utils import _bloch_multivector_data, _paulivec_data
from qiskit.circuit.tools.pi_check import pi_check
if HAS_MATPLOTLIB:
class Arrow3D(FancyArrowPatch):
"""Standard 3D arrow."""
def __init__(self, xs, ys, zs, *args, **kwargs):
"""Create arrow."""
FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs)
self._verts3d = xs, ys, zs
def draw(self, renderer):
"""Draw the arrow."""
xs3d, ys3d, zs3d = self._verts3d
xs, ys, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
FancyArrowPatch.draw(self, renderer)
[docs]@deprecate_arguments({'rho': 'state'})
def plot_state_hinton(state, title='', figsize=None, ax_real=None, ax_imag=None, *, rho=None):
"""Plot a hinton diagram for the density matrix of a quantum state.
Args:
state (Statevector or DensityMatrix or ndarray): An N-qubit quantum state.
title (str): a string that represents the plot title
figsize (tuple): Figure size in inches.
ax_real (matplotlib.axes.Axes): An optional Axes object to be used for
the visualization output. If none is specified a new matplotlib
Figure will be created and used. If this is specified without an
ax_imag only the real component plot will be generated.
Additionally, if specified there will be no returned Figure since
it is redundant.
ax_imag (matplotlib.axes.Axes): An optional Axes object to be used for
the visualization output. If none is specified a new matplotlib
Figure will be created and used. If this is specified without an
ax_imag only the real component plot will be generated.
Additionally, if specified there will be no returned Figure since
it is redundant.
Returns:
matplotlib.Figure:
The matplotlib.Figure of the visualization if
neither ax_real or ax_imag is set.
Raises:
ImportError: Requires matplotlib.
VisualizationError: if input is not a valid N-qubit state.
Example:
.. jupyter-execute::
from qiskit import QuantumCircuit
from qiskit.quantum_info import DensityMatrix
from qiskit.visualization import plot_state_hinton
%matplotlib inline
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
state = DensityMatrix.from_instruction(qc)
plot_state_hinton(state, title="New Hinton Plot")
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed. To install, run '
'"pip install matplotlib".')
# Figure data
rho = DensityMatrix(state)
num = rho.num_qubits
if num is None:
raise VisualizationError("Input is not a multi-qubit quantum state.")
max_weight = 2 ** np.ceil(np.log(np.abs(rho.data).max()) / np.log(2))
datareal = np.real(rho.data)
dataimag = np.imag(rho.data)
if figsize is None:
figsize = (8, 5)
if not ax_real and not ax_imag:
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=figsize)
else:
if ax_real:
fig = ax_real.get_figure()
else:
fig = ax_imag.get_figure()
ax1 = ax_real
ax2 = ax_imag
column_names = [bin(i)[2:].zfill(num) for i in range(2**num)]
row_names = [bin(i)[2:].zfill(num) for i in range(2**num)]
ly, lx = datareal.shape
# Real
if ax1:
ax1.patch.set_facecolor('gray')
ax1.set_aspect('equal', 'box')
ax1.xaxis.set_major_locator(plt.NullLocator())
ax1.yaxis.set_major_locator(plt.NullLocator())
for (x, y), w in np.ndenumerate(datareal):
color = 'white' if w > 0 else 'black'
size = np.sqrt(np.abs(w) / max_weight)
rect = plt.Rectangle([x - size / 2, y - size / 2], size, size,
facecolor=color, edgecolor=color)
ax1.add_patch(rect)
ax1.set_xticks(np.arange(0, lx+0.5, 1))
ax1.set_yticks(np.arange(0, ly+0.5, 1))
row_names.append('')
ax1.set_yticklabels(row_names, fontsize=14)
column_names.append('')
ax1.set_xticklabels(column_names, fontsize=14, rotation=90)
ax1.autoscale_view()
ax1.invert_yaxis()
ax1.set_title('Re[$\\rho$]', fontsize=14)
# Imaginary
if ax2:
ax2.patch.set_facecolor('gray')
ax2.set_aspect('equal', 'box')
ax2.xaxis.set_major_locator(plt.NullLocator())
ax2.yaxis.set_major_locator(plt.NullLocator())
for (x, y), w in np.ndenumerate(dataimag):
color = 'white' if w > 0 else 'black'
size = np.sqrt(np.abs(w) / max_weight)
rect = plt.Rectangle([x - size / 2, y - size / 2], size, size,
facecolor=color, edgecolor=color)
ax2.add_patch(rect)
ax2.set_xticks(np.arange(0, lx+0.5, 1))
ax2.set_yticks(np.arange(0, ly+0.5, 1))
ax2.set_yticklabels(row_names, fontsize=14)
ax2.set_xticklabels(column_names, fontsize=14, rotation=90)
ax2.autoscale_view()
ax2.invert_yaxis()
ax2.set_title('Im[$\\rho$]', fontsize=14)
if title:
fig.suptitle(title, fontsize=16)
if ax_real is None and ax_imag is None:
if get_backend() in ['module://ipykernel.pylab.backend_inline',
'nbAgg']:
plt.close(fig)
return fig
[docs]def plot_bloch_vector(bloch, title="", ax=None, figsize=None, coord_type="cartesian"):
"""Plot the Bloch sphere.
Plot a sphere, axes, the Bloch vector, and its projections onto each axis.
Args:
bloch (list[double]): array of three elements where [<x>, <y>, <z>] (cartesian)
or [<r>, <theta>, <phi>] (spherical in radians)
<theta> is inclination angle from +z direction
<phi> is azimuth from +x direction
title (str): a string that represents the plot title
ax (matplotlib.axes.Axes): An Axes to use for rendering the bloch
sphere
figsize (tuple): Figure size in inches. Has no effect is passing ``ax``.
coord_type (str): a string that specifies coordinate type for bloch
(cartesian or spherical), default is cartesian
Returns:
Figure: A matplotlib figure instance if ``ax = None``.
Raises:
ImportError: Requires matplotlib.
Example:
.. jupyter-execute::
from qiskit.visualization import plot_bloch_vector
%matplotlib inline
plot_bloch_vector([0,1,0], title="New Bloch Sphere")
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed. To install, run '
'"pip install matplotlib".')
if figsize is None:
figsize = (5, 5)
B = Bloch(axes=ax)
if coord_type == "spherical":
r, theta, phi = bloch[0], bloch[1], bloch[2]
bloch[0] = r*np.sin(theta)*np.cos(phi)
bloch[1] = r*np.sin(theta)*np.sin(phi)
bloch[2] = r*np.cos(theta)
B.add_vectors(bloch)
B.render(title=title)
if ax is None:
fig = B.fig
fig.set_size_inches(figsize[0], figsize[1])
if get_backend() in ['module://ipykernel.pylab.backend_inline',
'nbAgg']:
plt.close(fig)
return fig
return None
[docs]@deprecate_arguments({'rho': 'state'})
def plot_bloch_multivector(state, title='', figsize=None, *, rho=None):
"""Plot the Bloch sphere.
Plot a sphere, axes, the Bloch vector, and its projections onto each axis.
Args:
state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state.
title (str): a string that represents the plot title
figsize (tuple): Has no effect, here for compatibility only.
Returns:
matplotlib.Figure:
A matplotlib figure instance.
Raises:
ImportError: Requires matplotlib.
VisualizationError: if input is not a valid N-qubit state.
Example:
.. jupyter-execute::
from qiskit import QuantumCircuit
from qiskit.quantum_info import Statevector
from qiskit.visualization import plot_bloch_multivector
%matplotlib inline
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
state = Statevector.from_instruction(qc)
plot_bloch_multivector(state, title="New Bloch Multivector")
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed. To install, run "pip install '
'matplotlib".')
# Data
bloch_data = _bloch_multivector_data(state)
num = len(bloch_data)
width, height = plt.figaspect(1/num)
fig = plt.figure(figsize=(width, height))
for i in range(num):
ax = fig.add_subplot(1, num, i + 1, projection='3d')
plot_bloch_vector(bloch_data[i], "qubit " + str(i), ax=ax,
figsize=figsize)
fig.suptitle(title, fontsize=16)
if get_backend() in ['module://ipykernel.pylab.backend_inline',
'nbAgg']:
plt.close(fig)
return fig
[docs]@deprecate_arguments({'rho': 'state'})
def plot_state_city(state, title="", figsize=None, color=None,
alpha=1, ax_real=None, ax_imag=None, *, rho=None):
"""Plot the cityscape of quantum state.
Plot two 3d bar graphs (two dimensional) of the real and imaginary
part of the density matrix rho.
Args:
state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state.
title (str): a string that represents the plot title
figsize (tuple): Figure size in inches.
color (list): A list of len=2 giving colors for real and
imaginary components of matrix elements.
alpha (float): Transparency value for bars
ax_real (matplotlib.axes.Axes): An optional Axes object to be used for
the visualization output. If none is specified a new matplotlib
Figure will be created and used. If this is specified without an
ax_imag only the real component plot will be generated.
Additionally, if specified there will be no returned Figure since
it is redundant.
ax_imag (matplotlib.axes.Axes): An optional Axes object to be used for
the visualization output. If none is specified a new matplotlib
Figure will be created and used. If this is specified without an
ax_imag only the real component plot will be generated.
Additionally, if specified there will be no returned Figure since
it is redundant.
Returns:
matplotlib.Figure:
The matplotlib.Figure of the visualization if the
``ax_real`` and ``ax_imag`` kwargs are not set
Raises:
ImportError: Requires matplotlib.
ValueError: When 'color' is not a list of len=2.
VisualizationError: if input is not a valid N-qubit state.
Example:
.. jupyter-execute::
from qiskit import QuantumCircuit
from qiskit.quantum_info import DensityMatrix
from qiskit.visualization import plot_state_city
%matplotlib inline
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
state = DensityMatrix.from_instruction(qc)
plot_state_city(state, color=['midnightblue', 'midnightblue'],
title="New State City")
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed. To install, run "pip install '
'matplotlib".')
rho = DensityMatrix(state)
num = rho.num_qubits
if num is None:
raise VisualizationError("Input is not a multi-qubit quantum state.")
# get the real and imag parts of rho
datareal = np.real(rho.data)
dataimag = np.imag(rho.data)
# get the labels
column_names = [bin(i)[2:].zfill(num) for i in range(2**num)]
row_names = [bin(i)[2:].zfill(num) for i in range(2**num)]
lx = len(datareal[0]) # Work out matrix dimensions
ly = len(datareal[:, 0])
xpos = np.arange(0, lx, 1) # Set up a mesh of positions
ypos = np.arange(0, ly, 1)
xpos, ypos = np.meshgrid(xpos+0.25, ypos+0.25)
xpos = xpos.flatten()
ypos = ypos.flatten()
zpos = np.zeros(lx*ly)
dx = 0.5 * np.ones_like(zpos) # width of bars
dy = dx.copy()
dzr = datareal.flatten()
dzi = dataimag.flatten()
if color is None:
color = ["#648fff", "#648fff"]
else:
if len(color) != 2:
raise ValueError("'color' must be a list of len=2.")
if color[0] is None:
color[0] = "#648fff"
if color[1] is None:
color[1] = "#648fff"
if ax_real is None and ax_imag is None:
# set default figure size
if figsize is None:
figsize = (15, 5)
fig = plt.figure(figsize=figsize)
ax1 = fig.add_subplot(1, 2, 1, projection='3d')
ax2 = fig.add_subplot(1, 2, 2, projection='3d')
elif ax_real is not None:
fig = ax_real.get_figure()
ax1 = ax_real
if ax_imag is not None:
ax2 = ax_imag
else:
fig = ax_imag.get_figure()
ax1 = None
ax2 = ax_imag
max_dzr = max(dzr)
min_dzr = min(dzr)
min_dzi = np.min(dzi)
max_dzi = np.max(dzi)
if ax1 is not None:
fc1 = generate_facecolors(xpos, ypos, zpos, dx, dy, dzr, color[0])
for idx, cur_zpos in enumerate(zpos):
if dzr[idx] > 0:
zorder = 2
else:
zorder = 0
b1 = ax1.bar3d(xpos[idx], ypos[idx], cur_zpos,
dx[idx], dy[idx], dzr[idx],
alpha=alpha, zorder=zorder)
b1.set_facecolors(fc1[6*idx:6*idx+6])
xlim, ylim = ax1.get_xlim(), ax1.get_ylim()
x = [xlim[0], xlim[1], xlim[1], xlim[0]]
y = [ylim[0], ylim[0], ylim[1], ylim[1]]
z = [0, 0, 0, 0]
verts = [list(zip(x, y, z))]
pc1 = Poly3DCollection(verts, alpha=0.15, facecolor='k',
linewidths=1, zorder=1)
if min(dzr) < 0 < max(dzr):
ax1.add_collection3d(pc1)
ax1.set_xticks(np.arange(0.5, lx+0.5, 1))
ax1.set_yticks(np.arange(0.5, ly+0.5, 1))
if max_dzr != min_dzr:
ax1.axes.set_zlim3d(np.min(dzr), max(np.max(dzr) + 1e-9, max_dzi))
else:
if min_dzr == 0:
ax1.axes.set_zlim3d(np.min(dzr), max(np.max(dzr)+1e-9, np.max(dzi)))
else:
ax1.axes.set_zlim3d(auto=True)
ax1.get_autoscalez_on()
ax1.w_xaxis.set_ticklabels(row_names, fontsize=14, rotation=45,
ha='right', va='top')
ax1.w_yaxis.set_ticklabels(column_names, fontsize=14, rotation=-22.5,
ha='left', va='center')
ax1.set_zlabel('Re[$\\rho$]', fontsize=14)
for tick in ax1.zaxis.get_major_ticks():
tick.label.set_fontsize(14)
if ax2 is not None:
fc2 = generate_facecolors(xpos, ypos, zpos, dx, dy, dzi, color[1])
for idx, cur_zpos in enumerate(zpos):
if dzi[idx] > 0:
zorder = 2
else:
zorder = 0
b2 = ax2.bar3d(xpos[idx], ypos[idx], cur_zpos,
dx[idx], dy[idx], dzi[idx],
alpha=alpha, zorder=zorder)
b2.set_facecolors(fc2[6*idx:6*idx+6])
xlim, ylim = ax2.get_xlim(), ax2.get_ylim()
x = [xlim[0], xlim[1], xlim[1], xlim[0]]
y = [ylim[0], ylim[0], ylim[1], ylim[1]]
z = [0, 0, 0, 0]
verts = [list(zip(x, y, z))]
pc2 = Poly3DCollection(verts, alpha=0.2, facecolor='k',
linewidths=1, zorder=1)
if min(dzi) < 0 < max(dzi):
ax2.add_collection3d(pc2)
ax2.set_xticks(np.arange(0.5, lx+0.5, 1))
ax2.set_yticks(np.arange(0.5, ly+0.5, 1))
if min_dzi != max_dzi:
eps = 0
ax2.axes.set_zlim3d(np.min(dzi), max(np.max(dzr)+1e-9, np.max(dzi)+eps))
else:
if min_dzi == 0:
ax2.set_zticks([0])
eps = 1e-9
ax2.axes.set_zlim3d(np.min(dzi), max(np.max(dzr)+1e-9, np.max(dzi)+eps))
else:
ax2.axes.set_zlim3d(auto=True)
ax2.w_xaxis.set_ticklabels(row_names, fontsize=14, rotation=45,
ha='right', va='top')
ax2.w_yaxis.set_ticklabels(column_names, fontsize=14, rotation=-22.5,
ha='left', va='center')
ax2.set_zlabel('Im[$\\rho$]', fontsize=14)
for tick in ax2.zaxis.get_major_ticks():
tick.label.set_fontsize(14)
ax2.get_autoscalez_on()
fig.suptitle(title, fontsize=16)
if ax_real is None and ax_imag is None:
if get_backend() in ['module://ipykernel.pylab.backend_inline',
'nbAgg']:
plt.close(fig)
return fig
[docs]@deprecate_arguments({'rho': 'state'})
def plot_state_paulivec(state, title="", figsize=None, color=None, ax=None, *, rho=None):
"""Plot the paulivec representation of a quantum state.
Plot a bargraph of the mixed state rho over the pauli matrices
Args:
state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state.
title (str): a string that represents the plot title
figsize (tuple): Figure size in inches.
color (list or str): Color of the expectation value bars.
ax (matplotlib.axes.Axes): An optional Axes object to be used for
the visualization output. If none is specified a new matplotlib
Figure will be created and used. Additionally, if specified there
will be no returned Figure since it is redundant.
Returns:
matplotlib.Figure:
The matplotlib.Figure of the visualization if the
``ax`` kwarg is not set
Raises:
ImportError: Requires matplotlib.
VisualizationError: if input is not a valid N-qubit state.
Example:
.. jupyter-execute::
from qiskit import QuantumCircuit
from qiskit.quantum_info import Statevector
from qiskit.visualization import plot_state_paulivec
%matplotlib inline
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
state = Statevector.from_instruction(qc)
plot_state_paulivec(state, color='midnightblue',
title="New PauliVec plot")
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed. To install, run "pip install '
'matplotlib".')
labels, values = _paulivec_data(state)
numelem = len(values)
if figsize is None:
figsize = (7, 5)
if color is None:
color = "#648fff"
ind = np.arange(numelem) # the x locations for the groups
width = 0.5 # the width of the bars
if ax is None:
return_fig = True
fig, ax = plt.subplots(figsize=figsize)
else:
return_fig = False
fig = ax.get_figure()
ax.grid(zorder=0, linewidth=1, linestyle='--')
ax.bar(ind, values, width, color=color, zorder=2)
ax.axhline(linewidth=1, color='k')
# add some text for labels, title, and axes ticks
ax.set_ylabel('Expectation value', fontsize=14)
ax.set_xticks(ind)
ax.set_yticks([-1, -0.5, 0, 0.5, 1])
ax.set_xticklabels(labels, fontsize=14, rotation=70)
ax.set_xlabel('Pauli', fontsize=14)
ax.set_ylim([-1, 1])
ax.set_facecolor('#eeeeee')
for tick in ax.xaxis.get_major_ticks()+ax.yaxis.get_major_ticks():
tick.label.set_fontsize(14)
ax.set_title(title, fontsize=16)
if return_fig:
if get_backend() in ['module://ipykernel.pylab.backend_inline',
'nbAgg']:
plt.close(fig)
return fig
def n_choose_k(n, k):
"""Return the number of combinations for n choose k.
Args:
n (int): the total number of options .
k (int): The number of elements.
Returns:
int: returns the binomial coefficient
"""
if n == 0:
return 0
return reduce(lambda x, y: x * y[0] / y[1],
zip(range(n - k + 1, n + 1),
range(1, k + 1)), 1)
def lex_index(n, k, lst):
"""Return the lex index of a combination..
Args:
n (int): the total number of options .
k (int): The number of elements.
lst (list): list
Returns:
int: returns int index for lex order
Raises:
VisualizationError: if length of list is not equal to k
"""
if len(lst) != k:
raise VisualizationError("list should have length k")
comb = list(map(lambda x: n - 1 - x, lst))
dualm = sum([n_choose_k(comb[k - 1 - i], i + 1) for i in range(k)])
return int(dualm)
def bit_string_index(s):
"""Return the index of a string of 0s and 1s."""
n = len(s)
k = s.count("1")
if s.count("0") != n - k:
raise VisualizationError("s must be a string of 0 and 1")
ones = [pos for pos, char in enumerate(s) if char == "1"]
return lex_index(n, k, ones)
def phase_to_rgb(complex_number):
"""Map a phase of a complexnumber to a color in (r,g,b).
complex_number is phase is first mapped to angle in the range
[0, 2pi] and then to the HSL color wheel
"""
angles = (np.angle(complex_number) + (np.pi * 4)) % (np.pi * 2)
rgb = colorsys.hls_to_rgb(angles / (np.pi * 2), 0.5, 0.5)
return rgb
[docs]@deprecate_arguments({'rho': 'state'})
def plot_state_qsphere(state, figsize=None, ax=None, show_state_labels=True,
show_state_phases=False, use_degrees=False, *, rho=None):
"""Plot the qsphere representation of a quantum state.
Here, the size of the points is proportional to the probability
of the corresponding term in the state and the color represents
the phase.
Args:
state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state.
figsize (tuple): Figure size in inches.
ax (matplotlib.axes.Axes): An optional Axes object to be used for
the visualization output. If none is specified a new matplotlib
Figure will be created and used. Additionally, if specified there
will be no returned Figure since it is redundant.
show_state_labels (bool): An optional boolean indicating whether to
show labels for each basis state.
show_state_phases (bool): An optional boolean indicating whether to
show the phase for each basis state.
use_degrees (bool): An optional boolean indicating whether to use
radians or degrees for the phase values in the plot.
Returns:
Figure: A matplotlib figure instance if the ``ax`` kwag is not set
Raises:
ImportError: Requires matplotlib.
VisualizationError: if input is not a valid N-qubit state.
QiskitError: Input statevector does not have valid dimensions.
Example:
.. jupyter-execute::
from qiskit import QuantumCircuit
from qiskit.quantum_info import Statevector
from qiskit.visualization import plot_state_qsphere
%matplotlib inline
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
state = Statevector.from_instruction(qc)
plot_state_qsphere(state)
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed. To install, run "pip install '
'matplotlib".')
try:
import seaborn as sns
except ImportError:
raise ImportError('Must have seaborn installed to use '
'plot_state_qsphere. To install, run "pip install seaborn".')
rho = DensityMatrix(state)
num = rho.num_qubits
if num is None:
raise VisualizationError("Input is not a multi-qubit quantum state.")
# get the eigenvectors and eigenvalues
eigvals, eigvecs = linalg.eigh(rho.data)
if figsize is None:
figsize = (7, 7)
if ax is None:
return_fig = True
fig = plt.figure(figsize=figsize)
else:
return_fig = False
fig = ax.get_figure()
gs = gridspec.GridSpec(nrows=3, ncols=3)
ax = fig.add_subplot(gs[0:3, 0:3], projection='3d')
ax.axes.set_xlim3d(-1.0, 1.0)
ax.axes.set_ylim3d(-1.0, 1.0)
ax.axes.set_zlim3d(-1.0, 1.0)
ax.axes.grid(False)
ax.view_init(elev=5, azim=275)
# Force aspect ratio
# MPL 3.2 or previous do not have set_box_aspect
if hasattr(ax.axes, 'set_box_aspect'):
ax.axes.set_box_aspect((1, 1, 1))
# start the plotting
# Plot semi-transparent sphere
u = np.linspace(0, 2 * np.pi, 25)
v = np.linspace(0, np.pi, 25)
x = np.outer(np.cos(u), np.sin(v))
y = np.outer(np.sin(u), np.sin(v))
z = np.outer(np.ones(np.size(u)), np.cos(v))
ax.plot_surface(x, y, z, rstride=1, cstride=1, color=plt.rcParams['grid.color'],
alpha=0.2, linewidth=0)
# Get rid of the panes
ax.w_xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.w_yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
ax.w_zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))
# Get rid of the spines
ax.w_xaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
ax.w_yaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
ax.w_zaxis.line.set_color((1.0, 1.0, 1.0, 0.0))
# Get rid of the ticks
ax.set_xticks([])
ax.set_yticks([])
ax.set_zticks([])
# traversing the eigvals/vecs backward as sorted low->high
for idx in range(eigvals.shape[0]-1, -1, -1):
if eigvals[idx] > 0.001:
# get the max eigenvalue
state = eigvecs[:, idx]
loc = np.absolute(state).argmax()
# remove the global phase from max element
angles = (np.angle(state[loc]) + 2 * np.pi) % (2 * np.pi)
angleset = np.exp(-1j * angles)
state = angleset * state
d = num
for i in range(2 ** num):
# get x,y,z points
element = bin(i)[2:].zfill(num)
weight = element.count("1")
zvalue = -2 * weight / d + 1
number_of_divisions = n_choose_k(d, weight)
weight_order = bit_string_index(element)
angle = (float(weight) / d) * (np.pi * 2) + \
(weight_order * 2 * (np.pi / number_of_divisions))
if (weight > d / 2) or ((weight == d / 2) and
(weight_order >= number_of_divisions / 2)):
angle = np.pi - angle - (2 * np.pi / number_of_divisions)
xvalue = np.sqrt(1 - zvalue ** 2) * np.cos(angle)
yvalue = np.sqrt(1 - zvalue ** 2) * np.sin(angle)
# get prob and angle - prob will be shade and angle color
prob = np.real(np.dot(state[i], state[i].conj()))
if prob > 1: # See https://github.com/Qiskit/qiskit-terra/issues/4666
prob = 1
colorstate = phase_to_rgb(state[i])
alfa = 1
if yvalue >= 0.1:
alfa = 1.0 - yvalue
if not np.isclose(prob, 0) and show_state_labels:
rprime = 1.3
angle_theta = np.arctan2(np.sqrt(1 - zvalue ** 2), zvalue)
xvalue_text = rprime * np.sin(angle_theta) * np.cos(angle)
yvalue_text = rprime * np.sin(angle_theta) * np.sin(angle)
zvalue_text = rprime * np.cos(angle_theta)
element_text = '$\\vert' + element + '\\rangle$'
if show_state_phases:
element_angle = (np.angle(state[i]) + (np.pi * 4)) % (np.pi * 2)
if use_degrees:
element_text += '\n$%.1f^\\circ$' % (element_angle * 180/np.pi)
else:
element_angle = pi_check(element_angle, ndigits=3).replace('pi', '\\pi')
element_text += '\n$%s$' % (element_angle)
ax.text(xvalue_text, yvalue_text, zvalue_text, element_text,
ha='center', va='center', size=12)
ax.plot([xvalue], [yvalue], [zvalue],
markerfacecolor=colorstate,
markeredgecolor=colorstate,
marker='o', markersize=np.sqrt(prob) * 30, alpha=alfa)
a = Arrow3D([0, xvalue], [0, yvalue], [0, zvalue],
mutation_scale=20, alpha=prob, arrowstyle="-",
color=colorstate, lw=2)
ax.add_artist(a)
# add weight lines
for weight in range(d + 1):
theta = np.linspace(-2 * np.pi, 2 * np.pi, 100)
z = -2 * weight / d + 1
r = np.sqrt(1 - z ** 2)
x = r * np.cos(theta)
y = r * np.sin(theta)
ax.plot(x, y, z, color=(.5, .5, .5), lw=1, ls=':', alpha=.5)
# add center point
ax.plot([0], [0], [0], markerfacecolor=(.5, .5, .5),
markeredgecolor=(.5, .5, .5), marker='o', markersize=3,
alpha=1)
else:
break
n = 64
theta = np.ones(n)
ax2 = fig.add_subplot(gs[2:, 2:])
ax2.pie(theta, colors=sns.color_palette("hls", n), radius=0.75)
ax2.add_artist(Circle((0, 0), 0.5, color=plt.rcParams['figure.facecolor'], zorder=1))
offset = 0.95 # since radius of sphere is one.
if use_degrees:
labels = ['Phase\n(Deg)', '0', '90', '180 ', '270']
else:
labels = ['Phase', '$0$', '$\\pi/2$', '$\\pi$', '$3\\pi/2$']
ax2.text(0, 0, labels[0], horizontalalignment='center',
verticalalignment='center', fontsize=14)
ax2.text(offset, 0, labels[1], horizontalalignment='center',
verticalalignment='center', fontsize=14)
ax2.text(0, offset, labels[2], horizontalalignment='center',
verticalalignment='center', fontsize=14)
ax2.text(-offset, 0, labels[3], horizontalalignment='center',
verticalalignment='center', fontsize=14)
ax2.text(0, -offset, labels[4], horizontalalignment='center',
verticalalignment='center', fontsize=14)
if return_fig:
if get_backend() in ['module://ipykernel.pylab.backend_inline',
'nbAgg']:
plt.close(fig)
return fig
def generate_facecolors(x, y, z, dx, dy, dz, color):
"""Generates shaded facecolors for shaded bars.
This is here to work around a Matplotlib bug
where alpha does not work in Bar3D.
Args:
x (array_like): The x- coordinates of the anchor point of the bars.
y (array_like): The y- coordinates of the anchor point of the bars.
z (array_like): The z- coordinates of the anchor point of the bars.
dx (array_like): Width of bars.
dy (array_like): Depth of bars.
dz (array_like): Height of bars.
color (array_like): sequence of valid color specifications, optional
Returns:
list: Shaded colors for bars.
"""
cuboid = np.array([
# -z
(
(0, 0, 0),
(0, 1, 0),
(1, 1, 0),
(1, 0, 0),
),
# +z
(
(0, 0, 1),
(1, 0, 1),
(1, 1, 1),
(0, 1, 1),
),
# -y
(
(0, 0, 0),
(1, 0, 0),
(1, 0, 1),
(0, 0, 1),
),
# +y
(
(0, 1, 0),
(0, 1, 1),
(1, 1, 1),
(1, 1, 0),
),
# -x
(
(0, 0, 0),
(0, 0, 1),
(0, 1, 1),
(0, 1, 0),
),
# +x
(
(1, 0, 0),
(1, 1, 0),
(1, 1, 1),
(1, 0, 1),
),
])
# indexed by [bar, face, vertex, coord]
polys = np.empty(x.shape + cuboid.shape)
# handle each coordinate separately
for i, p, dp in [(0, x, dx), (1, y, dy), (2, z, dz)]:
p = p[..., np.newaxis, np.newaxis]
dp = dp[..., np.newaxis, np.newaxis]
polys[..., i] = p + dp * cuboid[..., i]
# collapse the first two axes
polys = polys.reshape((-1,) + polys.shape[2:])
facecolors = []
if len(color) == len(x):
# bar colors specified, need to expand to number of faces
for c in color:
facecolors.extend([c] * 6)
else:
# a single color specified, or face colors specified explicitly
facecolors = list(mcolors.to_rgba_array(color))
if len(facecolors) < len(x):
facecolors *= (6 * len(x))
normals = _generate_normals(polys)
return _shade_colors(facecolors, normals)
def _generate_normals(polygons):
"""Takes a list of polygons and return an array of their normals.
Normals point towards the viewer for a face with its vertices in
counterclockwise order, following the right hand rule.
Uses three points equally spaced around the polygon.
This normal of course might not make sense for polygons with more than
three points not lying in a plane, but it's a plausible and fast
approximation.
Args:
polygons (list): list of (M_i, 3) array_like, or (..., M, 3) array_like
A sequence of polygons to compute normals for, which can have
varying numbers of vertices. If the polygons all have the same
number of vertices and array is passed, then the operation will
be vectorized.
Returns:
normals: (..., 3) array_like
A normal vector estimated for the polygon.
"""
if isinstance(polygons, np.ndarray):
# optimization: polygons all have the same number of points, so can
# vectorize
n = polygons.shape[-2]
i1, i2, i3 = 0, n//3, 2*n//3
v1 = polygons[..., i1, :] - polygons[..., i2, :]
v2 = polygons[..., i2, :] - polygons[..., i3, :]
else:
# The subtraction doesn't vectorize because polygons is jagged.
v1 = np.empty((len(polygons), 3))
v2 = np.empty((len(polygons), 3))
for poly_i, ps in enumerate(polygons):
n = len(ps)
i1, i2, i3 = 0, n//3, 2*n//3
v1[poly_i, :] = ps[i1, :] - ps[i2, :]
v2[poly_i, :] = ps[i2, :] - ps[i3, :]
return np.cross(v1, v2)
def _shade_colors(color, normals, lightsource=None):
"""
Shade *color* using normal vectors given by *normals*.
*color* can also be an array of the same length as *normals*.
"""
if lightsource is None:
# chosen for backwards-compatibility
lightsource = LightSource(azdeg=225, altdeg=19.4712)
def mod(v):
return np.sqrt(v[0] ** 2 + v[1] ** 2 + v[2] ** 2)
shade = np.array([np.dot(n / mod(n), lightsource.direction)
if mod(n) else np.nan for n in normals])
mask = ~np.isnan(shade)
if mask.any():
norm = Normalize(min(shade[mask]), max(shade[mask]))
shade[~mask] = min(shade[mask])
color = mcolors.to_rgba_array(color)
# shape of color should be (M, 4) (where M is number of faces)
# shape of shade should be (M,)
# colors should have final shape of (M, 4)
alpha = color[:, 3]
colors = (0.5 + norm(shade)[:, np.newaxis] * 0.5) * color
colors[:, 3] = alpha
else:
colors = np.asanyarray(color).copy()
return colors