def plot_state_hinton(rho, title='', figsize=None):
"""Plot a hinton diagram for the quanum state.
Args:
rho (ndarray): Numpy array for state vector or density matrix.
title (str): a string that represents the plot title
figsize (tuple): Figure size in inches.
Returns:
matplotlib.Figure: The matplotlib.Figure of the visualization
Raises:
ImportError: Requires matplotlib.
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed.')
rho = _validate_input_state(rho)
if figsize is None:
figsize = (8, 5)
num = int(np.log2(len(rho)))
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=figsize)
max_weight = 2**np.ceil(np.log(np.abs(rho).max()) / np.log(2))
datareal = np.real(rho)
dataimag = np.imag(rho)
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])
# Real
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))
ax1.set_yticklabels(row_names, fontsize=14)
ax1.set_xticklabels(column_names, fontsize=14, rotation=90)
ax1.autoscale_view()
ax1.invert_yaxis()
ax1.set_title('Real[rho]', fontsize=14)
# Imaginary
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)
if np.any(dataimag != 0):
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('Imag[rho]', fontsize=14)
if title:
fig.suptitle(title, fontsize=16)
plt.tight_layout()
plt.close(fig)
return fig
def plot_state_city(rho, title="", figsize=None, color=None,
alpha=1, ax_real=None, ax_imag=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:
rho (ndarray): Numpy array for state vector or density matrix.
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.
Example:
.. jupyter-execute::
from qiskit import QuantumCircuit, BasicAer, execute
from qiskit.visualization import plot_state_city
%matplotlib inline
qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure([0, 1], [0, 1])
backend = BasicAer.get_backend('statevector_simulator')
job = execute(qc, backend).result()
plot_state_city(job.get_statevector(qc), color=['midnightblue', 'midnightblue'],
title="New State City")
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed.')
rho = _validate_input_state(rho)
num = int(np.log2(len(rho)))
# get the real and imag parts of rho
datareal = np.real(rho)
dataimag = np.imag(rho)
# 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
def plot_state_city(rho, title="", figsize=None, color=None, alpha=1):
"""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:
rho (ndarray): Numpy array for state vector or density matrix.
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
Returns:
matplotlib.Figure: The matplotlib.Figure of the visualization
Raises:
ImportError: Requires matplotlib.
ValueError: When 'color' is not a list of len=2.
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed.')
rho = _validate_input_state(rho)
num = int(np.log2(len(rho)))
# get the real and imag parts of rho
datareal = np.real(rho)
dataimag = np.imag(rho)
# 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"
# 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')
x = [0, max(xpos) + 0.5, max(xpos) + 0.5, 0]
y = [0, 0, max(ypos) + 0.5, max(ypos) + 0.5]
z = [0, 0, 0, 0]
verts = [list(zip(x, y, z))]
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])
pc1 = Poly3DCollection(verts,
alpha=0.15,
facecolor='k',
linewidths=1,
zorder=1)
if min(dzr) < 0 < max(dzr):
ax1.add_collection3d(pc1)
ax2 = fig.add_subplot(1, 2, 2, projection='3d')
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])
pc2 = Poly3DCollection(verts,
alpha=0.2,
facecolor='k',
linewidths=1,
zorder=1)
if min(dzi) < 0 < max(dzi):
ax2.add_collection3d(pc2)
ax1.set_xticks(np.arange(0.5, lx + 0.5, 1))
ax1.set_yticks(np.arange(0.5, ly + 0.5, 1))
max_dzr = max(dzr)
min_dzr = min(dzr)
if max_dzr != min_dzr:
ax1.axes.set_zlim3d(np.min(dzr), np.max(dzr) + 1e-9)
else:
if min_dzr == 0:
ax1.axes.set_zlim3d(np.min(dzr), np.max(dzr) + 1e-9)
else:
ax1.axes.set_zlim3d(auto=True)
ax1.zaxis.set_major_locator(MaxNLocator(5))
ax1.w_xaxis.set_ticklabels(row_names, fontsize=14, rotation=45)
ax1.w_yaxis.set_ticklabels(column_names, fontsize=14, rotation=-22.5)
ax1.set_zlabel("Real[rho]", fontsize=14)
for tick in ax1.zaxis.get_major_ticks():
tick.label.set_fontsize(14)
ax2.set_xticks(np.arange(0.5, lx + 0.5, 1))
ax2.set_yticks(np.arange(0.5, ly + 0.5, 1))
min_dzi = np.min(dzi)
max_dzi = np.max(dzi)
if min_dzi != max_dzi:
eps = 0
ax2.zaxis.set_major_locator(MaxNLocator(5))
ax2.axes.set_zlim3d(np.min(dzi), np.max(dzi) + eps)
else:
if min_dzi == 0:
ax2.set_zticks([0])
eps = 1e-9
ax2.axes.set_zlim3d(np.min(dzi), np.max(dzi) + eps)
else:
ax2.axes.set_zlim3d(auto=True)
ax2.w_xaxis.set_ticklabels(row_names, fontsize=14, rotation=45)
ax2.w_yaxis.set_ticklabels(column_names, fontsize=14, rotation=-22.5)
ax2.set_zlabel("Imag[rho]", fontsize=14)
for tick in ax2.zaxis.get_major_ticks():
tick.label.set_fontsize(14)
plt.suptitle(title, fontsize=16)
plt.tight_layout()
plt.close(fig)
return fig
def plot_state_qsphere(rho, figsize=None):
"""Plot the qsphere representation of a quantum state.
Args:
rho (ndarray): State vector or density matrix representation.
of quantum state.
figsize (tuple): Figure size in inches.
Returns:
Figure: A matplotlib figure instance.
Raises:
ImportError: Requires matplotlib.
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed.')
rho = _validate_input_state(rho)
if figsize is None:
figsize = (7, 7)
num = int(np.log2(len(rho)))
# get the eigenvectors and eigenvalues
we, stateall = linalg.eigh(rho)
for _ in range(2**num):
# start with the max
probmix = we.max()
prob_location = we.argmax()
if probmix > 0.001:
# get the max eigenvalue
state = stateall[:, prob_location]
loc = np.absolute(state).argmax()
# get the element location closes to lowest bin representation.
for j in range(2**num):
test = np.absolute(
np.absolute(state[j]) - np.absolute(state[loc]))
if test < 0.001:
loc = j
break
# remove the global phase
angles = (np.angle(state[loc]) + 2 * np.pi) % (2 * np.pi)
angleset = np.exp(-1j * angles)
# print(state)
# print(angles)
state = angleset * state
# print(state)
state.flatten()
# start the plotting
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(111, 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.set_aspect("equal")
ax.axes.grid(False)
# 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='k',
alpha=0.05,
linewidth=0)
# wireframe
# 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([])
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)
# if weight_order >= number_of_divisions / 2:
# com_key = compliment(element)
# weight_order_temp = bit_string_index(com_key)
# weight_order = np.floor(
# number_of_divisions / 2) + weight_order_temp + 1
angle = weight_order * 2 * np.pi / number_of_divisions
xvalue = np.sqrt(1 - zvalue**2) * np.cos(angle)
yvalue = np.sqrt(1 - zvalue**2) * np.sin(angle)
ax.plot([xvalue], [yvalue], [zvalue],
markerfacecolor=(.5, .5, .5),
markeredgecolor=(.5, .5, .5),
marker='o',
markersize=10,
alpha=1)
# get prob and angle - prob will be shade and angle color
prob = np.real(np.dot(state[i], state[i].conj()))
colorstate = phase_to_color_wheel(state[i])
a = Arrow3D([0, xvalue], [0, yvalue], [0, zvalue],
mutation_scale=20,
alpha=prob,
arrowstyle="-",
color=colorstate,
lw=10)
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))
# add center point
ax.plot([0], [0], [0],
markerfacecolor=(.5, .5, .5),
markeredgecolor=(.5, .5, .5),
marker='o',
markersize=10,
alpha=1)
we[prob_location] = 0
else:
break
plt.tight_layout()
plt.close(fig)
return fig
def plot_state_hinton(rho, title='', figsize=None, ax_real=None, ax_imag=None):
"""Plot a hinton diagram for the quanum state.
Args:
rho (ndarray): Numpy array for state vector or density matrix.
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.
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed.')
rho = _validate_input_state(rho)
if figsize is None:
figsize = (8, 5)
num = int(np.log2(len(rho)))
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
max_weight = 2**np.ceil(np.log(np.abs(rho).max()) / np.log(2))
datareal = np.real(rho)
dataimag = np.imag(rho)
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])
# 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))
ax1.set_yticklabels(row_names, fontsize=14)
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
def iplot_state_hinton(rho, figsize=None):
""" Create a hinton representation.
Graphical representation of the input array using a 2D city style
graph (hinton).
Args:
rho (array): Density matrix
figsize (tuple): Figure size in pixels.
Example:
.. code-block::
from qiskit import QuantumCircuit, BasicAer, execute
from qiskit.visualization import iplot_state_hinton
%matplotlib inline
qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure([0, 1], [0, 1])
backend = BasicAer.get_backend('statevector_simulator')
job = execute(qc, backend).result()
iplot_state_hinton(job.get_statevector(qc))
"""
# HTML
html_template = Template("""
<p>
<div id="hinton_$divNumber"></div>
</p>
""")
# JavaScript
javascript_template = Template("""
<script>
requirejs.config({
paths: {
qVisualization: "https://qvisualization.mybluemix.net/q-visualizations"
}
});
require(["qVisualization"], function(qVisualizations) {
qVisualizations.plotState("hinton_$divNumber",
"hinton",
$executions,
$options);
});
</script>
""")
rho = _validate_input_state(rho)
if figsize is None:
options = {}
else:
options = {'width': figsize[0], 'height': figsize[1]}
# Process data and execute
div_number = str(time.time())
div_number = re.sub('[.]', '', div_number)
# Process data and execute
real = []
imag = []
for xvalue in rho:
row_real = []
col_imag = []
for value_real in xvalue.real:
row_real.append(float(value_real))
real.append(row_real)
for value_imag in xvalue.imag:
col_imag.append(float(value_imag))
imag.append(col_imag)
html = html_template.substitute({
'divNumber': div_number
})
javascript = javascript_template.substitute({
'divNumber': div_number,
'executions': [{'data': real}, {'data': imag}],
'options': options
})
display(HTML(html + javascript))
def plot_state_paulivec(rho, title="", figsize=None, color=None, ax=None):
"""Plot the paulivec representation of a quantum state.
Plot a bargraph of the mixed state rho over the pauli matrices
Args:
rho (ndarray): Numpy array for state vector or density matrix
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.
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed.')
rho = _validate_input_state(rho)
if figsize is None:
figsize = (7, 5)
num = int(np.log2(len(rho)))
labels = list(map(lambda x: x.to_label(), pauli_group(num)))
values = list(
map(lambda x: np.real(np.trace(np.dot(x.to_matrix(), rho))),
pauli_group(num)))
numelem = len(values)
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 plot_state_qsphere(rho, figsize=None, ax=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:
rho (ndarray): State vector or density matrix representation.
of 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.
Returns:
Figure: A matplotlib figure instance if the ``ax`` kwag is not set
Raises:
ImportError: Requires matplotlib.
"""
if not HAS_MATPLOTLIB:
raise ImportError('Must have Matplotlib installed.')
try:
import seaborn as sns
except ImportError:
raise ImportError('Must have seaborn installed to use '
'plot_state_qsphere')
rho = _validate_input_state(rho)
if figsize is None:
figsize = (7, 7)
num = int(np.log2(len(rho)))
# get the eigenvectors and eigenvalues
we, stateall = linalg.eigh(rho)
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)
for _ in range(2**num):
# start with the max
probmix = we.max()
prob_location = we.argmax()
if probmix > 0.001:
# get the max eigenvalue
state = stateall[:, prob_location]
loc = np.absolute(state).argmax()
# get the element location closes to lowest bin representation.
for j in range(2**num):
test = np.absolute(
np.absolute(state[j]) - np.absolute(state[loc]))
if test < 0.001:
loc = j
break
# remove the global phase
angles = (np.angle(state[loc]) + 2 * np.pi) % (2 * np.pi)
angleset = np.exp(-1j * angles)
state = angleset * state
state.flatten()
# 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='k',
alpha=0.05,
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([])
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()))
colorstate = phase_to_rgb(state[i])
alfa = 1
if yvalue >= 0.1:
alfa = 1.0 - yvalue
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)
we[prob_location] = 0
else:
break
n = 32
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='white', zorder=1))
ax2.text(0,
0,
'Phase',
horizontalalignment='center',
verticalalignment='center',
fontsize=14)
offset = 0.95 # since radius of sphere is one.
ax2.text(offset,
0,
r'$0$',
horizontalalignment='center',
verticalalignment='center',
fontsize=14)
ax2.text(0,
offset,
r'$\pi/2$',
horizontalalignment='center',
verticalalignment='center',
fontsize=14)
ax2.text(-offset,
0,
r'$\pi$',
horizontalalignment='center',
verticalalignment='center',
fontsize=14)
ax2.text(0,
-offset,
r'$3\pi/2$',
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 iplot_state_paulivec(rho, figsize=None, slider=False, show_legend=False):
""" Create a paulivec representation.
Graphical representation of the input array.
Args:
rho (array): State vector or density matrix.
figsize (tuple): Figure size in pixels.
slider (bool): activate slider
show_legend (bool): show legend of graph content
"""
# HTML
html_template = Template("""
<p>
<div id="paulivec_$divNumber"></div>
</p>
""")
# JavaScript
javascript_template = Template("""
<script>
requirejs.config({
paths: {
qVisualization: "https://qvisualization.mybluemix.net/q-visualizations"
}
});
require(["qVisualization"], function(qVisualizations) {
qVisualizations.plotState("paulivec_$divNumber",
"paulivec",
$executions,
$options);
});
</script>
""")
rho = _validate_input_state(rho)
# set default figure size if none given
if figsize is None:
figsize = (7, 5)
options = {
'width': figsize[0],
'height': figsize[1],
'slider': int(slider),
'show_legend': int(show_legend)
}
# Process data and execute
div_number = str(time.time())
div_number = re.sub('[.]', '', div_number)
data_to_plot = []
rho_data = process_data(rho)
data_to_plot.append(dict(data=rho_data))
html = html_template.substitute({'divNumber': div_number})
javascript = javascript_template.substitute({
'divNumber': div_number,
'executions': data_to_plot,
'options': options
})
display(HTML(html + javascript))
def iplot_state_city(rho, figsize=None):
""" Create a cities representation.
Graphical representation of the input array using a city style graph.
Args:
rho (array): State vector or density matrix.
figsize (tuple): The figure size in pixels.
Example:
.. code-block::
from qiskit import QuantumCircuit, BasicAer, execute
from qiskit.visualization import iplot_state_city
%matplotlib inline
qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure([0, 1], [0, 1])
backend = BasicAer.get_backend('statevector_simulator')
job = execute(qc, backend).result()
iplot_state_city(job.get_statevector(qc))
"""
# HTML
html_template = Template("""
<p>
<div id="content_$divNumber" style="position: absolute; z-index: 1;">
<div id="cities_$divNumber"></div>
</div>
</p>
""")
# JavaScript
javascript_template = Template("""
<script>
requirejs.config({
paths: {
qVisualization: "https://qvisualization.mybluemix.net/q-visualizations"
}
});
require(["qVisualization"], function(qVisualizations) {
data = {
real: $real,
titleReal: "Real.[rho]",
imaginary: $imag,
titleImaginary: "Im.[rho]",
qbits: $qbits
};
qVisualizations.plotState("cities_$divNumber",
"cities",
data,
$options);
});
</script>
""")
rho = _validate_input_state(rho)
if figsize is None:
options = {}
else:
options = {'width': figsize[0], 'height': figsize[1]}
# Process data and execute
real = []
imag = []
for xvalue in rho:
row_real = []
col_imag = []
for value_real in xvalue.real:
row_real.append(float(value_real))
real.append(row_real)
for value_imag in xvalue.imag:
col_imag.append(float(value_imag))
imag.append(col_imag)
div_number = str(time.time())
div_number = re.sub('[.]', '', div_number)
html = html_template.substitute({'divNumber': div_number})
javascript = javascript_template.substitute({
'real': real,
'imag': imag,
'qbits': len(real),
'divNumber': div_number,
'options': options
})
display(HTML(html + javascript))
def iplot_bloch_multivector(rho, figsize=None):
""" Create a bloch sphere representation.
Graphical representation of the input array, using as much bloch
spheres as qubit are required.
Args:
rho (array): State vector or density matrix
figsize (tuple): Figure size in pixels.
Example:
.. code-block::
from qiskit import QuantumCircuit, BasicAer, execute
from qiskit.visualization import iplot_bloch_multivector
%matplotlib inline
qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure([0, 1], [0, 1])
backend = BasicAer.get_backend('statevector_simulator')
job = execute(qc, backend).result()
iplot_bloch_multivector(job.get_statevector(qc))
"""
# HTML
html_template = Template("""
<p>
<div id="content_$divNumber" style="position: absolute; z-index: 1;">
<div id="bloch_$divNumber"></div>
</div>
</p>
""")
# JavaScript
javascript_template = Template("""
<script>
requirejs.config({
paths: {
qVisualization: "https://qvisualization.mybluemix.net/q-visualizations"
}
});
data = $data;
dataValues = [];
for (var i = 0; i < data.length; i++) {
// Coordinates
var x = data[i][0];
var y = data[i][1];
var z = data[i][2];
var point = {'x': x,
'y': y,
'z': z};
dataValues.push(point);
}
require(["qVisualization"], function(qVisualizations) {
// Plot figure
qVisualizations.plotState("bloch_$divNumber",
"bloch",
dataValues,
$options);
});
</script>
""")
rho = _validate_input_state(rho)
if figsize is None:
options = {}
else:
options = {'width': figsize[0], 'height': figsize[1]}
# Process data and execute
num = int(np.log2(len(rho)))
bloch_data = []
for i in range(num):
pauli_singles = [Pauli.pauli_single(num, i, 'X'), Pauli.pauli_single(num, i, 'Y'),
Pauli.pauli_single(num, i, 'Z')]
bloch_state = list(map(lambda x: np.real(np.trace(np.dot(x.to_matrix(), rho))),
pauli_singles))
bloch_data.append(bloch_state)
div_number = str(time.time())
div_number = re.sub('[.]', '', div_number)
html = html_template.substitute({
'divNumber': div_number
})
javascript = javascript_template.substitute({
'data': bloch_data,
'divNumber': div_number,
'options': options
})
display(HTML(html + javascript))
def plot_state_qsphere(rho,
figsize=None,
ax=None,
show_state_labels=True,
show_state_phases=False,
use_degrees=False):
"""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:
rho (ndarray): State vector or density matrix representation of
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.
QiskitError: Input statevector does not have valid dimensions.
Example:
.. jupyter-execute::
from qiskit import QuantumCircuit, BasicAer, execute
from qiskit.visualization import plot_state_qsphere
%matplotlib inline
qc = QuantumCircuit(2)
qc.x(0)
qc.h(0)
qc.cx(0, 1)
backend = BasicAer.get_backend('statevector_simulator')
job = execute(qc, backend).result()
plot_state_qsphere(job.get_statevector(qc), show_state_phases=True)
"""
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".')
if figsize is None:
figsize = (7, 7)
IS_DM = False
# Input is a DM
if len(rho.shape) == 2:
rho = _validate_input_state(rho)
IS_DM = True
else:
if np.log2(rho.shape[0]) % 1:
raise QiskitError('Incorrect statevector dimensions.')
num = int(np.log2(rho.shape[0]))
# Do eigendecomposition if input is DM
if IS_DM:
eigvals, eigvecs = la.eigh(rho)
else:
eigvals = np.array([1])
eigvecs = rho
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)
# 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='k',
alpha=0.05,
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
if IS_DM:
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
else:
state = eigvecs
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()))
colorstate = phase_to_rgb(state[i])
alfa = 1
if yvalue >= 0.1:
alfa = 1.0 - yvalue
if 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='white', 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 iplot_state_qsphere(rho, figsize=None):
""" Create a Q sphere representation.
Graphical representation of the input array, using a Q sphere for each
eigenvalue.
Args:
rho (array): State vector or density matrix.
figsize (tuple): Figure size in pixels.
"""
# HTML
html_template = Template("""
<p>
<div id="content_$divNumber" style="position: absolute; z-index: 1;">
<div id="qsphere_$divNumber"></div>
</div>
</p>
""")
# JavaScript
javascript_template = Template("""
<script>
requirejs.config({
paths: {
qVisualization: "https://qvisualization.mybluemix.net/q-visualizations"
}
});
require(["qVisualization"], function(qVisualizations) {
data = $data;
qVisualizations.plotState("qsphere_$divNumber",
"qsphere",
data,
$options);
});
</script>
""")
rho = _validate_input_state(rho)
if figsize is None:
options = {}
else:
options = {'width': figsize[0], 'height': figsize[1]}
qspheres_data = []
# Process data and execute
num = int(np.log2(len(rho)))
# get the eigenvectors and eigenvalues
weig, stateall = linalg.eigh(rho)
for _ in range(2**num):
# start with the max
probmix = weig.max()
prob_location = weig.argmax()
if probmix > 0.001:
# print("The " + str(k) + "th eigenvalue = " + str(probmix))
# get the max eigenvalue
state = stateall[:, prob_location]
loc = np.absolute(state).argmax()
# get the element location closes to lowest bin representation.
for j in range(2**num):
test = np.absolute(
np.absolute(state[j]) - np.absolute(state[loc]))
if test < 0.001:
loc = j
break
# remove the global phase
angles = (np.angle(state[loc]) + 2 * np.pi) % (2 * np.pi)
angleset = np.exp(-1j * angles)
state = angleset * state
state.flatten()
spherepoints = []
for i in range(2**num):
# get x,y,z points
element = bin(i)[2:].zfill(num)
weight = element.count("1")
number_of_divisions = n_choose_k(num, weight)
weight_order = bit_string_index(element)
angle = weight_order * 2 * np.pi / number_of_divisions
zvalue = -2 * weight / num + 1
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()))
angles = (np.angle(state[i]) + 2 * np.pi) % (2 * np.pi)
qpoint = {
'x': xvalue,
'y': yvalue,
'z': zvalue,
'prob': prob,
'phase': angles
}
spherepoints.append(qpoint)
# Associate all points to one sphere
sphere = {'points': spherepoints, 'eigenvalue': probmix}
# Add sphere to the spheres array
qspheres_data.append(sphere)
weig[prob_location] = 0
div_number = str(time.time())
div_number = re.sub('[.]', '', div_number)
html = html_template.substitute({'divNumber': div_number})
javascript = javascript_template.substitute({
'data': qspheres_data,
'divNumber': div_number,
'options': options
})
display(HTML(html + javascript))
def iplot_state_paulivec(rho, figsize=None, slider=False, show_legend=False):
""" Create a paulivec representation.
Graphical representation of the input array.
Args:
rho (array): State vector or density matrix.
figsize (tuple): Figure size in pixels.
slider (bool): activate slider
show_legend (bool): show legend of graph content
Example:
.. code-block::
from qiskit import QuantumCircuit, BasicAer, execute
from qiskit.visualization import iplot_state_paulivec
%matplotlib inline
qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure([0, 1], [0, 1])
backend = BasicAer.get_backend('statevector_simulator')
job = execute(qc, backend).result()
iplot_state_paulivec(job.get_statevector(qc))
"""
# HTML
html_template = Template("""
<p>
<div id="paulivec_$divNumber"></div>
</p>
""")
# JavaScript
javascript_template = Template("""
<script>
requirejs.config({
paths: {
qVisualization: "https://qvisualization.mybluemix.net/q-visualizations"
}
});
require(["qVisualization"], function(qVisualizations) {
qVisualizations.plotState("paulivec_$divNumber",
"paulivec",
$executions,
$options);
});
</script>
""")
rho = _validate_input_state(rho)
# set default figure size if none given
if figsize is None:
figsize = (7, 5)
options = {
'width': figsize[0],
'height': figsize[1],
'slider': int(slider),
'show_legend': int(show_legend)
}
# Process data and execute
div_number = str(time.time())
div_number = re.sub('[.]', '', div_number)
data_to_plot = []
rho_data = process_data(rho)
data_to_plot.append(dict(data=rho_data))
html = html_template.substitute({'divNumber': div_number})
javascript = javascript_template.substitute({
'divNumber': div_number,
'executions': data_to_plot,
'options': options
})
display(HTML(html + javascript))
def iplot_state_hinton(rho, figsize=None):
""" Create a hinton representation.
Graphical representation of the input array using a 2D city style
graph (hinton).
Args:
rho (array): Density matrix
figsize (tuple): Figure size in pixels.
"""
# HTML
html_template = Template("""
<p>
<div id="hinton_$divNumber"></div>
</p>
""")
# JavaScript
javascript_template = Template("""
<script>
requirejs.config({
paths: {
qVisualization: "https://qvisualization.mybluemix.net/q-visualizations"
}
});
require(["qVisualization"], function(qVisualizations) {
qVisualizations.plotState("hinton_$divNumber",
"hinton",
$executions,
$options);
});
</script>
""")
rho = _validate_input_state(rho)
if figsize is None:
options = {}
else:
options = {'width': figsize[0], 'height': figsize[1]}
# Process data and execute
div_number = str(time.time())
div_number = re.sub('[.]', '', div_number)
# Process data and execute
real = []
imag = []
for xvalue in rho:
row_real = []
col_imag = []
for value_real in xvalue.real:
row_real.append(float(value_real))
real.append(row_real)
for value_imag in xvalue.imag:
col_imag.append(float(value_imag))
imag.append(col_imag)
html = html_template.substitute({'divNumber': div_number})
javascript = javascript_template.substitute({
'divNumber':
div_number,
'executions': [{
'data': real
}, {
'data': imag
}],
'options':
options
})
display(HTML(html + javascript))
