def unitarity(oper):
"""
Returns the unitarity of a quantum map, defined as the Frobenius norm
of the unital block of that map's superoperator representation.
Parameters
----------
oper : Qobj
Quantum map under consideration.
Returns
-------
u : float
Unitarity of ``oper``.
"""
Eu = _super_to_superpauli(oper).full()[1:, 1:]
#return np.real(np.trace(np.dot(Eu, Eu.conj().T))) / len(Eu)
return np.linalg.norm(Eu, 'fro')**2 / len(Eu)
def unitarity(oper):
"""
Returns the unitarity of a quantum map, defined as the Frobenius norm
of the unital block of that map's superoperator representation.
Parameters
----------
oper : Qobj
Quantum map under consideration.
Returns
-------
u : float
Unitarity of ``oper``.
"""
Eu = _super_to_superpauli(oper).full()[1:, 1:]
#return np.real(np.trace(np.dot(Eu, Eu.conj().T))) / len(Eu)
return np.linalg.norm(Eu, 'fro')**2 / len(Eu)
def hinton(rho, xlabels=None, ylabels=None, title=None, ax=None, cmap=None,
label_top=True):
"""Draws a Hinton diagram for visualizing a density matrix or superoperator.
Parameters
----------
rho : qobj
Input density matrix or superoperator.
xlabels : list of strings or False
list of x labels
ylabels : list of strings or False
list of y labels
title : string
title of the plot (optional)
ax : a matplotlib axes instance
The axes context in which the plot will be drawn.
cmap : a matplotlib colormap instance
Color map to use when plotting.
label_top : bool
If True, x-axis labels will be placed on top, otherwise
they will appear below the plot.
Returns
-------
fig, ax : tuple
A tuple of the matplotlib figure and axes instances used to produce
the figure.
Raises
------
ValueError
Input argument is not a quantum object.
"""
# Apply default colormaps.
# TODO: abstract this away into something that makes default
# colormaps.
cmap = (
(cm.Greys_r if settings.colorblind_safe else cm.RdBu)
if cmap is None else cmap
)
# Extract plotting data W from the input.
if isinstance(rho, Qobj):
if rho.isoper:
W = rho.full()
# Create default labels if none are given.
if xlabels is None or ylabels is None:
labels = _cb_labels(rho.dims[0])
xlabels = xlabels if xlabels is not None else list(labels[0])
ylabels = ylabels if ylabels is not None else list(labels[1])
elif rho.isoperket:
W = vector_to_operator(rho).full()
elif rho.isoperbra:
W = vector_to_operator(rho.dag()).full()
elif rho.issuper:
if not _isqubitdims(rho.dims):
raise ValueError("Hinton plots of superoperators are "
"currently only supported for qubits.")
# Convert to a superoperator in the Pauli basis,
# so that all the elements are real.
sqobj = _super_to_superpauli(rho)
nq = int(log2(sqobj.shape[0]) / 2)
W = sqobj.full().T
# Create default labels, too.
if (xlabels is None) or (ylabels is None):
labels = list(map("".join, it.product("IXYZ", repeat=nq)))
xlabels = xlabels if xlabels is not None else labels
ylabels = ylabels if ylabels is not None else labels
else:
raise ValueError(
"Input quantum object must be an operator or superoperator."
)
else:
W = rho
if ax is None:
fig, ax = plt.subplots(1, 1, figsize=(8, 6))
else:
fig = None
if not (xlabels or ylabels):
ax.axis('off')
ax.axis('equal')
ax.set_frame_on(False)
height, width = W.shape
w_max = 1.25 * max(abs(np.diag(np.matrix(W))))
if w_max <= 0.0:
w_max = 1.0
ax.fill(array([0, width, width, 0]), array([0, 0, height, height]),
color=cmap(128))
for x in range(width):
for y in range(height):
_x = x + 1
_y = y + 1
if np.real(W[x, y]) > 0.0:
_blob(_x - 0.5, height - _y + 0.5, abs(W[x,
y]), w_max, min(1, abs(W[x, y]) / w_max), cmap=cmap)
else:
_blob(_x - 0.5, height - _y + 0.5, -abs(W[
x, y]), w_max, min(1, abs(W[x, y]) / w_max), cmap=cmap)
# color axis
norm = mpl.colors.Normalize(-abs(W).max(), abs(W).max())
cax, kw = mpl.colorbar.make_axes(ax, shrink=0.75, pad=.1)
mpl.colorbar.ColorbarBase(cax, norm=norm, cmap=cmap)
# x axis
ax.xaxis.set_major_locator(plt.IndexLocator(1, 0.5))
if xlabels:
ax.set_xticklabels(xlabels)
if label_top:
ax.xaxis.tick_top()
ax.tick_params(axis='x', labelsize=14)
# y axis
ax.yaxis.set_major_locator(plt.IndexLocator(1, 0.5))
if ylabels:
ax.set_yticklabels(list(reversed(ylabels)))
ax.tick_params(axis='y', labelsize=14)
return fig, ax
def hinton(rho,
xlabels=None,
ylabels=None,
title=None,
ax=None,
cmap=None,
label_top=True):
"""Draws a Hinton diagram for visualizing a density matrix or superoperator.
Parameters
----------
rho : qobj
Input density matrix or superoperator.
xlabels : list of strings or False
list of x labels
ylabels : list of strings or False
list of y labels
title : string
title of the plot (optional)
ax : a matplotlib axes instance
The axes context in which the plot will be drawn.
cmap : a matplotlib colormap instance
Color map to use when plotting.
label_top : bool
If True, x-axis labels will be placed on top, otherwise
they will appear below the plot.
Returns
-------
fig, ax : tuple
A tuple of the matplotlib figure and axes instances used to produce
the figure.
Raises
------
ValueError
Input argument is not a quantum object.
"""
# Apply default colormaps.
# TODO: abstract this away into something that makes default
# colormaps.
cmap = ((cm.Greys_r if settings.colorblind_safe else cm.RdBu)
if cmap is None else cmap)
# Extract plotting data W from the input.
if isinstance(rho, Qobj):
if rho.isoper:
W = rho.full()
# Create default labels if none are given.
if xlabels is None or ylabels is None:
labels = _cb_labels(rho.dims[0])
xlabels = xlabels if xlabels is not None else list(labels[0])
ylabels = ylabels if ylabels is not None else list(labels[1])
elif rho.isoperket:
W = vector_to_operator(rho).full()
elif rho.isoperbra:
W = vector_to_operator(rho.dag()).full()
elif rho.issuper:
if not _isqubitdims(rho.dims):
raise ValueError("Hinton plots of superoperators are "
"currently only supported for qubits.")
# Convert to a superoperator in the Pauli basis,
# so that all the elements are real.
sqobj = _super_to_superpauli(rho)
nq = int(log2(sqobj.shape[0]) / 2)
W = sqobj.full().T
# Create default labels, too.
if (xlabels is None) or (ylabels is None):
labels = list(map("".join, it.product("IXYZ", repeat=nq)))
xlabels = xlabels if xlabels is not None else labels
ylabels = ylabels if ylabels is not None else labels
else:
raise ValueError(
"Input quantum object must be an operator or superoperator.")
else:
W = rho
if ax is None:
fig, ax = plt.subplots(1, 1, figsize=(8, 6))
else:
fig = None
if not (xlabels or ylabels):
ax.axis('off')
ax.axis('equal')
ax.set_frame_on(False)
height, width = W.shape
w_max = 1.25 * max(abs(np.diag(np.matrix(W))))
if w_max <= 0.0:
w_max = 1.0
ax.fill(array([0, width, width, 0]),
array([0, 0, height, height]),
color=cmap(128))
for x in range(width):
for y in range(height):
_x = x + 1
_y = y + 1
if np.real(W[x, y]) > 0.0:
_blob(_x - 0.5,
height - _y + 0.5,
abs(W[x, y]),
w_max,
min(1,
abs(W[x, y]) / w_max),
cmap=cmap)
else:
_blob(_x - 0.5,
height - _y + 0.5,
-abs(W[x, y]),
w_max,
min(1,
abs(W[x, y]) / w_max),
cmap=cmap)
# color axis
norm = mpl.colors.Normalize(-abs(W).max(), abs(W).max())
cax, kw = mpl.colorbar.make_axes(ax, shrink=0.75, pad=.1)
mpl.colorbar.ColorbarBase(cax, norm=norm, cmap=cmap)
# x axis
ax.xaxis.set_major_locator(plt.IndexLocator(1, 0.5))
if xlabels:
ax.set_xticklabels(xlabels)
if label_top:
ax.xaxis.tick_top()
ax.tick_params(axis='x', labelsize=14)
# y axis
ax.yaxis.set_major_locator(plt.IndexLocator(1, 0.5))
if ylabels:
ax.set_yticklabels(list(reversed(ylabels)))
ax.tick_params(axis='y', labelsize=14)
return fig, ax