__all__ = ['qpt_plot', 'qpt_plot_combined', 'qpt']
from numpy import hstack, real, imag
import scipy.linalg as la
from . import tensor, spre, spost, stack_columns, unstack_columns
from .visualization import matrix_histogram
import itertools
try:
import matplotlib.pyplot as plt
except:
pass
def _index_permutations(size_list):
"""
Generate a list with all index permutations.
Parameters
----------
size_list : list
A list that contains the sizes for each composite system.
Returns
-------
perm_idx : list
List containing index permutations.
"""
return itertools.product(*[range(N) for N in size_list])
[docs]def qpt_plot(chi, lbls_list, title=None, fig=None, axes=None):
"""
Visualize the quantum process tomography chi matrix. Plot the real and
imaginary parts separately.
Parameters
----------
chi : array
Input QPT chi matrix.
lbls_list : list
List of labels for QPT plot axes.
title : str, optional
Plot title.
fig : figure instance, optional
User defined figure instance used for generating QPT plot.
axes : list of figure axis instance, optional
User defined figure axis instance (list of two axes) used for
generating QPT plot.
Returns
-------
fig, ax : tuple
A tuple of the matplotlib figure and axes instances used to produce
the figure.
"""
if axes is None or len(axes) != 2:
if fig is None:
fig = plt.figure(figsize=(16, 8))
ax1 = fig.add_subplot(1, 2, 1, projection='3d', position=[0, 0, 1, 1])
ax2 = fig.add_subplot(1, 2, 2, projection='3d', position=[0, 0, 1, 1])
axes = [ax1, ax2]
xlabels = []
for inds in _index_permutations([len(lbls) for lbls in lbls_list]):
xlabels.append("".join([lbls_list[k][inds[k]]
for k in range(len(lbls_list))]))
matrix_histogram(real(chi), xlabels, xlabels, limits=[-1, 1], ax=axes[0])
axes[0].set_title(r"real($\chi$)")
matrix_histogram(imag(chi), xlabels, xlabels, limits=[-1, 1], ax=axes[1])
axes[1].set_title(r"imag($\chi$)")
if title and fig:
fig.suptitle(title)
return fig, axes
[docs]def qpt_plot_combined(chi, lbls_list, title=None,
fig=None, ax=None, figsize=(8, 6),
threshold=None):
"""
Visualize the quantum process tomography chi matrix. Plot bars with
height and color corresponding to the absolute value and phase,
respectively.
Parameters
----------
chi : array
Input QPT chi matrix.
lbls_list : list
List of labels for QPT plot axes.
title : str, optional
Plot title.
fig : figure instance, optional
User defined figure instance used for generating QPT plot.
figsize : (int, int), default: (8, 6)
Size of the figure when the ``fig`` is not provided.
ax : figure axis instance, optional
User defined figure axis instance used for generating QPT plot
(alternative to the fig argument).
threshold: float, optional
Threshold for when bars of smaller height should be transparent. If
not set, all bars are colored according to the color map.
Returns
-------
fig, ax : tuple
A tuple of the matplotlib figure and axes instances used to produce
the figure.
"""
if ax is None:
if fig is None:
fig = plt.figure(figsize=figsize)
ax = fig.add_subplot(1, 1, 1, projection='3d', position=[0, 0, 1, 1])
xlabels = []
for inds in _index_permutations([len(lbls) for lbls in lbls_list]):
xlabels.append("".join(
[lbls_list[k][inds[k]] for k in range(len(lbls_list))]))
if not title:
title = r"$\chi$"
matrix_histogram(chi, xlabels, xlabels, bar_style='abs',
color_style='phase',
options={'threshold': threshold}, ax=ax)
ax.set_title(title)
return fig, ax
[docs]def qpt(U, op_basis_list):
"""
Calculate the quantum process tomography chi matrix for a given (possibly
nonunitary) transformation matrix U, which transforms a density matrix in
vector form according to:
vec(rho) = U * vec(rho0)
or
rho = unstack_columns(U * stack_columns(rho0))
U can be calculated for an open quantum system using the QuTiP propagator
function.
Parameters
----------
U : Qobj
Transformation operator. Can be calculated using QuTiP propagator
function.
op_basis_list : list
A list of Qobj's representing the basis states.
Returns
-------
chi : array
QPT chi matrix
"""
E_ops = []
# loop over all index permutations
for inds in _index_permutations([len(ops) for ops in op_basis_list]):
# loop over all composite systems
E_op_list = [op_basis_list[k][inds[k]] for k in range(len(
op_basis_list))]
E_ops.append(tensor(E_op_list))
EE_ops = [spre(E1) * spost(E2.dag()) for E1 in E_ops for E2 in E_ops]
M = hstack([EE.full().ravel('F')[:, None] for EE in EE_ops])
Uvec = U.full().ravel('F')
chi_vec = la.solve(M, Uvec)
return chi_vec.reshape(U.shape).T