# Source code for qutip.tomography

# This file is part of QuTiP: Quantum Toolbox in Python.
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__all__ = ['qpt_plot', 'qpt_plot_combined', 'qpt']

from qutip.tensor import tensor
from qutip.superoperator import spre, spost, mat2vec, vec2mat
from numpy import hstack, real, imag
import scipy.linalg as la
from qutip.visualization import matrix_histogram, matrix_histogram_complex

try:
import matplotlib.pyplot as plt
except:
pass

def _index_permutations(size_list, perm=[]):
"""
Generate a list with all index permutations.

Parameters
----------
size_list : list
A list that contains the sizes for each composite system.
perm : list
A list of permutations

Returns
-------
perm_idx : list
List containing index permutations.

"""
if len(size_list) == 0:
yield perm
else:
for n in range(size_list[0]):
for ip in _index_permutations(size_list[1:], perm + [n]):
yield ip

[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 : string Plot title. fig : figure instance User defined figure instance used for generating QPT plot. axes : list of figure axis instance 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, title=r"real($\chi$)", limits=[-1, 1], ax=axes[0]) matrix_histogram(imag(chi), xlabels, xlabels, title=r"imag($\chi$)", limits=[-1, 1], ax=axes[1]) 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 : string Plot title. fig : figure instance User defined figure instance used for generating QPT plot. ax : figure axis instance User defined figure axis instance used for generating QPT plot (alternative to the fig argument). threshold: float (None) 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_complex(chi, xlabels, xlabels, title=title, ax=ax, threshold=threshold) 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 = vec2mat(U * mat2vec(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([mat2vec(EE.full()) for EE in EE_ops]) Uvec = mat2vec(U.full()) chi_vec = la.solve(M, Uvec) return vec2mat(chi_vec)