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This code is part of Qiskit.","#","# (C) Copyright IBM 2017, 2023.","#","# 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","# pylint: disable=missing-param-doc,missing-type-doc,unused-argument","","\"\"\"","Visualization functions for quantum states.","\"\"\"","","from typing import List, Union","from functools import reduce","import colorsys","","import numpy as np","from qiskit import user_config","from qiskit.quantum_info.states.statevector import Statevector","from qiskit.quantum_info.operators.operator import Operator","from qiskit.quantum_info.operators.symplectic import PauliList, SparsePauliOp","from qiskit.quantum_info.states.densitymatrix import DensityMatrix","from qiskit.utils import optionals as _optionals","from qiskit.circuit.tools.pi_check import pi_check","","from .array import _num_to_latex, array_to_latex","from .utils import matplotlib_close_if_inline","from .exceptions import VisualizationError","","","@_optionals.HAS_MATPLOTLIB.require_in_call","def plot_state_hinton(state, title=\"\", figsize=None, ax_real=None, ax_imag=None, *, filename=None):"," \"\"\"Plot a hinton diagram for the density matrix of a quantum state.",""," The hinton diagram represents the values of a matrix using"," squares, whose size indicate the magnitude of their corresponding value"," and their color, its sign. A white square means the value is positive and"," a black one means negative.",""," 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."," filename (str): file path to save image to."," 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:"," :class:`matplotlib:matplotlib.figure.Figure` :"," The matplotlib.Figure of the visualization if"," neither ax_real or ax_imag is set.",""," Raises:"," MissingOptionalLibraryError: Requires matplotlib."," VisualizationError: if input is not a valid N-qubit state.",""," Examples:"," .. plot::"," :include-source:",""," import numpy as np"," from qiskit import QuantumCircuit"," from qiskit.quantum_info import DensityMatrix"," from qiskit.visualization import plot_state_hinton",""," qc = QuantumCircuit(2)"," qc.h([0, 1])"," qc.cz(0,1)"," qc.ry(np.pi/3 , 0)"," qc.rx(np.pi/5, 1)",""," state = DensityMatrix(qc)"," plot_state_hinton(state, title=\"New Hinton Plot\")",""," \"\"\""," from matplotlib import pyplot as plt",""," # 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"," # Reversal is to account for Qiskit's endianness."," 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)][::-1]"," 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):"," # Convert from matrix co-ordinates to plot co-ordinates."," plot_x, plot_y = y, lx - x - 1"," color = \"white\" if w > 0 else \"black\""," size = np.sqrt(np.abs(w) / max_weight)"," rect = plt.Rectangle("," [0.5 + plot_x - size / 2, 0.5 + plot_y - size / 2],"," size,"," size,"," facecolor=color,"," edgecolor=color,"," )"," ax1.add_patch(rect)",""," ax1.set_xticks(0.5 + np.arange(lx))"," ax1.set_yticks(0.5 + np.arange(ly))"," ax1.set_xlim([0, lx])"," ax1.set_ylim([0, ly])"," ax1.set_yticklabels(row_names, fontsize=14)"," ax1.set_xticklabels(column_names, fontsize=14, rotation=90)"," 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):"," # Convert from matrix co-ordinates to plot co-ordinates."," plot_x, plot_y = y, lx - x - 1"," color = \"white\" if w > 0 else \"black\""," size = np.sqrt(np.abs(w) / max_weight)"," rect = plt.Rectangle("," [0.5 + plot_x - size / 2, 0.5 + plot_y - size / 2],"," size,"," size,"," facecolor=color,"," edgecolor=color,"," )"," ax2.add_patch(rect)",""," ax2.set_xticks(0.5 + np.arange(lx))"," ax2.set_yticks(0.5 + np.arange(ly))"," ax2.set_xlim([0, lx])"," ax2.set_ylim([0, ly])"," ax2.set_yticklabels(row_names, fontsize=14)"," ax2.set_xticklabels(column_names, fontsize=14, rotation=90)"," ax2.set_title(\"Im[$\\\\rho$]\", fontsize=14)"," fig.tight_layout()"," if title:"," fig.suptitle(title, fontsize=16)"," if ax_real is None and ax_imag is None:"," matplotlib_close_if_inline(fig)"," if filename is None:"," return fig"," else:"," return fig.savefig(filename)","","","@_optionals.HAS_MATPLOTLIB.require_in_call","def plot_bloch_vector("," bloch, title=\"\", ax=None, figsize=None, coord_type=\"cartesian\", font_size=None","):"," \"\"\"Plot the Bloch sphere.",""," Plot a Bloch sphere with the specified coordinates, that can be given in both"," cartesian and spherical systems.",""," Args:"," bloch (list[double]): array of three elements where [, , ] (Cartesian)"," or [, , ] (spherical in radians)"," is inclination angle from +z direction"," 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"," font_size (float): Font size.",""," Returns:"," :class:`matplotlib:matplotlib.figure.Figure` : A matplotlib figure instance if ``ax = None``.",""," Raises:"," MissingOptionalLibraryError: Requires matplotlib.",""," Examples:"," .. plot::"," :include-source:",""," from qiskit.visualization import plot_bloch_vector",""," plot_bloch_vector([0,1,0], title=\"New Bloch Sphere\")",""," .. plot::"," :include-source:",""," import numpy as np"," from qiskit.visualization import plot_bloch_vector",""," # You can use spherical coordinates instead of cartesian.",""," plot_bloch_vector([1, np.pi/2, np.pi/3], coord_type='spherical')",""," \"\"\""," from .bloch import Bloch",""," if figsize is None:"," figsize = (5, 5)"," B = Bloch(axes=ax, font_size=font_size)"," 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])"," matplotlib_close_if_inline(fig)"," return fig"," return None","","","@_optionals.HAS_MATPLOTLIB.require_in_call","def plot_bloch_multivector("," state,"," title=\"\","," figsize=None,"," *,"," reverse_bits=False,"," filename=None,"," font_size=None,"," title_font_size=None,"," title_pad=1,","):"," r\"\"\"Plot a Bloch sphere for each qubit.",""," Each component :math:`(x,y,z)` of the Bloch sphere labeled as 'qubit i' represents the expected"," value of the corresponding Pauli operator acting only on that qubit, that is, the expected value"," of :math:`I_{N-1} \\otimes\\dotsb\\otimes I_{i+1}\\otimes P_i \\otimes I_{i-1}\\otimes\\dotsb\\otimes"," I_0`, where :math:`N` is the number of qubits, :math:`P\\in \\{X,Y,Z\\}` and :math:`I` is the"," identity operator.",""," Args:"," state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state."," title (str): a string that represents the plot title"," figsize (tuple): size of each individual Bloch sphere figure, in inches."," reverse_bits (bool): If True, plots qubits following Qiskit's convention [Default:False]."," font_size (float): Font size for the Bloch ball figures."," title_font_size (float): Font size for the title."," title_pad (float): Padding for the title (suptitle `y` position is `y=1+title_pad/100`).",""," Returns:"," :class:`matplotlib:matplotlib.figure.Figure` :"," A matplotlib figure instance.",""," Raises:"," MissingOptionalLibraryError: Requires matplotlib."," VisualizationError: if input is not a valid N-qubit state.",""," Examples:"," .. plot::"," :include-source:",""," from qiskit import QuantumCircuit"," from qiskit.quantum_info import Statevector"," from qiskit.visualization import plot_bloch_multivector",""," qc = QuantumCircuit(2)"," qc.h(0)"," qc.x(1)",""," state = Statevector(qc)"," plot_bloch_multivector(state)",""," .. plot::"," :include-source:",""," from qiskit import QuantumCircuit"," from qiskit.quantum_info import Statevector"," from qiskit.visualization import plot_bloch_multivector",""," qc = QuantumCircuit(2)"," qc.h(0)"," qc.x(1)",""," # You can reverse the order of the qubits.",""," from qiskit.quantum_info import DensityMatrix",""," qc = QuantumCircuit(2)"," qc.h([0, 1])"," qc.t(1)"," qc.s(0)"," qc.cx(0,1)",""," matrix = DensityMatrix(qc)"," plot_bloch_multivector(matrix, title='My Bloch Spheres', reverse_bits=True)",""," \"\"\""," from matplotlib import pyplot as plt",""," # Data"," bloch_data = ("," _bloch_multivector_data(state)[::-1] if reverse_bits else _bloch_multivector_data(state)"," )"," num = len(bloch_data)"," if figsize is not None:"," width, height = figsize"," width *= num"," else:"," width, height = plt.figaspect(1 / num)"," default_title_font_size = font_size if font_size is not None else 16"," title_font_size = title_font_size if title_font_size is not None else default_title_font_size"," fig = plt.figure(figsize=(width, height))"," for i in range(num):"," pos = num - 1 - i if reverse_bits else i"," ax = fig.add_subplot(1, num, i + 1, projection=\"3d\")"," plot_bloch_vector("," bloch_data[i], \"qubit \" + str(pos), ax=ax, figsize=figsize, font_size=font_size"," )"," fig.suptitle(title, fontsize=title_font_size, y=1.0 + title_pad / 100)"," matplotlib_close_if_inline(fig)"," if filename is None:"," return fig"," else:"," return fig.savefig(filename)","","","@_optionals.HAS_MATPLOTLIB.require_in_call","def plot_state_city("," state,"," title=\"\","," figsize=None,"," color=None,"," alpha=1,"," ax_real=None,"," ax_imag=None,"," *,"," filename=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_real only the imaginary component plot will be generated."," Additionally, if specified there will be no returned Figure since"," it is redundant.",""," Returns:"," :class:`matplotlib:matplotlib.figure.Figure` :"," The matplotlib.Figure of the visualization if the"," ``ax_real`` and ``ax_imag`` kwargs are not set",""," Raises:"," MissingOptionalLibraryError: Requires matplotlib."," ValueError: When 'color' is not a list of len=2."," VisualizationError: if input is not a valid N-qubit state.",""," Examples:"," .. plot::"," :include-source:",""," # You can choose different colors for the real and imaginary parts of the density matrix.",""," from qiskit import QuantumCircuit"," from qiskit.quantum_info import DensityMatrix"," from qiskit.visualization import plot_state_city",""," qc = QuantumCircuit(2)"," qc.h(0)"," qc.cx(0, 1)",""," state = DensityMatrix(qc)"," plot_state_city(state, color=['midnightblue', 'crimson'], title=\"New State City\")",""," .. plot::"," :include-source:",""," # You can make the bars more transparent to better see the ones that are behind"," # if they overlap.",""," import numpy as np"," from qiskit.quantum_info import Statevector"," from qiskit.visualization import plot_state_city"," from qiskit import QuantumCircuit",""," qc = QuantumCircuit(2)"," qc.h(0)"," qc.cx(0, 1)","",""," qc = QuantumCircuit(2)"," qc.h([0, 1])"," qc.cz(0,1)"," qc.ry(np.pi/3, 0)"," qc.rx(np.pi/5, 1)",""," state = Statevector(qc)"," plot_state_city(state, alpha=0.6)",""," \"\"\""," import matplotlib.colors as mcolors"," from matplotlib import pyplot as plt"," from mpl_toolkits.mplot3d.art3d import Poly3DCollection",""," 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)]",""," ly, lx = datareal.shape[:2]"," 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:"," real_color, imag_color = \"#648fff\", \"#648fff\""," else:"," if len(color) != 2:"," raise ValueError(\"'color' must be a list of len=2.\")"," real_color = \"#648fff\" if color[0] is None else color[0]"," imag_color = \"#648fff\" if color[1] is None else color[1]"," if ax_real is None and ax_imag is None:"," # set default figure size"," if figsize is None:"," figsize = (16, 8)",""," fig = plt.figure(figsize=figsize, facecolor=\"w\")"," ax1 = fig.add_subplot(1, 2, 1, projection=\"3d\", computed_zorder=False)"," ax2 = fig.add_subplot(1, 2, 2, projection=\"3d\", computed_zorder=False)",""," elif ax_real is not None:"," fig = ax_real.get_figure()"," ax1 = ax_real"," ax2 = ax_imag"," else:"," fig = ax_imag.get_figure()"," ax1 = None"," ax2 = ax_imag",""," fig.tight_layout()",""," max_dzr = np.max(dzr)"," max_dzi = np.max(dzi)",""," # Figure scaling variables since fig.tight_layout won't work"," fig_width, fig_height = fig.get_size_inches()"," max_plot_size = min(fig_width / 2.25, fig_height)"," max_font_size = int(3 * max_plot_size)"," max_zoom = 10 / (10 + np.sqrt(max_plot_size))",""," for ax, dz, col, zlabel in ("," (ax1, dzr, real_color, \"Real\"),"," (ax2, dzi, imag_color, \"Imaginary\"),"," ):",""," if ax is None:"," continue",""," max_dz = np.max(dz)"," min_dz = np.min(dz)",""," if isinstance(col, str) and col.startswith(\"#\"):"," col = mcolors.to_rgba_array(col)",""," dzn = dz < 0"," if np.any(dzn):"," fc = generate_facecolors("," xpos[dzn], ypos[dzn], zpos[dzn], dx[dzn], dy[dzn], dz[dzn], col"," )"," negative_bars = ax.bar3d("," xpos[dzn],"," ypos[dzn],"," zpos[dzn],"," dx[dzn],"," dy[dzn],"," dz[dzn],"," alpha=alpha,"," zorder=0.625,"," )"," negative_bars.set_facecolor(fc)",""," if min_dz < 0 < max_dz:"," xlim, ylim = [0, lx], [0, ly]"," verts = [list(zip(xlim + xlim[::-1], np.repeat(ylim, 2), [0] * 4))]"," plane = Poly3DCollection(verts, alpha=0.25, facecolor=\"k\", linewidths=1)"," plane.set_zorder(0.75)"," ax.add_collection3d(plane)",""," dzp = dz >= 0"," if np.any(dzp):"," fc = generate_facecolors("," xpos[dzp], ypos[dzp], zpos[dzp], dx[dzp], dy[dzp], dz[dzp], col"," )"," positive_bars = ax.bar3d("," xpos[dzp],"," ypos[dzp],"," zpos[dzp],"," dx[dzp],"," dy[dzp],"," dz[dzp],"," alpha=alpha,"," zorder=0.875,"," )"," positive_bars.set_facecolor(fc)",""," ax.set_title(f\"{zlabel} Amplitude (ρ)\", fontsize=max_font_size)",""," ax.set_xticks(np.arange(0.5, lx + 0.5, 1))"," ax.set_yticks(np.arange(0.5, ly + 0.5, 1))"," if max_dz != min_dz:"," ax.axes.set_zlim3d(min_dz, max(max_dzr + 1e-9, max_dzi))"," else:"," if min_dz == 0:"," ax.axes.set_zlim3d(min_dz, max(max_dzr + 1e-9, max_dzi))"," else:"," ax.axes.set_zlim3d(auto=True)"," ax.get_autoscalez_on()",""," ax.xaxis.set_ticklabels("," row_names, fontsize=max_font_size, rotation=45, ha=\"right\", va=\"top\""," )"," ax.yaxis.set_ticklabels("," column_names, fontsize=max_font_size, rotation=-22.5, ha=\"left\", va=\"center\""," )",""," for tick in ax.zaxis.get_major_ticks():"," tick.label1.set_fontsize(max_font_size)"," tick.label1.set_horizontalalignment(\"left\")"," tick.label1.set_verticalalignment(\"bottom\")",""," ax.set_box_aspect(aspect=(4, 4, 4), zoom=max_zoom)"," ax.set_xmargin(0)"," ax.set_ymargin(0)",""," fig.suptitle(title, fontsize=max_font_size * 1.25)"," fig.subplots_adjust(top=0.9, bottom=0, left=0, right=1, hspace=0, wspace=0)"," if ax_real is None and ax_imag is None:"," matplotlib_close_if_inline(fig)"," if filename is None:"," return fig"," else:"," return fig.savefig(filename)","","","@_optionals.HAS_MATPLOTLIB.require_in_call","def plot_state_paulivec(state, title=\"\", figsize=None, color=None, ax=None, *, filename=None):"," r\"\"\"Plot the Pauli-vector representation of a quantum state as bar graph.",""," The Pauli-vector of a density matrix :math:`\\rho` is defined by the expectation of each"," possible tensor product of single-qubit Pauli operators (including the identity), that is",""," .. math ::",""," \\rho = \\frac{1}{2^n} \\sum_{\\sigma \\in \\{I, X, Y, Z\\}^{\\otimes n}}"," \\mathrm{Tr}(\\sigma \\rho) \\sigma.",""," This function plots the coefficients :math:`\\mathrm{Tr}(\\sigma\\rho)` as bar graph.",""," 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 coefficient 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:"," :class:`matplotlib:matplotlib.figure.Figure` :"," The matplotlib.Figure of the visualization if the"," ``ax`` kwarg is not set",""," Raises:"," MissingOptionalLibraryError: Requires matplotlib."," VisualizationError: if input is not a valid N-qubit state.",""," Examples:"," .. plot::"," :include-source:",""," # You can set a color for all the bars.",""," from qiskit import QuantumCircuit"," from qiskit.quantum_info import Statevector"," from qiskit.visualization import plot_state_paulivec",""," qc = QuantumCircuit(2)"," qc.h(0)"," qc.cx(0, 1)",""," state = Statevector(qc)"," plot_state_paulivec(state, color='midnightblue', title=\"New PauliVec plot\")",""," .. plot::"," :include-source:",""," # If you introduce a list with less colors than bars, the color of the bars will"," # alternate following the sequence from the list.",""," import numpy as np"," from qiskit.quantum_info import DensityMatrix"," from qiskit import QuantumCircuit"," from qiskit.visualization import plot_state_paulivec",""," qc = QuantumCircuit(2)"," qc.h(0)"," qc.cx(0, 1)",""," qc = QuantumCircuit(2)"," qc.h([0, 1])"," qc.cz(0, 1)"," qc.ry(np.pi/3, 0)"," qc.rx(np.pi/5, 1)",""," matrix = DensityMatrix(qc)"," plot_state_paulivec(matrix, color=['crimson', 'midnightblue', 'seagreen'])"," \"\"\""," from matplotlib import pyplot as plt",""," 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(\"Coefficients\", 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.label1.set_fontsize(14)"," ax.set_title(title, fontsize=16)"," if return_fig:"," matplotlib_close_if_inline(fig)"," if filename is None:"," return fig"," else:"," return fig.savefig(filename)","","","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 = [n - 1 - x for x in 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 * 5 / 4)) % (np.pi * 2)"," rgb = colorsys.hls_to_rgb(angles / (np.pi * 2), 0.5, 0.5)"," return rgb","","","@_optionals.HAS_MATPLOTLIB.require_in_call","@_optionals.HAS_SEABORN.require_in_call","def plot_state_qsphere("," state,"," figsize=None,"," ax=None,"," show_state_labels=True,"," show_state_phases=False,"," use_degrees=False,"," *,"," filename=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:"," :class:`matplotlib:matplotlib.figure.Figure` :"," A matplotlib figure instance if the ``ax`` kwarg is not set",""," Raises:"," MissingOptionalLibraryError: Requires matplotlib."," VisualizationError: if input is not a valid N-qubit state.",""," QiskitError: Input statevector does not have valid dimensions.",""," Examples:"," .. plot::"," :include-source:",""," from qiskit import QuantumCircuit"," from qiskit.quantum_info import Statevector"," from qiskit.visualization import plot_state_qsphere",""," qc = QuantumCircuit(2)"," qc.h(0)"," qc.cx(0, 1)",""," state = Statevector(qc)"," plot_state_qsphere(state)",""," .. plot::"," :include-source:",""," # You can show the phase of each state and use"," # degrees instead of radians",""," from qiskit.quantum_info import DensityMatrix"," import numpy as np"," from qiskit import QuantumCircuit"," from qiskit.visualization import plot_state_qsphere",""," qc = QuantumCircuit(2)"," qc.h([0, 1])"," qc.cz(0,1)"," qc.ry(np.pi/3, 0)"," qc.rx(np.pi/5, 1)"," qc.z(1)",""," matrix = DensityMatrix(qc)"," plot_state_qsphere(matrix,"," show_state_phases = True, use_degrees = True)"," \"\"\""," from matplotlib import gridspec"," from matplotlib import pyplot as plt"," from matplotlib.patches import Circle"," import seaborn as sns"," from scipy import linalg"," from .bloch import Arrow3D",""," 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.xaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))"," ax.yaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))"," ax.zaxis.set_pane_color((1.0, 1.0, 1.0, 0.0))",""," # Get rid of the spines"," ax.xaxis.line.set_color((1.0, 1.0, 1.0, 0.0))"," ax.yaxis.line.set_color((1.0, 1.0, 1.0, 0.0))"," ax.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()))"," prob = min(prob, 1) # See https://github.com/Qiskit/qiskit-terra/issues/4666"," 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=(0.5, 0.5, 0.5), lw=1, ls=\":\", alpha=0.5)",""," # add center point"," ax.plot("," [0],"," [0],"," [0],"," markerfacecolor=(0.5, 0.5, 0.5),"," markeredgecolor=(0.5, 0.5, 0.5),"," marker=\"o\","," markersize=3,"," alpha=1,"," )"," else:"," break",""," n = 64"," theta = np.ones(n)"," colors = sns.hls_palette(n)",""," ax2 = fig.add_subplot(gs[2:, 2:])"," ax2.pie(theta, colors=colors[5 * n // 8 :] + colors[: 5 * n // 8], 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:"," matplotlib_close_if_inline(fig)"," if filename is None:"," return fig"," else:"," return fig.savefig(filename)","","","@_optionals.HAS_MATPLOTLIB.require_in_call","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."," Raises:"," MissingOptionalLibraryError: If matplotlib is not installed"," \"\"\""," import matplotlib.colors as mcolors",""," 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*."," \"\"\""," from matplotlib.colors import Normalize, LightSource"," import matplotlib.colors as mcolors",""," 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","","","def state_to_latex("," state: Union[Statevector, DensityMatrix], dims: bool = None, convention: str = \"ket\", **args",") -> str:"," \"\"\"Return a Latex representation of a state. Wrapper function"," for `qiskit.visualization.array_to_latex` for convention 'vector'."," Adds dims if necessary."," Intended for use within `state_drawer`.",""," Args:"," state: State to be drawn"," dims (bool): Whether to display the state's `dims`"," convention (str): Either 'vector' or 'ket'. For 'ket' plot the state in the ket-notation."," Otherwise plot as a vector"," **args: Arguments to be passed directly to `array_to_latex` for convention 'ket'",""," Returns:"," Latex representation of the state"," \"\"\""," if dims is None: # show dims if state is not only qubits"," if set(state.dims()) == {2}:"," dims = False"," else:"," dims = True",""," prefix = \"\""," suffix = \"\""," if dims:"," prefix = \"\\\\begin{align}\\n\""," dims_str = state._op_shape.dims_l()"," suffix = f\"\\\\\\\\\\n\\\\text{{dims={dims_str}}}\\n\\\\end{{align}}\"",""," operator_shape = state._op_shape"," # we only use the ket convetion for qubit statevectors"," # this means the operator shape should hve no input dimensions and all output dimensions equal to 2"," is_qubit_statevector = len(operator_shape.dims_r()) == 0 and set(operator_shape.dims_l()) == {2}"," if convention == \"ket\" and is_qubit_statevector:"," latex_str = _state_to_latex_ket(state._data, **args)"," else:"," latex_str = array_to_latex(state._data, source=True, **args)"," return prefix + latex_str + suffix","","","def _numbers_to_latex_terms(numbers: List[complex], decimals: int = 10) -> List[str]:"," \"\"\"Convert a list of numbers to latex formatted terms",""," The first non-zero term is treated differently. For this term a leading + is suppressed.",""," Args:"," numbers: List of numbers to format"," decimals: Number of decimal places to round to (default: 10)."," Returns:"," List of formatted terms"," \"\"\""," first_term = True"," terms = []"," for number in numbers:"," term = _num_to_latex(number, decimals=decimals, first_term=first_term, coefficient=True)"," terms.append(term)"," first_term = False"," return terms","","","def _state_to_latex_ket("," data: List[complex], max_size: int = 12, prefix: str = \"\", decimals: int = 10",") -> str:"," \"\"\"Convert state vector to latex representation",""," Args:"," data: State vector"," max_size: Maximum number of non-zero terms in the expression. If the number of"," non-zero terms is larger than the max_size, then the representation is truncated."," prefix: Latex string to be prepended to the latex, intended for labels."," decimals: Number of decimal places to round to (default: 10).",""," Returns:"," String with LaTeX representation of the state vector"," \"\"\""," num = int(np.log2(len(data)))",""," def ket_name(i):"," return bin(i)[2:].zfill(num)",""," data = np.around(data, decimals)"," nonzero_indices = np.where(data != 0)[0].tolist()"," if len(nonzero_indices) > max_size:"," nonzero_indices = ("," nonzero_indices[: max_size // 2] + [0] + nonzero_indices[-max_size // 2 + 1 :]"," )"," latex_terms = _numbers_to_latex_terms(data[nonzero_indices], decimals)"," nonzero_indices[max_size // 2] = None"," else:"," latex_terms = _numbers_to_latex_terms(data[nonzero_indices], decimals)",""," latex_str = \"\""," for idx, ket_idx in enumerate(nonzero_indices):"," if ket_idx is None:"," latex_str += r\" + \\ldots \""," else:"," term = latex_terms[idx]"," ket = ket_name(ket_idx)"," latex_str += f\"{term} |{ket}\\\\rangle\""," return prefix + latex_str","","","class TextMatrix:"," \"\"\"Text representation of an array, with `__str__` method so it"," displays nicely in Jupyter notebooks\"\"\"",""," def __init__(self, state, max_size=8, dims=None, prefix=\"\", suffix=\"\"):"," self.state = state"," self.max_size = max_size"," if dims is None: # show dims if state is not only qubits"," if (isinstance(state, (Statevector, DensityMatrix)) and set(state.dims()) == {2}) or ("," isinstance(state, Operator)"," and len(state.input_dims()) == len(state.output_dims())"," and set(state.input_dims()) == set(state.output_dims()) == {2}"," ):"," dims = False"," else:"," dims = True"," self.dims = dims"," self.prefix = prefix"," self.suffix = suffix"," if isinstance(max_size, int):"," self.max_size = max_size"," elif isinstance(state, DensityMatrix):"," # density matrices are square, so threshold for"," # summarization is shortest side squared"," self.max_size = min(max_size) ** 2"," else:"," self.max_size = max_size[0]",""," def __str__(self):"," threshold = self.max_size"," data = np.array2string("," self.state._data, prefix=self.prefix, threshold=threshold, separator=\",\""," )"," dimstr = \"\""," if self.dims:"," data += \",\\n\""," dimstr += \" \" * len(self.prefix)"," if isinstance(self.state, (Statevector, DensityMatrix)):"," dimstr += f\"dims={self.state._op_shape.dims_l()}\""," else:"," dimstr += f\"input_dims={self.state.input_dims()}, \""," dimstr += f\"output_dims={self.state.output_dims()}\"",""," return self.prefix + data + dimstr + self.suffix",""," def __repr__(self):"," return self.__str__()","","","def state_drawer(state, output=None, **drawer_args):"," \"\"\"Returns a visualization of the state.",""," **repr**: ASCII TextMatrix of the state's ``_repr_``.",""," **text**: ASCII TextMatrix that can be printed in the console.",""," **latex**: An IPython Latex object for displaying in Jupyter Notebooks.",""," **latex_source**: Raw, uncompiled ASCII source to generate array using LaTeX.",""," **qsphere**: Matplotlib figure, rendering of statevector using `plot_state_qsphere()`.",""," **hinton**: Matplotlib figure, rendering of statevector using `plot_state_hinton()`.",""," **bloch**: Matplotlib figure, rendering of statevector using `plot_bloch_multivector()`.",""," **city**: Matplotlib figure, rendering of statevector using `plot_state_city()`.",""," **paulivec**: Matplotlib figure, rendering of statevector using `plot_state_paulivec()`.",""," Args:"," output (str): Select the output method to use for drawing the"," circuit. Valid choices are ``text``, ``latex``, ``latex_source``,"," ``qsphere``, ``hinton``, ``bloch``, ``city`` or ``paulivec``."," Default is `'text`'."," drawer_args: Arguments to be passed to the relevant drawer. For"," 'latex' and 'latex_source' see ``array_to_latex``",""," Returns:"," :class:`matplotlib.figure` or :class:`str` or"," :class:`TextMatrix` or :class:`IPython.display.Latex`:"," Drawing of the state.",""," Raises:"," MissingOptionalLibraryError: when `output` is `latex` and IPython is not installed."," ValueError: when `output` is not a valid selection."," \"\"\""," config = user_config.get_config()"," # Get default 'output' from config file else use 'repr'"," default_output = \"repr\""," if output is None:"," if config:"," default_output = config.get(\"state_drawer\", \"repr\")"," output = default_output"," output = output.lower()",""," # Choose drawing backend:"," drawers = {"," \"text\": TextMatrix,"," \"latex_source\": state_to_latex,"," \"qsphere\": plot_state_qsphere,"," \"hinton\": plot_state_hinton,"," \"bloch\": plot_bloch_multivector,"," \"city\": plot_state_city,"," \"paulivec\": plot_state_paulivec,"," }"," if output == \"latex\":"," _optionals.HAS_IPYTHON.require_now(\"state_drawer\")"," from IPython.display import Latex",""," draw_func = drawers[\"latex_source\"]"," return Latex(f\"$${draw_func(state, **drawer_args)}$$\")",""," if output == \"repr\":"," return state.__repr__()",""," try:"," draw_func = drawers[output]"," return draw_func(state, **drawer_args)"," except KeyError as err:"," raise ValueError("," \"\"\"'{}' is not a valid option for drawing {} objects. Please choose from:"," 'text', 'latex', 'latex_source', 'qsphere', 'hinton',"," 'bloch', 'city' or 'paulivec'.\"\"\".format("," output, type(state).__name__"," )"," ) from err","","","def _bloch_multivector_data(state):"," \"\"\"Return list of Bloch vectors for each qubit",""," Args:"," state (DensityMatrix or Statevector): an N-qubit state.",""," Returns:"," list: list of Bloch vectors (x, y, z) for each qubit.",""," Raises:"," VisualizationError: if input is not an N-qubit state."," \"\"\""," rho = DensityMatrix(state)"," num = rho.num_qubits"," if num is None:"," raise VisualizationError(\"Input is not a multi-qubit quantum state.\")"," pauli_singles = PauliList([\"X\", \"Y\", \"Z\"])"," bloch_data = []"," for i in range(num):"," if num > 1:"," paulis = PauliList.from_symplectic("," np.zeros((3, (num - 1)), dtype=bool), np.zeros((3, (num - 1)), dtype=bool)"," ).insert(i, pauli_singles, qubit=True)"," else:"," paulis = pauli_singles"," bloch_state = [np.real(np.trace(np.dot(mat, 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