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Source code for qiskit.visualization.state_visualization

# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2018.
#
# 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,ungrouped-imports,import-error
# pylint: disable=inconsistent-return-statements,unsubscriptable-object
# pylint: disable=missing-param-doc,missing-type-doc,unused-argument

"""
Visualization functions for quantum states.
"""

from functools import reduce
import colorsys
import numpy as np
from scipy import linalg
from qiskit.quantum_info.states import DensityMatrix
from qiskit.util import deprecate_arguments
from .matplotlib import HAS_MATPLOTLIB

if HAS_MATPLOTLIB:
    from matplotlib import get_backend
    from matplotlib import pyplot as plt
    from matplotlib.patches import FancyArrowPatch
    from matplotlib.patches import Circle
    import matplotlib.colors as mcolors
    from matplotlib.colors import Normalize, LightSource
    import matplotlib.gridspec as gridspec
    from mpl_toolkits.mplot3d import proj3d
    from mpl_toolkits.mplot3d.art3d import Poly3DCollection
    from qiskit.visualization.exceptions import VisualizationError
    from qiskit.visualization.bloch import Bloch
    from qiskit.visualization.utils import _bloch_multivector_data, _paulivec_data
    from qiskit.circuit.tools.pi_check import pi_check


if HAS_MATPLOTLIB:
    class Arrow3D(FancyArrowPatch):
        """Standard 3D arrow."""

        def __init__(self, xs, ys, zs, *args, **kwargs):
            """Create arrow."""
            FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs)
            self._verts3d = xs, ys, zs

        def draw(self, renderer):
            """Draw the arrow."""
            xs3d, ys3d, zs3d = self._verts3d
            xs, ys, _ = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
            self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
            FancyArrowPatch.draw(self, renderer)


[docs]@deprecate_arguments({'rho': 'state'}) def plot_state_hinton(state, title='', figsize=None, ax_real=None, ax_imag=None, *, rho=None): """Plot a hinton diagram for the density matrix of a quantum state. 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. 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. VisualizationError: if input is not a valid N-qubit state. Example: .. jupyter-execute:: from qiskit import QuantumCircuit from qiskit.quantum_info import DensityMatrix from qiskit.visualization import plot_state_hinton %matplotlib inline qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) state = DensityMatrix.from_instruction(qc) plot_state_hinton(state, title="New Hinton Plot") """ if not HAS_MATPLOTLIB: raise ImportError('Must have Matplotlib installed. To install, run ' '"pip install matplotlib".') # 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 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 # 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)) row_names.append('') ax1.set_yticklabels(row_names, fontsize=14) column_names.append('') 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
[docs]def plot_bloch_vector(bloch, title="", ax=None, figsize=None, coord_type="cartesian"): """Plot the Bloch sphere. Plot a sphere, axes, the Bloch vector, and its projections onto each axis. Args: bloch (list[double]): array of three elements where [<x>, <y>, <z>] (cartesian) or [<r>, <theta>, <phi>] (spherical in radians) <theta> is inclination angle from +z direction <phi> 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 Returns: Figure: A matplotlib figure instance if ``ax = None``. Raises: ImportError: Requires matplotlib. Example: .. jupyter-execute:: from qiskit.visualization import plot_bloch_vector %matplotlib inline plot_bloch_vector([0,1,0], title="New Bloch Sphere") """ if not HAS_MATPLOTLIB: raise ImportError('Must have Matplotlib installed. To install, run ' '"pip install matplotlib".') if figsize is None: figsize = (5, 5) B = Bloch(axes=ax) 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]) if get_backend() in ['module://ipykernel.pylab.backend_inline', 'nbAgg']: plt.close(fig) return fig return None
[docs]@deprecate_arguments({'rho': 'state'}) def plot_bloch_multivector(state, title='', figsize=None, *, rho=None): """Plot the Bloch sphere. Plot a sphere, axes, the Bloch vector, and its projections onto each axis. Args: state (Statevector or DensityMatrix or ndarray): an N-qubit quantum state. title (str): a string that represents the plot title figsize (tuple): Has no effect, here for compatibility only. Returns: matplotlib.Figure: A matplotlib figure instance. Raises: ImportError: Requires matplotlib. VisualizationError: if input is not a valid N-qubit state. Example: .. jupyter-execute:: from qiskit import QuantumCircuit from qiskit.quantum_info import Statevector from qiskit.visualization import plot_bloch_multivector %matplotlib inline qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) state = Statevector.from_instruction(qc) plot_bloch_multivector(state, title="New Bloch Multivector") """ if not HAS_MATPLOTLIB: raise ImportError('Must have Matplotlib installed. To install, run "pip install ' 'matplotlib".') # Data bloch_data = _bloch_multivector_data(state) num = len(bloch_data) width, height = plt.figaspect(1/num) fig = plt.figure(figsize=(width, height)) for i in range(num): ax = fig.add_subplot(1, num, i + 1, projection='3d') plot_bloch_vector(bloch_data[i], "qubit " + str(i), ax=ax, figsize=figsize) fig.suptitle(title, fontsize=16) if get_backend() in ['module://ipykernel.pylab.backend_inline', 'nbAgg']: plt.close(fig) return fig
[docs]@deprecate_arguments({'rho': 'state'}) def plot_state_city(state, title="", figsize=None, color=None, alpha=1, ax_real=None, ax_imag=None, *, rho=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_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. VisualizationError: if input is not a valid N-qubit state. Example: .. jupyter-execute:: from qiskit import QuantumCircuit from qiskit.quantum_info import DensityMatrix from qiskit.visualization import plot_state_city %matplotlib inline qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) state = DensityMatrix.from_instruction(qc) plot_state_city(state, color=['midnightblue', 'midnightblue'], title="New State City") """ if not HAS_MATPLOTLIB: raise ImportError('Must have Matplotlib installed. To install, run "pip install ' 'matplotlib".') 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)] 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
[docs]@deprecate_arguments({'rho': 'state'}) def plot_state_paulivec(state, title="", figsize=None, color=None, ax=None, *, rho=None): """Plot the paulivec representation of a quantum state. Plot a bargraph of the mixed state rho over the pauli matrices 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 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. VisualizationError: if input is not a valid N-qubit state. Example: .. jupyter-execute:: from qiskit import QuantumCircuit from qiskit.quantum_info import Statevector from qiskit.visualization import plot_state_paulivec %matplotlib inline qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) state = Statevector.from_instruction(qc) plot_state_paulivec(state, color='midnightblue', title="New PauliVec plot") """ if not HAS_MATPLOTLIB: raise ImportError('Must have Matplotlib installed. To install, run "pip install ' 'matplotlib".') 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('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 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 = list(map(lambda x: n - 1 - x, 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 * 4)) % (np.pi * 2) rgb = colorsys.hls_to_rgb(angles / (np.pi * 2), 0.5, 0.5) return rgb
[docs]@deprecate_arguments({'rho': 'state'}) def plot_state_qsphere(state, figsize=None, ax=None, show_state_labels=True, show_state_phases=False, use_degrees=False, *, rho=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: Figure: A matplotlib figure instance if the ``ax`` kwag is not set Raises: ImportError: Requires matplotlib. VisualizationError: if input is not a valid N-qubit state. QiskitError: Input statevector does not have valid dimensions. Example: .. jupyter-execute:: from qiskit import QuantumCircuit from qiskit.quantum_info import Statevector from qiskit.visualization import plot_state_qsphere %matplotlib inline qc = QuantumCircuit(2) qc.h(0) qc.cx(0, 1) state = Statevector.from_instruction(qc) plot_state_qsphere(state) """ 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".') 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.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 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())) if prob > 1: # See https://github.com/Qiskit/qiskit-terra/issues/4666 prob = 1 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=(.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=plt.rcParams['figure.facecolor'], 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 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. """ 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*. """ 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

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