Source code for qutip.bloch

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__all__ = ['Bloch']

import os

from numpy import (ndarray, array, linspace, pi, outer, cos, sin, ones, size,
                   sqrt, real, mod, append, ceil, arange)

from qutip.qobj import Qobj
from qutip.expect import expect
from qutip.operators import sigmax, sigmay, sigmaz

try:
    import matplotlib.pyplot as plt
    from mpl_toolkits.mplot3d import Axes3D
    from matplotlib.patches import FancyArrowPatch
    from mpl_toolkits.mplot3d import proj3d

    class Arrow3D(FancyArrowPatch):
        def __init__(self, xs, ys, zs, *args, **kwargs):
            FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs)

            self._verts3d = xs, ys, zs

        def draw(self, renderer):
            xs3d, ys3d, zs3d = self._verts3d
            xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)

            self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
            FancyArrowPatch.draw(self, renderer)
except:
    pass

try:
    from IPython.display import display
except:
    pass


[docs]class Bloch(): """Class for plotting data on the Bloch sphere. Valid data can be either points, vectors, or qobj objects. Attributes ---------- axes : instance {None} User supplied Matplotlib axes for Bloch sphere animation. fig : instance {None} User supplied Matplotlib Figure instance for plotting Bloch sphere. font_color : str {'black'} Color of font used for Bloch sphere labels. font_size : int {20} Size of font used for Bloch sphere labels. frame_alpha : float {0.1} Sets transparency of Bloch sphere frame. frame_color : str {'gray'} Color of sphere wireframe. frame_width : int {1} Width of wireframe. point_color : list {["b","r","g","#CC6600"]} List of colors for Bloch sphere point markers to cycle through. i.e. By default, points 0 and 4 will both be blue ('b'). point_marker : list {["o","s","d","^"]} List of point marker shapes to cycle through. point_size : list {[25,32,35,45]} List of point marker sizes. Note, not all point markers look the same size when plotted! sphere_alpha : float {0.2} Transparency of Bloch sphere itself. sphere_color : str {'#FFDDDD'} Color of Bloch sphere. figsize : list {[7,7]} Figure size of Bloch sphere plot. Best to have both numbers the same; otherwise you will have a Bloch sphere that looks like a football. vector_color : list {["g","#CC6600","b","r"]} List of vector colors to cycle through. vector_width : int {5} Width of displayed vectors. vector_style : str {'-|>', 'simple', 'fancy', ''} Vector arrowhead style (from matplotlib's arrow style). vector_mutation : int {20} Width of vectors arrowhead. view : list {[-60,30]} Azimuthal and Elevation viewing angles. xlabel : list {["$x$",""]} List of strings corresponding to +x and -x axes labels, respectively. xlpos : list {[1.1,-1.1]} Positions of +x and -x labels respectively. ylabel : list {["$y$",""]} List of strings corresponding to +y and -y axes labels, respectively. ylpos : list {[1.2,-1.2]} Positions of +y and -y labels respectively. zlabel : list {[r'$\\left|0\\right>$',r'$\\left|1\\right>$']} List of strings corresponding to +z and -z axes labels, respectively. zlpos : list {[1.2,-1.2]} Positions of +z and -z labels respectively. """ def __init__(self, fig=None, axes=None, view=None, figsize=None, background=False): # Figure and axes self.fig = fig self.axes = axes # Background axes, default = False self.background = background # The size of the figure in inches, default = [5,5]. self.figsize = figsize if figsize else [5, 5] # Azimuthal and Elvation viewing angles, default = [-60,30]. self.view = view if view else [-60, 30] # Color of Bloch sphere, default = #FFDDDD self.sphere_color = '#FFDDDD' # Transparency of Bloch sphere, default = 0.2 self.sphere_alpha = 0.2 # Color of wireframe, default = 'gray' self.frame_color = 'gray' # Width of wireframe, default = 1 self.frame_width = 1 # Transparency of wireframe, default = 0.2 self.frame_alpha = 0.2 # Labels for x-axis (in LaTex), default = ['$x$', ''] self.xlabel = ['$x$', ''] # Position of x-axis labels, default = [1.2, -1.2] self.xlpos = [1.2, -1.2] # Labels for y-axis (in LaTex), default = ['$y$', ''] self.ylabel = ['$y$', ''] # Position of y-axis labels, default = [1.1, -1.1] self.ylpos = [1.2, -1.2] # Labels for z-axis (in LaTex), # default = [r'$\left|0\right>$', r'$\left|1\right>$'] self.zlabel = [r'$\left|0\right>$', r'$\left|1\right>$'] # Position of z-axis labels, default = [1.2, -1.2] self.zlpos = [1.2, -1.2] # ---font options--- # Color of fonts, default = 'black' self.font_color = 'black' # Size of fonts, default = 20 self.font_size = 20 # ---vector options--- # List of colors for Bloch vectors, default = ['b','g','r','y'] self.vector_color = ['g', '#CC6600', 'b', 'r'] #: Width of Bloch vectors, default = 5 self.vector_width = 3 #: Style of Bloch vectors, default = '-|>' (or 'simple') self.vector_style = '-|>' #: Sets the width of the vectors arrowhead self.vector_mutation = 20 # ---point options--- # List of colors for Bloch point markers, default = ['b','g','r','y'] self.point_color = ['b', 'r', 'g', '#CC6600'] # Size of point markers, default = 25 self.point_size = [25, 32, 35, 45] # Shape of point markers, default = ['o','^','d','s'] self.point_marker = ['o', 's', 'd', '^'] # ---data lists--- # Data for point markers self.points = [] # Data for Bloch vectors self.vectors = [] # Data for annotations self.annotations = [] # Number of times sphere has been saved self.savenum = 0 # Style of points, 'm' for multiple colors, 's' for single color self.point_style = [] # status of rendering self._rendered = False # status of showing if fig is None: self._shown = False else: self._shown = True
[docs] def set_label_convention(self, convention): """Set x, y and z labels according to one of conventions. Parameters ---------- convention : string One of the following: - "original" - "xyz" - "sx sy sz" - "01" - "polarization jones" - "polarization jones letters" see also: http://en.wikipedia.org/wiki/Jones_calculus - "polarization stokes" see also: http://en.wikipedia.org/wiki/Stokes_parameters """ ketex = "$\\left.|%s\\right\\rangle$" # \left.| is on purpose, so that every ket has the same size if convention == "original": self.xlabel = ['$x$', ''] self.ylabel = ['$y$', ''] self.zlabel = ['$\\left|0\\right>$', '$\\left|1\\right>$'] elif convention == "xyz": self.xlabel = ['$x$', ''] self.ylabel = ['$y$', ''] self.zlabel = ['$z$', ''] elif convention == "sx sy sz": self.xlabel = ['$s_x$', ''] self.ylabel = ['$s_y$', ''] self.zlabel = ['$s_z$', ''] elif convention == "01": self.xlabel = ['', ''] self.ylabel = ['', ''] self.zlabel = ['$\\left|0\\right>$', '$\\left|1\\right>$'] elif convention == "polarization jones": self.xlabel = [ketex % "\\nearrow\\hspace{-1.46}\\swarrow", ketex % "\\nwarrow\\hspace{-1.46}\\searrow"] self.ylabel = [ketex % "\\circlearrowleft", ketex % "\\circlearrowright"] self.zlabel = [ketex % "\\leftrightarrow", ketex % "\\updownarrow"] elif convention == "polarization jones letters": self.xlabel = [ketex % "D", ketex % "A"] self.ylabel = [ketex % "L", ketex % "R"] self.zlabel = [ketex % "H", ketex % "V"] elif convention == "polarization stokes": self.ylabel = ["$\\nearrow\\hspace{-1.46}\\swarrow$", "$\\nwarrow\\hspace{-1.46}\\searrow$"] self.zlabel = ["$\\circlearrowleft$", "$\\circlearrowright$"] self.xlabel = ["$\\leftrightarrow$", "$\\updownarrow$"] else: raise Exception("No such convention.")
def __str__(self): s = "" s += "Bloch data:\n" s += "-----------\n" s += "Number of points: " + str(len(self.points)) + "\n" s += "Number of vectors: " + str(len(self.vectors)) + "\n" s += "\n" s += "Bloch sphere properties:\n" s += "------------------------\n" s += "font_color: " + str(self.font_color) + "\n" s += "font_size: " + str(self.font_size) + "\n" s += "frame_alpha: " + str(self.frame_alpha) + "\n" s += "frame_color: " + str(self.frame_color) + "\n" s += "frame_width: " + str(self.frame_width) + "\n" s += "point_color: " + str(self.point_color) + "\n" s += "point_marker: " + str(self.point_marker) + "\n" s += "point_size: " + str(self.point_size) + "\n" s += "sphere_alpha: " + str(self.sphere_alpha) + "\n" s += "sphere_color: " + str(self.sphere_color) + "\n" s += "figsize: " + str(self.figsize) + "\n" s += "vector_color: " + str(self.vector_color) + "\n" s += "vector_width: " + str(self.vector_width) + "\n" s += "vector_style: " + str(self.vector_style) + "\n" s += "vector_mutation: " + str(self.vector_mutation) + "\n" s += "view: " + str(self.view) + "\n" s += "xlabel: " + str(self.xlabel) + "\n" s += "xlpos: " + str(self.xlpos) + "\n" s += "ylabel: " + str(self.ylabel) + "\n" s += "ylpos: " + str(self.ylpos) + "\n" s += "zlabel: " + str(self.zlabel) + "\n" s += "zlpos: " + str(self.zlpos) + "\n" return s def _repr_png_(self): from IPython.core.pylabtools import print_figure self.render() fig_data = print_figure(self.fig, 'png') plt.close(self.fig) return fig_data def _repr_svg_(self): from IPython.core.pylabtools import print_figure self.render() fig_data = print_figure(self.fig, 'svg').decode('utf-8') plt.close(self.fig) return fig_data
[docs] def clear(self): """Resets Bloch sphere data sets to empty. """ self.points = [] self.vectors = [] self.point_style = [] self.annotations = []
[docs] def add_points(self, points, meth='s'): """Add a list of data points to bloch sphere. Parameters ---------- points : array/list Collection of data points. meth : str {'s', 'm', 'l'} Type of points to plot, use 'm' for multicolored, 'l' for points connected with a line. """ if not isinstance(points[0], (list, ndarray)): points = [[points[0]], [points[1]], [points[2]]] points = array(points) if meth == 's': if len(points[0]) == 1: pnts = array([[points[0][0]], [points[1][0]], [points[2][0]]]) pnts = append(pnts, points, axis=1) else: pnts = points self.points.append(pnts) self.point_style.append('s') elif meth == 'l': self.points.append(points) self.point_style.append('l') else: self.points.append(points) self.point_style.append('m')
[docs] def add_states(self, state, kind='vector'): """Add a state vector Qobj to Bloch sphere. Parameters ---------- state : qobj Input state vector. kind : str {'vector','point'} Type of object to plot. """ if isinstance(state, Qobj): state = [state] for st in state: vec = [expect(sigmax(), st), expect(sigmay(), st), expect(sigmaz(), st)] if kind == 'vector': self.add_vectors(vec) elif kind == 'point': self.add_points(vec)
[docs] def add_vectors(self, vectors): """Add a list of vectors to Bloch sphere. Parameters ---------- vectors : array_like Array with vectors of unit length or smaller. """ if isinstance(vectors[0], (list, ndarray)): for vec in vectors: self.vectors.append(vec) else: self.vectors.append(vectors)
[docs] def add_annotation(self, state_or_vector, text, **kwargs): """Add a text or LaTeX annotation to Bloch sphere, parametrized by a qubit state or a vector. Parameters ---------- state_or_vector : Qobj/array/list/tuple Position for the annotaion. Qobj of a qubit or a vector of 3 elements. text : str/unicode Annotation text. You can use LaTeX, but remember to use raw string e.g. r"$\\langle x \\rangle$" or escape backslashes e.g. "$\\\\langle x \\\\rangle$". **kwargs : Options as for mplot3d.axes3d.text, including: fontsize, color, horizontalalignment, verticalalignment. """ if isinstance(state_or_vector, Qobj): vec = [expect(sigmax(), state_or_vector), expect(sigmay(), state_or_vector), expect(sigmaz(), state_or_vector)] elif isinstance(state_or_vector, (list, ndarray, tuple)) \ and len(state_or_vector) == 3: vec = state_or_vector else: raise Exception("Position needs to be specified by a qubit " + "state or a 3D vector.") self.annotations.append({'position': vec, 'text': text, 'opts': kwargs})
[docs] def make_sphere(self): """ Plots Bloch sphere and data sets. """ self.render(self.fig, self.axes)
def run_from_ipython(self): try: __IPYTHON__ return True except NameError: return False
[docs] def render(self, fig=None, axes=None): """ Render the Bloch sphere and its data sets in on given figure and axes. """ if self._rendered: self.axes.clear() self._rendered = True # Figure instance for Bloch sphere plot if not fig: self.fig = plt.figure(figsize=self.figsize) if not axes: self.axes = Axes3D(self.fig, azim=self.view[0], elev=self.view[1]) if self.background: self.axes.clear() self.axes.set_xlim3d(-1.3, 1.3) self.axes.set_ylim3d(-1.3, 1.3) self.axes.set_zlim3d(-1.3, 1.3) else: self.plot_axes() self.axes.set_axis_off() self.axes.set_xlim3d(-0.7, 0.7) self.axes.set_ylim3d(-0.7, 0.7) self.axes.set_zlim3d(-0.7, 0.7) self.axes.grid(False) self.plot_back() self.plot_points() self.plot_vectors() self.plot_front() self.plot_axes_labels() self.plot_annotations()
def plot_back(self): # back half of sphere u = linspace(0, pi, 25) v = linspace(0, pi, 25) x = outer(cos(u), sin(v)) y = outer(sin(u), sin(v)) z = outer(ones(size(u)), cos(v)) self.axes.plot_surface(x, y, z, rstride=2, cstride=2, color=self.sphere_color, linewidth=0, alpha=self.sphere_alpha) # wireframe self.axes.plot_wireframe(x, y, z, rstride=5, cstride=5, color=self.frame_color, alpha=self.frame_alpha) # equator self.axes.plot(1.0 * cos(u), 1.0 * sin(u), zs=0, zdir='z', lw=self.frame_width, color=self.frame_color) self.axes.plot(1.0 * cos(u), 1.0 * sin(u), zs=0, zdir='x', lw=self.frame_width, color=self.frame_color) def plot_front(self): # front half of sphere u = linspace(-pi, 0, 25) v = linspace(0, pi, 25) x = outer(cos(u), sin(v)) y = outer(sin(u), sin(v)) z = outer(ones(size(u)), cos(v)) self.axes.plot_surface(x, y, z, rstride=2, cstride=2, color=self.sphere_color, linewidth=0, alpha=self.sphere_alpha) # wireframe self.axes.plot_wireframe(x, y, z, rstride=5, cstride=5, color=self.frame_color, alpha=self.frame_alpha) # equator self.axes.plot(1.0 * cos(u), 1.0 * sin(u), zs=0, zdir='z', lw=self.frame_width, color=self.frame_color) self.axes.plot(1.0 * cos(u), 1.0 * sin(u), zs=0, zdir='x', lw=self.frame_width, color=self.frame_color) def plot_axes(self): # axes span = linspace(-1.0, 1.0, 2) self.axes.plot(span, 0 * span, zs=0, zdir='z', label='X', lw=self.frame_width, color=self.frame_color) self.axes.plot(0 * span, span, zs=0, zdir='z', label='Y', lw=self.frame_width, color=self.frame_color) self.axes.plot(0 * span, span, zs=0, zdir='y', label='Z', lw=self.frame_width, color=self.frame_color) def plot_axes_labels(self): # axes labels opts = {'fontsize': self.font_size, 'color': self.font_color, 'horizontalalignment': 'center', 'verticalalignment': 'center'} self.axes.text(0, -self.xlpos[0], 0, self.xlabel[0], **opts) self.axes.text(0, -self.xlpos[1], 0, self.xlabel[1], **opts) self.axes.text(self.ylpos[0], 0, 0, self.ylabel[0], **opts) self.axes.text(self.ylpos[1], 0, 0, self.ylabel[1], **opts) self.axes.text(0, 0, self.zlpos[0], self.zlabel[0], **opts) self.axes.text(0, 0, self.zlpos[1], self.zlabel[1], **opts) for a in (self.axes.w_xaxis.get_ticklines() + self.axes.w_xaxis.get_ticklabels()): a.set_visible(False) for a in (self.axes.w_yaxis.get_ticklines() + self.axes.w_yaxis.get_ticklabels()): a.set_visible(False) for a in (self.axes.w_zaxis.get_ticklines() + self.axes.w_zaxis.get_ticklabels()): a.set_visible(False) def plot_vectors(self): # -X and Y data are switched for plotting purposes for k in range(len(self.vectors)): xs3d = self.vectors[k][1] * array([0, 1]) ys3d = -self.vectors[k][0] * array([0, 1]) zs3d = self.vectors[k][2] * array([0, 1]) color = self.vector_color[mod(k, len(self.vector_color))] if self.vector_style == '': # simple line style self.axes.plot(xs3d, ys3d, zs3d, zs=0, zdir='z', label='Z', lw=self.vector_width, color=color) else: # decorated style, with arrow heads a = Arrow3D(xs3d, ys3d, zs3d, mutation_scale=self.vector_mutation, lw=self.vector_width, arrowstyle=self.vector_style, color=color) self.axes.add_artist(a) def plot_points(self): # -X and Y data are switched for plotting purposes for k in range(len(self.points)): num = len(self.points[k][0]) dist = [sqrt(self.points[k][0][j] ** 2 + self.points[k][1][j] ** 2 + self.points[k][2][j] ** 2) for j in range(num)] if any(abs(dist - dist[0]) / dist[0] > 1e-12): # combine arrays so that they can be sorted together zipped = list(zip(dist, range(num))) zipped.sort() # sort rates from lowest to highest dist, indperm = zip(*zipped) indperm = array(indperm) else: indperm = arange(num) if self.point_style[k] == 's': self.axes.scatter( real(self.points[k][1][indperm]), - real(self.points[k][0][indperm]), real(self.points[k][2][indperm]), s=self.point_size[mod(k, len(self.point_size))], alpha=1, edgecolor=None, zdir='z', color=self.point_color[mod(k, len(self.point_color))], marker=self.point_marker[mod(k, len(self.point_marker))]) elif self.point_style[k] == 'm': pnt_colors = array(self.point_color * int(ceil(num / float(len(self.point_color))))) pnt_colors = pnt_colors[0:num] pnt_colors = list(pnt_colors[indperm]) marker = self.point_marker[mod(k, len(self.point_marker))] s = self.point_size[mod(k, len(self.point_size))] self.axes.scatter(real(self.points[k][1][indperm]), -real(self.points[k][0][indperm]), real(self.points[k][2][indperm]), s=s, alpha=1, edgecolor=None, zdir='z', color=pnt_colors, marker=marker) elif self.point_style[k] == 'l': color = self.point_color[mod(k, len(self.point_color))] self.axes.plot(real(self.points[k][1]), -real(self.points[k][0]), real(self.points[k][2]), alpha=0.75, zdir='z', color=color) def plot_annotations(self): # -X and Y data are switched for plotting purposes for annotation in self.annotations: vec = annotation['position'] opts = {'fontsize': self.font_size, 'color': self.font_color, 'horizontalalignment': 'center', 'verticalalignment': 'center'} opts.update(annotation['opts']) self.axes.text(vec[1], -vec[0], vec[2], annotation['text'], **opts)
[docs] def show(self): """ Display Bloch sphere and corresponding data sets. """ self.render(self.fig, self.axes) if self.run_from_ipython(): if self._shown: display(self.fig) else: self.fig.show() self._shown = True
[docs] def save(self, name=None, format='png', dirc=None, dpin=None): """Saves Bloch sphere to file of type ``format`` in directory ``dirc``. Parameters ---------- name : str Name of saved image. Must include path and format as well. i.e. '/Users/Paul/Desktop/bloch.png' This overrides the 'format' and 'dirc' arguments. format : str Format of output image. dirc : str Directory for output images. Defaults to current working directory. dpin : int Resolution in dots per inch. Returns ------- File containing plot of Bloch sphere. """ self.render(self.fig, self.axes) # Conditional variable for first argument to savefig # that is set in subsequent if-elses complete_path = "" if dirc: if not os.path.isdir(os.getcwd() + "/" + str(dirc)): os.makedirs(os.getcwd() + "/" + str(dirc)) if name is None: if dirc: complete_path = os.getcwd() + "/" + str(dirc) + '/bloch_' \ + str(self.savenum) + '.' + format else: complete_path = os.getcwd() + '/bloch_' + \ str(self.savenum) + '.' + format else: complete_path = name if dpin: self.fig.savefig(complete_path, dpi=dpin) else: self.fig.savefig(complete_path) self.savenum += 1 if self.fig: plt.close(self.fig)
def _hide_tick_lines_and_labels(axis): ''' Set visible property of ticklines and ticklabels of an axis to False ''' for a in axis.get_ticklines() + axis.get_ticklabels(): a.set_visible(False)