python实现对布洛赫球(Bloch Sphere)动画可视化的方法

布洛赫球可以表示任意一个量子力学中的二能级系统，任何一个二能级量子态都能在布洛赫球上找到对应的点。

静态可视化布洛赫球：

当我们只需要在布洛赫球上绘制一个静态的量子态或者一个测量基矢时，只需要import qutip即可：参见Plotting on the Bloch Sphere — QuTiP 4.6 Documentation。

需要注意的是，qutip提供3d布洛赫球和2d布洛赫球的选项，2d布洛赫球使用matplotlib库画三维图，图上的箭头和遮挡关系都不正确。

而3d布洛赫球使用mayavi库进行绘图，除了3d的箭头，正确的遮挡关系，甚至可以选择透视关系。但是mayavi库的安装真是一言难尽。。。，具体可以参见(6条消息) python3.7-3.9安装mayavi教程_Dodo·D·Caster的博客-优快云博客_python安装mayavi

动态可视化布洛赫球：

如果要在布洛赫球上绘制3d动画，qutip就不支持了，但是mayavi是支持3d动画的，可以修改一下qutip的源代码中的bloch3d，让它可以支持3d动画：

__all__ = ['new_Bloch3d']

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


class new_Bloch3d():
    """Class for plotting data on a 3D Bloch sphere using mayavi.
    Valid data can be either points, vectors, or qobj objects
    corresponding to state vectors or density matrices. for
    a two-state system (or subsystem).

    Attributes
    ----------
    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_scale : float {0.08}
        Scale for font used for Bloch sphere labels.
    frame : bool {True}
        Draw frame for Bloch sphere
    frame_alpha : float {0.05}
        Sets transparency of Bloch sphere frame.
    frame_color : str {'gray'}
        Color of sphere wireframe.
    frame_num : int {8}
        Number of frame elements to draw.
    frame_radius : floats {0.005}
        Width of wireframe.
    point_color : list {['r', 'g', 'b', 'y']}
        List of colors for Bloch sphere point markers to cycle through.
        i.e. By default, points 0 and 4 will both be blue ('r').
    point_mode : string {'sphere','cone','cube','cylinder','point'}
        Point marker shapes.
    point_size : float {0.075}
        Size of points on Bloch sphere.
    sphere_alpha : float {0.1}
        Transparency of Bloch sphere itself.
    sphere_color : str {'#808080'}
        Color of Bloch sphere.
    size : list {[500,500]}
        Size of Bloch sphere plot in pixels. Best to have both numbers the same
        otherwise you will have a Bloch sphere that looks like a football.
    vector_color : list {['r', 'g', 'b', 'y']}
        List of vector colors to cycle through.
    vector_width : int {3}
        Width of displayed vectors.
    view : list {[45,65]}
        Azimuthal and Elevation viewing angles.
    xlabel : list {['|x>', '']}
        List of strings corresponding to +x and -x axes labels, respectively.
    xlpos : list {[1.07,-1.07]}
        Positions of +x and -x labels respectively.
    ylabel : list {['|y>', '']}
        List of strings corresponding to +y and -y axes labels, respectively.
    ylpos : list {[1.07,-1.07]}
        Positions of +y and -y labels respectively.
    zlabel : list {['|0>', '|1>']}
        List of strings corresponding to +z and -z axes labels, respectively.
    zlpos : list {[1.07,-1.07]}
        Positions of +z and -z labels respectively.

    Notes
    -----
    The use of mayavi for 3D rendering of the Bloch sphere comes with
    a few limitations: I) You can not embed a Bloch3d figure into a
    matplotlib window. II) The use of LaTex is not supported by the
    mayavi rendering engine. Therefore all labels must be defined using
    standard text. Of course you can post-process the generated figures
    later to add LaTeX using other software if needed.


    """
    def __init__(self, fig):
        # ----check for mayavi-----
        try:
            from mayavi import mlab
        except:
            raise Exception("This function requires the mayavi module.")

        # ---Image options---
        self.fig = None
        self.user_fig = None
        # check if user specified figure or axes.
        if fig:
            self.user_fig = fig
        # The size of the figure in inches, default = [500,500].
        self.size = [500, 500]
        # Azimuthal and Elvation viewing angles, default = [45,65].
        self.view = [45, 65]
        # Image background color
        self.bgcolor = 'white'
        # Image foreground color. Other options can override.
        self.fgcolor = 'black'

        # ---Sphere options---
        # Color of Bloch sphere, default = #808080
        self.sphere_color = '#808080'