Xtykutl

I'm trying to build something called bloch sphere. This represents a state of a quantum bits in the form of an arrow in a sphere, whose radius is 1.0.

I wrote the codes below.

from mpl_toolkits.mplot3d import Axes3D

import matplotlib.pyplot as plt

import numpy as np

from itertools import product, combinations



print("Put angle theta and phi, 0≤theta≤180, 0≤phi≤360")

theta = input("theta:")

phi = input("phi:")

theta = float(theta)

phi = float(phi)

X = np.sin(phi)

Y = np.sin(theta)

Z = np.cos(theta)



class quantum_gates:

def __init__(self,X,Y,Z):

    self.X = float(X)

    self.Y = float(Y)

    self.Z = float(Z)



    if theta <0 or theta >180 or phi < 0 or phi >360:

        print("Put the value of angles again")

    else:

        fig = plt.figure()

        ax = fig.gca(projection='3d')

        ax.set_aspect("equal")

        u, v = np.mgrid[0:2*np.pi:20j, 0:np.pi:10j]

        x = np.cos(u)*np.sin(v)

        y = np.sin(u)*np.sin(v)

        z = np.cos(v)

        ax.set_xlabel('y')

        ax.set_ylabel('x')

        ax.set_zlabel('z')

        ax.plot_wireframe(y, x, z, color="black")

        ax.quiver(0,0,0,Y,X,Z,color="red",length=1.0)

When I put (theta, phi) = (30,0), the tip of the arrow reaches the surface of the sphere. However, when I put (theta,phi) = (30,30), the tip of the arrow goes outside of the sphere.

You can see the image of the current situation from the link below.

I guess you perform transformation between coordinates in a wrong way. X, Y, and Z should be calculated as follows (wikipedia link):

X = np.sin(theta) * np.cos(phi)

Y = np.sin(theta) * np.sin(phi)

Z = np.cos(theta)

Also, numpy trigonometric functions accept values in radians. So, theta should be in the range [0, pi], phi should be in the range [0, 2 * pi). To convert degrees to radians you may use numpy.radians().