Python 量子運算（七）：球面上的量子位元

Python 量子運算（七）：球面上的量子位元

2022/11/25

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Fig. 7.1. Qubit Psi on the Bloch sphere.

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代碼 7.1

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# Program 7.1：Quantum bit Psi import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt from qiskit.visualization import plot_bloch_vector # figure setting mpl.rcParams['text.usetex'] = True mpl.rcParams['text.latex.preamble'] = r'\usepackage{{amsmath}}' mpl.rcParams['font.size'] = 80 fig = plt.figure(figsize=(16, 16)) ax1 = fig.add_subplot(111, projection='3d') # 3d subplot # vector Psi setting radius = 1 theta_max = np.pi / 6 # angle between Psi and z axis phi_max = np.pi / 3 # angle between Psi and x axis Psi_z = radius * np.cos(theta_max) Psi_xy = radius * np.sin(theta_max) Psi_x = Psi_xy * np.cos(phi_max) Psi_y = Psi_xy * np.sin(phi_max) # draw the Bloch sphere and vector Psi plot_bloch_vector([Psi_x, Psi_y, Psi_z], ax=ax1) # ax1.scatter(Psi_y, -Psi_x, 0) # projection(Psi) on xy plane # lables(standard) ax1.text(0, -1.8, 0, r"$x$") ax1.text(1.4, 0, 0, r"$y$") ax1.text(0, 0, 1.4, r"$z$") ax1.text(-0.4, 0, 1.2, r"$\vert0\rangle$") ax1.text(0, 0, -1.8, r"$\vert1\rangle$") # lables(Psi) ax1.text(0.35, 0, 0.8, r"$\vert\Psi\rangle$") ax1.text(0.05, 0, 0.4, r"$\theta$") ax1.text(-0.1, 0, -0.45, r"$\phi$") # projection lines(Psi): vertical and horozantal ax1.plot([Psi_y, Psi_y], [-Psi_x, -Psi_x], zs=[0, Psi_z]) # vertical ax1.plot([0, Psi_y], [0, -Psi_x], zs=[0, 0]) # horizontal # curves: theta and phi phi_offset = -np.pi / 2 # xy coordinate rotation from matplotlib to qiskit curve_radius = 0.3 n = 20 c1 = np.linspace(0, theta_max, n) x1 = curve_radius * np.sin(c1) * np.cos(phi_max+phi_offset) y1 = curve_radius * np.sin(c1) * np.sin(phi_max+phi_offset) z1 = curve_radius * np.cos(c1) ax1.plot(x1, y1, z1, 'g', lw=2) # curve theta c2 = np.linspace(phi_offset, phi_max+phi_offset, n) x2 = curve_radius * np.cos(c2) y2 = curve_radius * np.sin(c2) z2 = c2 * 0 ax1.plot(x2, y2, z2, 'r', lw=2) # curve phi # plt.savefig('/content/drive/My Drive/pqc/0007_001.png')

解說：

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References

# Bloch sphere

[1] Bloch sphere - Wikipedia

https://en.wikipedia.org/wiki/Bloch_sphere

# 3d line

[2] python - How can I make a simple 3D line with Matplotlib? - Stack Overflow

https://stackoverflow.com/questions/11541123/how-can-i-make-a-simple-3d-line-with-matplotlib

# 3d curve

[3] Depicting a helix

https://scipython.com/book/chapter-7-matplotlib/examples/depicting-a-helix/

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Python 量子運算（目錄）

https://mandhistory.blogspot.com/2022/01/quantum-computing.html

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