State Visualization

State visualization displays quantum states and operators for understanding and debugging. QuTiP provides plotting functions for populations, densities, Wigner functions, and more.

Plot populations (diagonal elements of density matrix):

from qutip import *
import matplotlib.pyplot as plt
 
# Time evolution of a damped qubit
H = 0.5 * sigmaz()
c_ops = [0.1 * sigmam()]
times = np.linspace(0, 10, 100)
psi0 = basis(2, 1)
 
result = mesolve(H, psi0, times, c_ops, [sigmaz()])
 
# Plot expectation values
fig, ax = plt.subplots()
ax.plot(times, result.expect[0], 'b-', label='<σ_z>')
ax.set_xlabel('Time')
ax.set_ylabel('Expectation Value')
ax.legend()
plt.show()

Visualize density matrix elements:

rho = mesolve(H, psi0, [0, 5], c_ops, []).states[-1]
 
# Heatmap of |ρ_ij|
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))
ax1.imshow(np.abs(rho.full()))
ax1.set_title('|ρ|')
ax2.imshow(np.angle(rho.full()))
ax2.set_title('arg(ρ)')
plt.show()

For harmonic oscillators, the Wigner function is a quasi-probability on phase space:

# Coherent state
N = 20  # Hilbert space dimension
alpha = 2.0
psi = coherent(N, alpha)
 
# Wigner function
xvec = np.linspace(-4, 4, 200)
W = wigner(psi, xvec, xvec)
 
fig, ax = plt.subplots()
contourf = ax.contourf(xvec, xvec, W, levels=20)
ax.set_xlabel('Re(α)')
ax.set_ylabel('Im(α)')
plt.colorbar(contourf)
plt.show()

Visualization is essential for understanding quantum dynamics and debugging simulations.