Plotting of an example Porter-Thomas distribution

plot_pt.py

n_qubits = 4
porter_thomas = quantum_sample_probability(n_qubits, 10_000)

# theoretical Porter-Thomas distribution
dim = 2**n_qubits
xspace = np.linspace(0.0, 1.0, 100)
yspace = dim * np.exp(-dim*xspace)

# plot both empirical and theoretical calculations
plt.figure(figsize=(9, 6))
plt.hist(porter_thomas, bins=50, density=True, label='Empirical Distribution')
plt.plot(xspace, yspace, label='Theoretical Porter-Thomas Distribution')
# plot the uniform distribution for reference
plt.axvline(x=1/dim, linestyle='dotted', color='r', label='Uniform Distribution')

plt.xlabel("Probability p")
plt.ylabel("Probability that the random bistring occurs with probability p")
plt.legend(loc='best')
plt.show()