extract_theta_phi.py

from qutip import *
import numpy as np

# Consider image relative to |+> in cos(\theta) |+> + e^(i\phi) |-> representation.
def extract_theta_phi(single_qubit_gate, b=snot() * basis(2,0)):
    # apply gate to |+>
    ket = single_qubit_gate * b

    alpha = ket.full()[0][0]
    beta = ket.full()[1][0]
    # rewrite in x-basis
    ket_raw = [(alpha + beta) / 2, (alpha - beta) / 2]
    ket_raw = ket_raw / np.linalg.norm(ket_raw)

    theta = 0
    phi = 0

    if ket_raw[0] * ket_raw[0].conj() < 1e-6:
        theta = np.pi
        phi = 0
    elif ket_raw[1] * ket_raw[1].conj() < 1e-6:
        theta = 0
        phi = 0
    else:
        theta = 2 * np.arccos(np.sqrt(ket_raw[0] * ket_raw[0].conj()))
        phi = (np.angle(ket_raw[0].conj() * ket_raw[1]
               / (np.sqrt(ket_raw[0] * ket_raw[0].conj())
               * np.sqrt(ket_raw[1] * ket_raw[1].conj()))))

    return theta, phi