%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np

from qutip import *

g = 1.0 * 2 * pi # coupling strength
g1 = 0.75        # relaxation rate
g2 = 0.25        # dephasing rate
n_th = 1.5       # bath temperature

T = pi/(4*g)

H = g * (tensor(sigmax(), sigmax()) + tensor(sigmay(), sigmay()))
psi0 = tensor(basis(2,1), basis(2,0))

c_ops = []

# qubit 1 collapse operators
sm1 = tensor(sigmam(), qeye(2))
sz1 = tensor(sigmaz(), qeye(2))
c_ops.append(sqrt(g1 * (1+n_th)) * sm1)
c_ops.append(sqrt(g1 * n_th) * sm1.dag())
c_ops.append(sqrt(g2) * sz1)

# qubit 2 collapse operators
sm2 = tensor(qeye(2), sigmam())
sz2 = tensor(qeye(2), sigmaz())
c_ops.append(sqrt(g1 * (1+n_th)) * sm2)
c_ops.append(sqrt(g1 * n_th) * sm2.dag())
c_ops.append(sqrt(g2) * sz2)

op_basis = [[qeye(2), sigmax(), sigmay(), sigmaz()]] * 2
op_label = [["i", "x", "y", "z"]] * 2

# calculate the propagator for the ideal gate
U_psi = (-1j * H * T).expm()

# propagator in superoperator form
U_ideal = spre(U_psi) * spost(U_psi.dag())

# calculate the process tomography chi matrix from the superoperator propagator
chi = qpt(U_ideal, op_basis)

fig = plt.figure(figsize=(8,6))
fig = qpt_plot_combined(chi, op_label, fig=fig)

# dissipative gate propagator
U_diss = propagator(H, T, c_ops)

# calculate the process tomography chi matrix for the dissipative propagator
chi = qpt(U_diss, op_basis)

fig = plt.figure(figsize=(8,6))
fig = qpt_plot_combined(chi, op_label, fig=fig)

from qutip.ipynbtools import version_table

version_table()