#!/usr/bin/env python
# coding: utf-8

# # Lecture 7 - Two-qubit iSWAP gate and process tomography
# 
# Author: J. R. Johansson (robert@riken.jp), https://jrjohansson.github.io/
# 
# This lecture series was developed by J.R. Johannson. The original lecture notebooks are available [here](https://github.com/jrjohansson/qutip-lectures).
# 
# This is a slightly modified version of the lectures, to work with the current release of QuTiP. You can find these lectures as a part of the [qutip-tutorials repository](https://github.com/qutip/qutip-tutorials). This lecture and other tutorial notebooks are indexed at the [QuTiP Tutorial webpage](https://qutip.org/tutorials.html).

# In[1]:


import matplotlib.pyplot as plt
import numpy as np
from qutip import (about, basis, propagator, qeye, qpt, qpt_plot_combined,
                   sigmam, sigmax, sigmay, sigmaz, spost, spre, tensor)

get_ipython().run_line_magic('matplotlib', 'inline')


# ### Introduction
# 
# Let's consider a simple protocol for implementing the two-qubit iSWAP gate: During a time $T=\pi/4g$, the qubits are subject to the coupling Hamiltonian 
# 
# $\displaystyle H = g \left(\sigma_x\otimes\sigma_x + \sigma_y\otimes\sigma_y\right)$
# 
# where $g$ is the coupling strength. Under ideal conditions this coupling realizes the $i$-SWAP gate between the two qubit states. 
# 
# Here we will solve for the dynamics of the two qubits subject to this Hamiltonian, and look at the deterioating effects of adding decoherence. We will use process tomography to visualize the gate.

# ### Parameters

# In[2]:


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

T = np.pi / (4 * g)


# ### Hamiltonian and initial state

# In[3]:


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


# ### Collapse operators
# 
# Define a list of collapse operators that describe the coupling of the qubits to their environment (assumed to be uncorrelated)

# In[4]:


c_ops = []

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

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


# ### Process tomography basis

# In[5]:


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


# ### Ideal evolution (nondissipative, perfect timing, etc)

# In[6]:


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


# In[7]:


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


# In[8]:


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


# In[9]:


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


# ### Dissipative evolution

# In[10]:


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


# In[11]:


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


# In[12]:


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


# ### Software versions:

# In[13]:


about()