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

# # Tutorial

# In[1]:


# NBVAL_IGNORE_OUTPUT
get_ipython().run_line_magic('load_ext', 'watermark')
import numpy as np
import qutip
import matplotlib
import matplotlib.pylab as plt
import weylchamber
from weylchamber.visualize import WeylChamber
get_ipython().run_line_magic('watermark', '-v --iversions')


# $\newcommand{Re}[0]{\operatorname{Re}}
# \newcommand{Im}[0]{\operatorname{Im}}
# \newcommand{dd}[0]{\,\text{d}}
# \newcommand{abs}[0]{\operatorname{abs}}$

# Every two-qubit gate is associated with a point in the "Weyl-chamber" that may be visualized in three dimensions as the following polyhedron:

# In[2]:


WeylChamber().plot()


# Note: if you run this interactively, and switch to an interactive matplotlib backend, e.g.
# 
#     %matplotlib tk
#     
# you will be able to rotate the 3D plot to get a better intuition.

# Consider the following common two-qubit gates:

# In[3]:


IDENTITY = qutip.gates.identity([2,2])
IDENTITY


# In[4]:


CNOT = qutip.gates.cnot()
CNOT


# In[5]:


CPHASE = qutip.gates.cphase(np.pi)
CPHASE


# In[6]:


BGATE = qutip.gates.berkeley()
BGATE


# In[7]:


iSWAP = qutip.gates.iswap()
iSWAP


# In[8]:


sqrtISWAP = qutip.gates.sqrtiswap()
sqrtISWAP


# In[9]:


sqrtSWAP = qutip.gates.sqrtswap()
sqrtSWAP


# In[10]:


MGATE = weylchamber.canonical_gate(3/4, 1/4, 0)
MGATE


# All of these gates are situatated at special points in the Weyl chamber. We can print their Weyl chamber coordinates and add a point in the graphical representation

# In[11]:


w = WeylChamber();
list_of_gates = [
    ('Identity', IDENTITY),
    ('CNOT', CNOT), ('CPHASE', CPHASE), ('BGATE', BGATE),
    ('iSWAP', iSWAP), ('sqrtISWAP', sqrtISWAP),
    ('sqrtSWAP', sqrtSWAP), ('MGATE', MGATE)]
print("Weyl Chamber Coordinates")
print("----------------------------------")
for (name, gate) in list_of_gates:
    c1, c2, c3 = weylchamber.c1c2c3(gate)
    print("%10s: \t%.2fπ %.2fπ %.2fπ" % (name, c1, c2, c3))
    w.add_point(c1, c2, c3)
w.plot()


# The gates locally equivalent to the controlled-phase gates are on an the axis 0 - A1 in the Weyl chamber:

# In[12]:


w.scatter(*zip(*[
    weylchamber.c1c2c3(qutip.gates.cphase(phase))
    for phase in np.linspace(0, 2*np.pi, 20)]))


# In[13]:


w.plot()


# The Weyl chamber coordinates $(c_1, c_2, c_3)$ are closely associated with the *local invariants* $(g_1, g_2, g_3)$

# In[14]:


print("Local Invariants")
print("----------------------------------")
for (name, gate) in list_of_gates:
    g1, g2, g3 = weylchamber.g1g2g3(gate)
    print("%10s: \t%5.2f %5.2f %5.2f" % (name, g1, g2, g3))


# This shows that the MGATE and $\sqrt{\text{iSWAP}}$ are actually locally equivalent, despite being different Weyl chamber coordinates (M and Q, respectively)