In [1]:

    

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


    

In [2]:

    

from qutip import *
from qutip.control import *


    

In [3]:

    

T = 1
times = np.linspace(0, T, 100)


    

In [4]:

    

U = iswap()
R = 50
H_ops = [#tensor(sigmax(), identity(2)),
         #tensor(sigmay(), identity(2)),
         #tensor(sigmaz(), identity(2)),
         #tensor(identity(2), sigmax()),
         #tensor(identity(2), sigmay()),
         #tensor(identity(2), sigmaz()),
         tensor(sigmax(), sigmax()),
         tensor(sigmay(), sigmay()),
         tensor(sigmaz(), sigmaz())]

H_labels = [#r'$u_{1x}$',
            #r'$u_{1y}$',
            #r'$u_{1z}$',
            #r'$u_{2x}$',
            #r'$u_{2y}$',
            #r'$u_{2z}$',
            r'$u_{xx}$',
            r'$u_{yy}$',
            r'$u_{zz}$',
        ]


    

In [5]:

    

H0 = 0 * np.pi * (tensor(sigmaz(), identity(2)) + tensor(identity(2), sigmaz()))


    

In [6]:

    

from qutip.control.grape import plot_grape_control_fields, _overlap, grape_unitary_adaptive, cy_grape_unitary


    

In [7]:

    

from scipy.interpolate import interp1d
from qutip.ui.progressbar import TextProgressBar


    

In [8]:

    

u0 = np.array([np.random.rand(len(times)) * (2 * np.pi / T) * 0.01 for _ in range(len(H_ops))])

u0 = [np.convolve(np.ones(10)/10, u0[idx, :], mode='same') for idx in range(len(H_ops))]


    

In [9]:

    

result = cy_grape_unitary(U, H0, H_ops, R, times, u_start=u0, eps=2*np.pi/T,
                          progress_bar=TextProgressBar())


    

    




10.0%. Run time:   2.36s. Est. time left: 00:00:00:21
20.0%. Run time:   4.51s. Est. time left: 00:00:00:18
30.0%. Run time:   6.54s. Est. time left: 00:00:00:15
40.0%. Run time:   8.39s. Est. time left: 00:00:00:12
50.0%. Run time:  10.22s. Est. time left: 00:00:00:10
60.0%. Run time:  12.09s. Est. time left: 00:00:00:08
70.0%. Run time:  14.41s. Est. time left: 00:00:00:06
80.0%. Run time:  16.58s. Est. time left: 00:00:00:04
90.0%. Run time:  18.91s. Est. time left: 00:00:00:02
Total run time:  20.49s

In [10]:

    

#result = grape_unitary(U, H0, H_ops, R, times, u_start=u0, eps=2*np.pi/T,
#                       progress_bar=TextProgressBar())


    

In [11]:

    

plot_grape_control_fields(times, result.u / (2 * np.pi), H_labels, uniform_axes=True);


    

In [12]:

    

# compare to the analytical results
np.mean(result.u[-1,0,:]), np.mean(result.u[-1,1,:]), np.pi/(4 * T)


    

    
Out[12]:





(-0.74169008690613769, -0.74154800819245748, 0.7853981633974483)

In [13]:

    

U


    

    
Out[13]:





Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}1.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 1.0j & 0.0\\0.0 & 1.0j & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 1.0\\\end{array}\right)\end{equation*}

In [14]:

    

result.U_f.tidyup(1e-2)


    

    
Out[14]:





Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}1.000 & 0.0 & 0.0 & 0.0\\0.0 & 0.094 & 0.996j & 0.0\\0.0 & 0.996j & 0.094 & 0.0\\0.0 & 0.0 & 0.0 & 1.000\\\end{array}\right)\end{equation*}

In [15]:

    

_overlap(U, result.U_f).real


    

    
Out[15]:





0.9978028739003396

In [16]:

    

c_ops = []


    

In [17]:

    

U_f_numerical = propagator(result.H_t, times[-1], c_ops, args={})


    

In [18]:

    

U_f_numerical


    

    
Out[18]:





Quantum object: dims = [[2, 2], [2, 2]], shape = (4, 4), type = oper, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}(1.000+0.009j) & 0.0 & 0.0 & (5.637\times10^{-05}-0.006j)\\0.0 & (0.060-5.619\times10^{-04}j) & (0.009+0.998j) & 0.0\\0.0 & (0.009+0.998j) & (0.060-5.619\times10^{-04}j) & 0.0\\(5.637\times10^{-05}-0.006j) & 0.0 & 0.0 & (1.000+0.009j)\\\end{array}\right)\end{equation*}

In [19]:

    

_overlap(U, U_f_numerical).real


    

    
Out[19]:





0.9990426580571616

In [20]:

    

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


    

In [21]:

    

fig = plt.figure(figsize=(8,6))

U_ideal = spre(U) * spost(U.dag())

chi = qpt(U_ideal, op_basis)

fig = qpt_plot_combined(chi, op_label, fig=fig, threshold=0.001)


    

In [22]:

    

fig = plt.figure(figsize=(8,6))

U_ideal = to_super(result.U_f)

chi = qpt(U_ideal, op_basis)

fig = qpt_plot_combined(chi, op_label, fig=fig, threshold=0.001)


    

In [23]:

    

from qutip.ipynbtools import version_table

version_table()


    

    
Out[23]:




Software
Version
QuTiP
4.2.0
Numpy
1.13.1
SciPy
0.19.1
matplotlib
2.0.2
Cython
0.25.2
Number of CPUs
2
BLAS Info
INTEL MKL
IPython
6.1.0
Python
3.6.1 |Anaconda custom (x86_64)| (default, May 11 2017, 13:04:09) 
[GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]
OS
posix [darwin]
Wed Jul 19 22:11:52 2017 MDT