# GRAPE calculation of control fields for iSWAP implementation¶

Robert Johansson ([email protected])

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()))


# GRAPE¶

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())


## Plot control fields for iSWAP gate in the presense of single-qubit tunnelling¶

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)

## Fidelity¶

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

## Test numerical integration of GRAPE pulse¶

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

# Process tomography¶

## Ideal iSWAP gate¶

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)


## iSWAP gate calculated using GRAPE¶

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)


## Versions¶

In [23]:
from qutip.ipynbtools import version_table

version_table()

Out[23]:
SoftwareVersion
QuTiP4.2.0
Numpy1.13.1
SciPy0.19.1
matplotlib2.0.2
Cython0.25.2
Number of CPUs2
BLAS InfoINTEL MKL
IPython6.1.0
Python3.6.1 |Anaconda custom (x86_64)| (default, May 11 2017, 13:04:09) [GCC 4.2.1 Compatible Apple LLVM 6.0 (clang-600.0.57)]
OSposix [darwin]
Wed Jul 19 22:11:52 2017 MDT