QuTiP example: Physical implementation of Cavity-Qubit model

Author: Anubhav Vardhan (anubhavvardhan@gmail.com)

For more information about QuTiP see http://qutip.org



In [1]:

    
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib



In [2]:

    
from qutip import *



In [3]:

    
from qutip.qip.models.circuitprocessor import *



In [4]:

    
from qutip.qip.models.cqed import *

Hamoltonian:

hamiltonian

The cavity-qubit model using a resonator as a bus can be implemented using the DispersivecQED class.

Circuit Setup



In [5]:

    
N = 3
qc = QubitCircuit(N)

qc.add_gate("ISWAP", targets=[0,1])

qc.png









    Out[5]:



In [6]:

    
U_ideal = gate_sequence_product(qc.propagators())

U_ideal









    Out[6]:





Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = [8, 8], type = oper, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 1.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 1.0j & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0j & 0.0 & 0.0\\0.0 & 0.0 & 1.0j & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 1.0j & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.0\\\end{array}\right)\end{equation*}

Dispersive cQED Model Implementation:



In [7]:

    
p1 = DispersivecQED(N, correct_global_phase=True)

U_list = p1.run(qc)

U_physical = gate_sequence_product(U_list)

U_physical.tidyup(atol=1e-3)









    Out[7]:





Quantum object: dims = [[2, 2, 2], [2, 2, 2]], shape = [8, 8], type = oper, isherm = False\begin{equation*}\left(\begin{array}{*{11}c}1.000 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 1.000 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 1.000j & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.000j & 0.0 & 0.0\\0.0 & 0.0 & 1.000j & 0.0 & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 1.000j & 0.0 & 0.0 & 0.0 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.000 & 0.0\\0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 0.0 & 1.000\\\end{array}\right)\end{equation*}



In [8]:

    
(U_ideal - U_physical).norm()









    Out[8]:





4.7506788969364782e-07

The results obtained from the physical implementation agree with the ideal result.



In [9]:

    
p1.qc0.gates









    Out[9]:





[Gate(ISWAP, targets=[0, 1], controls=None)]

The gates are first transformed into the ISWAP basis, which is redundant in this example.



In [10]:

    
p1.qc1.gates









    Out[10]:





[Gate(ISWAP, targets=[0, 1], controls=None)]

An RZ gate, followed by a Globalphase, is applied to all ISWAP and SQRTISWAP gates to normalize the propagator matrix. Arg_value for the ISWAP case is pi/2, while for the SQRTISWAP case, it is pi/4.



In [11]:

    
p1.qc2.gates









    Out[11]:





[Gate(ISWAP, targets=[0, 1], controls=None),
 Gate(RZ, targets=[0], controls=None),
 Gate(RZ, targets=[1], controls=None),
 Gate(GLOBALPHASE, targets=None, controls=None)]

The time for each applied gate:



In [12]:

    
p1.T_list









    Out[12]:





[2500.0000000000027, 0.013157894736842106, 0.013157894736842106]

The pulse can be plotted as:



In [13]:

    
p1.plot_pulses();

Software versions:



In [14]:

    
from qutip.ipynbtools import version_table
version_table()









    Out[14]:




Software Version
IPython 2.0.0
Cython 0.20.1post0
OS posix [linux]
QuTiP 3.0.0.dev-11ff7e7
Numpy 1.8.1
matplotlib 1.3.1
SciPy 0.13.3
Python 3.4.1 (default, Jul  7 2014, 05:33:58) 
[GCC 4.8.3]
Mon Jul 14 13:49:25 2014 JST

Software	Version
IPython	2.0.0
Cython	0.20.1post0
OS	posix [linux]
QuTiP	3.0.0.dev-11ff7e7
Numpy	1.8.1
matplotlib	1.3.1
SciPy	0.13.3
Python	3.4.1 (default, Jul 7 2014, 05:33:58) [GCC 4.8.3]
Mon Jul 14 13:49:25 2014 JST