def setUp(self):
#Setup a simple non-coupled two qubit system
self.systemParams = SystemParams()
self.Q1 = SCQubit(2, 5e9, name='Q1')
self.systemParams.add_sub_system(self.Q1)
self.Q2 = SCQubit(2, 6e9, name='Q2')
self.systemParams.add_sub_system(self.Q2)
X = 0.5 * (self.Q1.loweringOp + self.Q1.raisingOp)
Y = 0.5 * (-1j * self.Q1.loweringOp + 1j * self.Q2.raisingOp)
self.systemParams.add_control_ham(
inphase=Hamiltonian(self.systemParams.expand_operator('Q1', X)),
quadrature=Hamiltonian(self.systemParams.expand_operator('Q1', Y)))
self.systemParams.add_control_ham(
inphase=Hamiltonian(self.systemParams.expand_operator('Q2', X)),
quadrature=Hamiltonian(self.systemParams.expand_operator('Q2', Y)))
self.systemParams.measurement = self.systemParams.expand_operator(
'Q1', self.Q1.pauliZ) + self.systemParams.expand_operator(
'Q2', self.Q2.pauliZ)
self.systemParams.create_full_Ham()
#Define Rabi frequency and pulse lengths
self.rabiFreq = 10e6
#Define the initial state as the ground state
self.rhoIn = np.zeros((self.systemParams.dim, self.systemParams.dim))
self.rhoIn[0, 0] = 1
def testInversion(self):
'''
Try a simple three level SC qubit system and see if can prepare the excited state.
'''
#Setup a three level qubit and a 100MHz delta
Q1 = SCQubit(3, 4.987456e9, -100e6, name='Q1')
systemParams = SystemParams()
systemParams.add_sub_system(Q1)
systemParams.add_control_ham(
inphase=Hamiltonian(0.5 * (Q1.loweringOp + Q1.raisingOp)),
quadrature=Hamiltonian(0.5 *
(-1j * Q1.loweringOp + 1j * Q1.raisingOp)))
systemParams.create_full_Ham()
systemParams.measurement = Q1.levelProjector(1)
#Setup the pulse parameters for the optimization
pulseParams = PulseParams()
pulseParams.timeSteps = 1e-9 * np.ones(30)
pulseParams.rhoStart = Q1.levelProjector(0)
pulseParams.rhoGoal = Q1.levelProjector(1)
pulseParams.add_control_line(freq=-Q1.omega)
pulseParams.H_int = Hamiltonian(Q1.omega * np.diag(np.arange(Q1.dim)))
pulseParams.optimType = 'state2state'
#Call the optimization
optimize_pulse(pulseParams, systemParams)
#Now test the optimized pulse and make sure it puts all the population in the excited state
result = simulate_sequence(pulseParams,
systemParams,
pulseParams.rhoStart,
simType='unitary')[0]
assert result > 0.99
def testYPhase(self):
'''
Make sure the frame-handedness matches what we expect: i.e. if the qubit frequency is
greater than the driver frequency this corresponds to a positive rotation.
'''
#Setup the system
self.systemParams.subSystems[0] = SCQubit(2, 5e9, 'Q1')
self.systemParams.create_full_Ham()
#Add a Y control Hamiltonian
self.systemParams.add_control_ham(
inphase=Hamiltonian(0.5 * self.qubit.pauliX),
quadrature=Hamiltonian(0.5 * self.qubit.pauliY))
#Setup the pulseSequences
delays = np.linspace(0, 8e-6, 200)
t90 = 0.25 * (1 / self.rabiFreq)
offRes = 1.2345e6
pulseSeqs = []
for delay in delays:
tmpPulseSeq = PulseSequence()
#Shift the pulsing frequency down by offRes
tmpPulseSeq.add_control_line(freq=-(5.0e9 - offRes), phase=0)
tmpPulseSeq.add_control_line(freq=-(5.0e9 - offRes), phase=-pi / 2)
#Pulse sequence is X90, delay, Y90
tmpPulseSeq.controlAmps = self.rabiFreq * np.array(
[[1, 0, 0], [0, 0, 1]], dtype=np.float64)
tmpPulseSeq.timeSteps = np.array([t90, delay, t90])
#Interaction frame with some odd frequency
tmpPulseSeq.H_int = Hamiltonian(
np.array([[0, 0], [0, 5.00e9]], dtype=np.complex128))
pulseSeqs.append(tmpPulseSeq)
results = simulate_sequence_stack(pulseSeqs,
self.systemParams,
self.rhoIn,
simType='lindblad')[0]
expectedResults = -np.sin(2 * pi * offRes * (delays + t90))
if plotResults:
plt.figure()
plt.plot(1e6 * delays, results)
plt.plot(1e6 * delays,
expectedResults,
color='r',
linestyle='--',
linewidth=2)
plt.title('Ramsey Fringes {0:.2f} MHz Off-Resonance'.format(
offRes / 1e6))
plt.xlabel('Pulse Spacing (us)')
plt.ylabel(r'$\sigma_z$')
plt.legend(('Simulated Results',
' {0:.2f} MHz -Sin.'.format(offRes / 1e6)))
plt.show()
def testRamsey(self):
'''
Just look at Ramsey decay to make sure we get the off-resonance right.
'''
#Setup the system
self.systemParams.subSystems[0] = SCQubit(2, 5e9, 'Q1')
self.systemParams.create_full_Ham()
self.systemParams.dissipators = [Dissipator(self.qubit.T1Dissipator)]
#Setup the pulseSequences
delays = np.linspace(0, 8e-6, 200)
t90 = 0.25 * (1 / self.rabiFreq)
offRes = 0.56789e6
pulseSeqs = []
for delay in delays:
tmpPulseSeq = PulseSequence()
#Shift the pulsing frequency down by offRes
tmpPulseSeq.add_control_line(freq=-(5.0e9 - offRes), phase=0)
#Pulse sequence is X90, delay, X90
tmpPulseSeq.controlAmps = self.rabiFreq * np.array(
[[1, 0, 1]], dtype=np.float64)
tmpPulseSeq.timeSteps = np.array([t90, delay, t90])
#Interaction frame with some odd frequency
tmpPulseSeq.H_int = Hamiltonian(
np.array([[0, 0], [0, 5.00e9]], dtype=np.complex128))
pulseSeqs.append(tmpPulseSeq)
results = simulate_sequence_stack(pulseSeqs,
self.systemParams,
self.rhoIn,
simType='lindblad')[0]
expectedResults = -np.cos(2 * pi * offRes *
(delays + t90)) * np.exp(-delays /
(2 * self.qubit.T1))
if plotResults:
plt.figure()
plt.plot(1e6 * delays, results)
plt.plot(1e6 * delays,
expectedResults,
color='r',
linestyle='--',
linewidth=2)
plt.title('Ramsey Fringes 0.56789MHz Off-Resonance')
plt.xlabel('Pulse Spacing (us)')
plt.ylabel(r'$\sigma_z$')
plt.legend(
('Simulated Results', '0.57MHz Cosine with T1 limited decay.'))
plt.show()
def setUp(self):
#Setup the system
self.systemParams = SystemParams()
self.qubit = SCQubit(2, 0e9, name='Q1', T1=1e-6)
self.systemParams.add_sub_system(self.qubit)
#self.systemParams.add_control_ham(inphase = Hamiltonian(0.5*(self.qubit.loweringOp + self.qubit.raisingOp)), quadrature = Hamiltonian(0.5*(-1j*self.qubit.loweringOp + 1j*self.qubit.raisingOp)))
self.systemParams.add_control_ham(
inphase=Hamiltonian(0.5 * self.qubit.pauliX),
quadrature=Hamiltonian(0.5 * self.qubit.pauliY))
self.systemParams.measurement = self.qubit.pauliZ
self.systemParams.create_full_Ham()
#Define Rabi frequency and pulse lengths
self.rabiFreq = 10e6
self.pulseLengths = np.linspace(0, 100e-9, 40)
#Define the initial state as the ground state
self.rhoIn = self.qubit.levelProjector(0)
def testRabiInteractionFrame(self):
'''
Test Rabi oscillations after moving into an interaction frame that is different to the pulsing frame and with an irrational timestep for good measure.
'''
#Setup the system
self.systemParams.subSystems[0] = SCQubit(2, 5e9, 'Q1')
self.systemParams.create_full_Ham()
#Setup the pulseSequences
pulseSeqs = []
for pulseLength in self.pulseLengths:
tmpPulseSeq = PulseSequence()
tmpPulseSeq.add_control_line(freq=-5.0e9, phase=0)
tmpPulseSeq.controlAmps = self.rabiFreq * np.array(
[[1]], dtype=np.float64)
tmpPulseSeq.timeSteps = np.array([pulseLength])
tmpPulseSeq.maxTimeStep = pi / 2 * 1e-10
tmpPulseSeq.H_int = Hamiltonian(
np.array([[0, 0], [0, 5.005e9]], dtype=np.complex128))
pulseSeqs.append(tmpPulseSeq)
results = simulate_sequence_stack(pulseSeqs,
self.systemParams,
self.rhoIn,
simType='unitary')[0]
expectedResults = np.cos(2 * pi * self.rabiFreq * self.pulseLengths)
if plotResults:
plt.figure()
plt.plot(self.pulseLengths, results)
plt.plot(self.pulseLengths,
expectedResults,
color='r',
linestyle='--',
linewidth=2)
plt.title('10MHz Rabi Oscillations in Interaction Frame')
plt.xlabel('Pulse Length')
plt.ylabel(r'$\sigma_z$')
plt.legend(('Simulated Results', '10MHz Cosine'))
plt.show()
np.testing.assert_allclose(results, expectedResults, atol=1e-4)
def setUp(self):
#Setup the system
self.systemParams = SystemParams()
self.qubit = SCQubit(3, 5e9, -100e6, name='Q1', T1=2e-6)
self.systemParams.add_sub_system(self.qubit)
self.systemParams.add_control_ham(
inphase=Hamiltonian(
0.5 * (self.qubit.loweringOp + self.qubit.raisingOp)),
quadrature=Hamiltonian(
-0.5 *
(-1j * self.qubit.loweringOp + 1j * self.qubit.raisingOp)))
self.systemParams.measurement = self.qubit.pauliZ
self.systemParams.create_full_Ham()
#Add the 2us T1 dissipator
self.systemParams.dissipators = [Dissipator(self.qubit.T1Dissipator)]
#Define the initial state as the ground state
self.rhoIn = self.qubit.levelProjector(0)
from scipy.constants import pi
from scipy.linalg import eigh
from PySim.SystemParams import SystemParams
from PySim.QuantumSystems import Hamiltonian, Dissipator
from PySim.PulseSequence import PulseSequence
from PySim.Simulation import simulate_sequence_stack, simulate_sequence
from PySim.QuantumSystems import SCQubit
from PySim.OptimalControl import optimize_pulse, PulseParams
#Setup the system
systemParams = SystemParams()
#First the two qubits defined in the lab frame
Q1 = SCQubit(numLevels=3, omega=4.76093e9, delta=-244e6, name='Q1', T1=10e-6)
systemParams.add_sub_system(Q1)
Q2 = SCQubit(numLevels=3, omega=5.34012e9, delta=-224e6, name='Q2', T1=10e-6)
systemParams.add_sub_system(Q2)
#Add an interaction between the qubits to get the the cross-resonance effect
systemParams.add_interaction('Q1', 'Q2', 'FlipFlop', 2e6)
#Create the full Hamiltonian
systemParams.create_full_Ham()
#Calculate the eigenframe for the natural Hamiltonian
d,v = eigh(systemParams.Hnat.matrix)
#Reorder the transformation matrix to maintain the computational basis ordering
from scipy.constants import pi
from scipy.linalg import expm
import matplotlib.pyplot as plt
from PySim.SystemParams import SystemParams
from PySim.PulseSequence import PulseSequence
from PySim.Simulation import simulate_sequence_stack
from PySim.QuantumSystems import SCQubit, Hamiltonian
from copy import deepcopy
#Setup the system
systemParams = SystemParams()
qubit = SCQubit(2, 0e9, delta=200e6, name='Q1', T1=1e-6)
systemParams.add_sub_system(qubit)
systemParams.add_control_ham(
inphase=Hamiltonian(0.5 * (qubit.loweringOp + qubit.raisingOp)),
quadrature=Hamiltonian(0.5 *
(-1j * qubit.loweringOp + 1j * qubit.raisingOp)))
systemParams.add_control_ham(
inphase=Hamiltonian(0.5 * (qubit.loweringOp + qubit.raisingOp)),
quadrature=Hamiltonian(0.5 *
(-1j * qubit.loweringOp + 1j * qubit.raisingOp)))
systemParams.measurement = qubit.pauliZ
systemParams.create_full_Ham()
#Define the initial state as the ground state
rhoIn = qubit.levelProjector(0)
def testDRAG(self):
'''
Try a unitary inversion pulse on a three level SCQuibt and see if we get something close to DRAG
'''
#Setup a three level qubit and a 100MHz delta
Q1 = SCQubit(3, 4.987456e9, -150e6, name='Q1')
systemParams = SystemParams()
systemParams.add_sub_system(Q1)
systemParams.add_control_ham(
inphase=Hamiltonian(0.5 * (Q1.loweringOp + Q1.raisingOp)),
quadrature=Hamiltonian(0.5 *
(-1j * Q1.loweringOp + 1j * Q1.raisingOp)))
systemParams.add_control_ham(
inphase=Hamiltonian(0.5 * (Q1.loweringOp + Q1.raisingOp)),
quadrature=Hamiltonian(0.5 *
(-1j * Q1.loweringOp + 1j * Q1.raisingOp)))
systemParams.create_full_Ham()
systemParams.measurement = Q1.levelProjector(1)
#Setup the pulse parameters for the optimization
numPoints = 30
pulseTime = 15e-9
pulseParams = PulseParams()
pulseParams.timeSteps = (pulseTime / numPoints) * np.ones(numPoints)
pulseParams.rhoStart = Q1.levelProjector(0)
pulseParams.rhoGoal = Q1.levelProjector(1)
pulseParams.Ugoal = Q1.pauliX
pulseParams.add_control_line(freq=-Q1.omega,
bandwidth=300e6,
maxAmp=200e6)
pulseParams.add_control_line(freq=-Q1.omega,
phase=-np.pi / 2,
bandwidth=300e6,
maxAmp=200e6)
pulseParams.H_int = Hamiltonian(
(Q1.omega) * np.diag(np.arange(Q1.dim)))
pulseParams.optimType = 'unitary'
pulseParams.derivType = 'finiteDiff'
#Start with a Gaussian
tmpGauss = np.exp(-np.linspace(-2, 2, numPoints)**2)
tmpScale = 0.5 / (np.sum(pulseParams.timeSteps * tmpGauss))
pulseParams.startControlAmps = np.vstack(
(tmpScale * tmpGauss, np.zeros(numPoints)))
#Call the optimization
optimize_pulse(pulseParams, systemParams)
if plotResults:
plt.plot(
np.cumsum(pulseParams.timeSteps) * 1e9,
pulseParams.controlAmps.T / 1e6)
plt.ylabel('Pulse Amplitude (MHz)')
plt.xlabel('Time (ns)')
plt.legend(('X Quadrature', 'Y Quadrature'))
plt.title('DRAG Pulse from Optimal Control')
plt.show()
#Now test the optimized pulse and make sure it does give us the desired unitary
result = simulate_sequence(pulseParams,
systemParams,
pulseParams.rhoStart,
simType='unitary')
assert np.abs(np.trace(np.dot(
result[1].conj().T, pulseParams.Ugoal)))**2 / np.abs(
np.trace(np.dot(pulseParams.Ugoal.conj().T,
pulseParams.Ugoal)))**2 > 0.99
def setup_system():
'''
Should probably take in some parameters, but for now hard-code things.
'''
#Setup the system
systemParams = SystemParams()
#First the two qubits defined in the lab frame
Q1 = SCQubit(numLevels=3, omega=4.279e9, delta=-239e6, name='Q1', T1=10e-6)
systemParams.add_sub_system(Q1)
Q2 = SCQubit(numLevels=3, omega=4.06e9, delta=-224e6, name='Q2', T1=10e-6)
systemParams.add_sub_system(Q2)
#Add an interaction between the qubits to get the the cross-resonance effect
systemParams.add_interaction('Q1', 'Q2', 'FlipFlop', 2e6)
#Create the full Hamiltonian
systemParams.create_full_Ham()
#Calculate the eigenframe for the natural Hamiltonian
d, v = eigh(systemParams.Hnat.matrix)
#Reorder the transformation matrix to maintain the computational basis ordering
sortOrder = np.argsort(np.argmax(np.abs(v), axis=0))
v = v[:, sortOrder]
systemParams.Hnat.matrix = np.complex128(np.diag(d[sortOrder]))
#Some operators for the controls
X = 0.5 * (Q1.loweringOp + Q1.raisingOp)
Y = 0.5 * (-1j * Q1.loweringOp + 1j * Q1.raisingOp)
#The cross-coupling between the drives
crossCoupling12 = 5.0 / 20
crossCoupling21 = 2.0 / 30
#Add the Q1 drive Hamiltonians
inPhaseHam = Hamiltonian(
np.dot(
v.conj().T,
np.dot(
systemParams.expand_operator('Q1', X) +
crossCoupling12 * systemParams.expand_operator('Q2', X), v)))
quadratureHam = Hamiltonian(
np.dot(
v.conj().T,
np.dot(
systemParams.expand_operator('Q1', Y) +
crossCoupling12 * systemParams.expand_operator('Q2', Y), v)))
systemParams.add_control_ham(inphase=inPhaseHam, quadrature=quadratureHam)
systemParams.add_control_ham(inphase=inPhaseHam, quadrature=quadratureHam)
#Add the cross-drive Hamiltonians (same drive line as Q1)
inPhaseHam = Hamiltonian(
np.dot(
v.conj().T,
np.dot(
systemParams.expand_operator('Q1', X) +
crossCoupling12 * systemParams.expand_operator('Q2', X), v)))
quadratureHam = Hamiltonian(
np.dot(
v.conj().T,
np.dot(
systemParams.expand_operator('Q1', Y) +
crossCoupling12 * systemParams.expand_operator('Q2', Y), v)))
systemParams.add_control_ham(inphase=inPhaseHam, quadrature=quadratureHam)
systemParams.add_control_ham(inphase=inPhaseHam, quadrature=quadratureHam)
#Add the Q2 drive Hamiltonians
inPhaseHam = Hamiltonian(
np.dot(
v.conj().T,
np.dot(
systemParams.expand_operator('Q2', X) +
crossCoupling21 * systemParams.expand_operator('Q1', X), v)))
quadratureHam = Hamiltonian(
np.dot(
v.conj().T,
np.dot(
systemParams.expand_operator('Q2', Y) +
crossCoupling21 * systemParams.expand_operator('Q1', Y), v)))
systemParams.add_control_ham(inphase=inPhaseHam, quadrature=quadratureHam)
systemParams.add_control_ham(inphase=inPhaseHam, quadrature=quadratureHam)
#Setup the measurement operator
systemParams.measurement = np.diag(
np.array([0.088, 0.082, 0.080, 0.080, 0.78, 0.75, 0.078, 0.074,
0.072]))
##Add the T1 dissipators
#systemParams.dissipators.append(Dissipator(systemParams.expand_operator('Q1', Q1.T1Dissipator)))
#systemParams.dissipators.append(Dissipator(systemParams.expand_operator('Q2', Q2.T1Dissipator)))
#
return systemParams, (Q1, Q2)
'''
from PySim.SystemParams import SystemParams
from PySim.QuantumSystems import SCQubit, Hamiltonian, Dissipator
from PySim.PulseSequence import PulseSequence
from PySim.Simulation import simulate_sequence_stack, simulate_sequence
from PySim.OptimalControl import optimize_pulse, PulseParams
import numpy as np
import matplotlib.pyplot as plt
from scipy.constants import pi
'''System Setup'''
systemParams = SystemParams()
qubit = SCQubit(3, 0e9, -100e6, name='Q1', T1=50e-9)
systemParams.add_sub_system(qubit)
systemParams.add_control_ham(
inphase=Hamiltonian(0.5 * (qubit.loweringOp + qubit.raisingOp)),
quadrature=Hamiltonian(-0.5 *
(-1j * qubit.loweringOp + 1j * qubit.raisingOp)))
systemParams.add_control_ham(
inphase=Hamiltonian(0.5 * (qubit.loweringOp + qubit.raisingOp)),
quadrature=Hamiltonian(-0.5 *
(-1j * qubit.loweringOp + 1j * qubit.raisingOp)))
systemParams.measurement = qubit.levelProjector(1)
systemParams.create_full_Ham()
#Add the T1 dissipator
systemParams.dissipators = [Dissipator(qubit.T1Dissipator)]
'''
import scipy.optimize
from PySim.SystemParams import SystemParams
from PySim.QuantumSystems import Hamiltonian, Dissipator
from PySim.PulseSequence import PulseSequence
from PySim.Simulation import simulate_sequence_stack, simulate_sequence
from PySim.QuantumSystems import SCQubit
if __name__ == '__main__':
#Setup the system
systemParams = SystemParams()
#First the two qubits
Q1 = SCQubit(numLevels=3,
omega=4.8636e9,
delta=-321.7e6,
name='Q1',
T1=5.2e-6)
systemParams.add_sub_system(Q1)
Q2 = SCQubit(numLevels=3,
omega=5.1934e9,
delta=-313.656e6,
name='Q2',
T1=4.4e-6)
systemParams.add_sub_system(Q2)
#Our carrier frequencies
drive1Freq = 4.8626e9
drive2Freq = 5.193e9
#Add a 2MHz ZZ interaction
Test script to play around with 2D Rabi vs drive frequency experiments
"""
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm
from PySim.SystemParams import SystemParams
from PySim.PulseSequence import PulseSequence
from PySim.Simulation import simulate_sequence_stack
from PySim.QuantumSystems import SCQubit, Hamiltonian
#Setup the system
systemParams = SystemParams()
qubit = SCQubit(6, 4.76e9, delta=-200e6, name='Q1', T1=1e-6)
systemParams.add_sub_system(qubit)
systemParams.add_control_ham(
inphase=Hamiltonian(0.5 * (qubit.loweringOp + qubit.raisingOp)),
quadrature=Hamiltonian(0.5 *
(-1j * qubit.loweringOp + 1j * qubit.raisingOp)))
systemParams.create_full_Ham()
systemParams.measurement = np.diag([0.72, 0.70, 0.69, 0.685, 0.6825, 0.68125])
#Define the initial state as the ground state
rhoIn = qubit.levelProjector(0)
#Some parameters for the pulse
timeStep = 1 / 1.2e9
pulseAmps = 250e6 * np.linspace(-1, 1, 81)
freqs = np.linspace(4.3e9, 4.9e9, 450)
from scipy.signal import decimate
from scipy.constants import pi
from scipy.linalg import eigh, expm
from PySim.SystemParams import SystemParams
from PySim.QuantumSystems import Hamiltonian, Dissipator
from PySim.PulseSequence import PulseSequence
from PySim.Simulation import simulate_sequence_stack, simulate_sequence
from PySim.QuantumSystems import SCQubit
from PySim.OptimalControl import optimize_pulse, PulseParams
#Setup the system
systemParams = SystemParams()
#First the two qubits
Q1 = SCQubit(numLevels=3, omega=1e6, delta=-321.7e6, name='Q1', T1=5.2e-6)
systemParams.add_sub_system(Q1)
Q2 = SCQubit(numLevels=3, omega=329.8e6, delta=-314.4e6, name='Q2', T1=4.4e-6)
systemParams.add_sub_system(Q2)
#Add a 2MHz ZZ interaction through a flip-flop interaction
systemParams.add_interaction('Q1', 'Q2', 'FlipFlop', 4.3e6)
#Create the full Hamiltonian
systemParams.create_full_Ham()
#Calculate the eigenframe for the natural Hamiltonian
d, v = eigh(systemParams.Hnat.matrix)
#Reorder the transformation matrix to maintain the computational basis ordering
sortOrder = np.argsort(np.argmax(np.abs(v), axis=0))
# AWGFreq = 1.2e9
# x = np.linspace(-2,2,numPoints)
# #Hermite 180
## pulseAmps = (1-0.956*x**2)*np.exp(-(x**2))
# #Hermite 90
# pulseAmps = (1-0.677*x**2)*np.exp(-(x**2))
# #Gaussian
## pulseAmps = np.exp(-(x**2))
''' Try to recreate the Bell-Rabi spectroscopy '''
#Setup the system
systemParams = SystemParams()
#First the two qubits
Q1 = SCQubit(numLevels=3, omega=4.863e9-1e6, delta=-300e6, name='Q1', T1=5.2e-6)
systemParams.add_sub_system(Q1)
Q2 = SCQubit(numLevels=3, omega=5.193e9-1e6, delta=-313.656e6, name='Q2', T1=4.4e-6)
systemParams.add_sub_system(Q2)
#Add a 2MHz ZZ interaction
systemParams.add_interaction('Q1', 'Q2', 'ZZ', -2e6)
#Create the full Hamiltonian
systemParams.create_full_Ham()
#Some Pauli operators for the controls
X = 0.5*(Q1.loweringOp + Q1.raisingOp)
Y = 0.5*(-1j*Q1.loweringOp + 1j*Q2.raisingOp)
#The cross-coupling from Q1 drive to Q2
crossCoupling = 1
