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 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 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
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) #First the basic sequence basePulseSeq = PulseSequence() basePulseSeq.add_control_line(freq=0e9, phase=0) basePulseSeq.add_control_line(freq=0e9, phase=pi/2) basePulseSeq.H_int = None #Some parameters for the pulse timeStep = 1.0/1.2e9 #How many discrete timesteps to break it up into
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)
#Add the cross-drive Hamiltonians (same drive line as Q2)
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([0.862, 0.855, 0.850, 0.850, 0.845, 0.840, 0.845, 0.840, 0.835]))
##Add the T1 dissipators
#systemParams.dissipators.append(Dissipator(systemParams.expand_operator('Q1', Q1.T1Dissipator)))
#systemParams.dissipators.append(Dissipator(systemParams.expand_operator('Q2', Q2.T1Dissipator)))
#
#Setup the initial state as the ground state
rhoIn = np.zeros((systemParams.dim, systemParams.dim))
rhoIn[0,0] = 1
#Setup the control pulses
sampRate = 1.2e9
timeStep = 1.0/sampRate
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)
#First the basic sequence
basePulseSeq = PulseSequence()
basePulseSeq.add_control_line(freq=0e9, phase=0)
basePulseSeq.add_control_line(freq=0e9, phase=pi / 2)
basePulseSeq.H_int = None
#Some parameters for the pulse
timeStep = 1.0 / 1.2e9
#How many discrete timesteps to break it up into
stepsArray = np.arange(12, 61)
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 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)]
'''
Simple Rabi Driving
We'll vary the Rabi power (but always keep the time to a calibrated pi pulse. We expect to see a maximum at some intermediate regime
where we have a balance between selectivity and T1 decay
'''
pulseSeqs = []
pulseTimes = 1e-9 * np.arange(4, 100, 2)
rhoIn = qubit.levelProjector(0)
for pulseTime in pulseTimes:
systemParams.expand_operator('Q1', X) +
systemParams.expand_operator('Q2', X)),
quadrature=Hamiltonian(crossCoupling21 *
systemParams.expand_operator('Q1', Y) +
systemParams.expand_operator('Q2', Y)))
systemParams.add_control_ham(
inphase=Hamiltonian(crossCoupling21 *
systemParams.expand_operator('Q1', X) +
systemParams.expand_operator('Q2', X)),
quadrature=Hamiltonian(crossCoupling21 *
systemParams.expand_operator('Q1', Y) +
systemParams.expand_operator('Q2', Y)))
#Setup the measurement operator
# systemParams.measurement = -systemParams.expand_operator('Q1', Q1.pauliZ)
systemParams.measurement = np.diag(
np.array([0.55, 0.7, 0.75, 0.72, 0.76, 0.76, 0.76, 0.78, 0.80]))
#Add the T1 dissipators
systemParams.dissipators.append(
Dissipator(systemParams.expand_operator('Q1', Q1.T1Dissipator)))
systemParams.dissipators.append(
Dissipator(systemParams.expand_operator('Q2', Q2.T1Dissipator)))
#Setup the initial state as the ground state
rhoIn = np.kron(Q1.levelProjector(0), Q2.levelProjector(0))
sampRate = 1.2e9
timeStep = 1.0 / sampRate
drive1Freq = Q1.omega - 1e6
drive2Freq = Q2.omega - 1e6
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)
numSteps = 160
xPts = np.linspace(-2, 2, numSteps)
gaussPulse = np.exp(-0.5 * (xPts**2)) - np.exp(-0.5 * 2**2)
pulseSeqs = []
for tmpFreq in freqs:
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) numSteps = 160 xPts = np.linspace(-2,2,numSteps) gaussPulse = np.exp(-0.5*(xPts**2)) - np.exp(-0.5*2**2)
#Add the Q1 drive Hamiltonians
systemParams.add_control_ham(inphase = Hamiltonian(systemParams.expand_operator('Q1', X) + crossCoupling12*systemParams.expand_operator('Q2', X)),
quadrature = Hamiltonian(systemParams.expand_operator('Q1', Y) + crossCoupling12*systemParams.expand_operator('Q2', Y)))
systemParams.add_control_ham(inphase = Hamiltonian(systemParams.expand_operator('Q1', X) + crossCoupling12*systemParams.expand_operator('Q2', X)),
quadrature = Hamiltonian(systemParams.expand_operator('Q1', Y) + crossCoupling12*systemParams.expand_operator('Q2', Y)))
#Add the Q2 drive Hamiltonians
systemParams.add_control_ham(inphase = Hamiltonian(crossCoupling21*systemParams.expand_operator('Q1', X) + systemParams.expand_operator('Q2', X)),
quadrature = Hamiltonian(crossCoupling21*systemParams.expand_operator('Q1', Y) + systemParams.expand_operator('Q2', Y)))
systemParams.add_control_ham(inphase = Hamiltonian(crossCoupling21*systemParams.expand_operator('Q1', X) + systemParams.expand_operator('Q2', X)),
quadrature = Hamiltonian(crossCoupling21*systemParams.expand_operator('Q1', Y) + systemParams.expand_operator('Q2', Y)))
#Setup the measurement operator
# systemParams.measurement = -systemParams.expand_operator('Q1', Q1.pauliZ)
systemParams.measurement = np.diag(np.array([0.55, 0.7, 0.75, 0.72, 0.76, 0.76, 0.76, 0.78, 0.80]))
#Add the T1 dissipators
systemParams.dissipators.append(Dissipator(systemParams.expand_operator('Q1', Q1.T1Dissipator)))
systemParams.dissipators.append(Dissipator(systemParams.expand_operator('Q2', Q2.T1Dissipator)))
#Setup the initial state as the ground state
rhoIn = np.kron(Q1.levelProjector(0), Q2.levelProjector(0))
sampRate = 1.2e9
timeStep = 1.0/sampRate
drive1Freq = Q1.omega-1e6
drive2Freq = Q2.omega-1e6
#Calibrate a 240ns Gaussian pulse on Q1
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)
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
#Add the Q1 drive Hamiltonians
systemParams.add_control_ham(inphase = Hamiltonian(systemParams.expand_operator('Q1', X) + crossCoupling*systemParams.expand_operator('Q2', X)),
quadrature = Hamiltonian(systemParams.expand_operator('Q1', Y) + crossCoupling*systemParams.expand_operator('Q2', Y)))
#Setup the measurement operator
# systemParams.measurement = np.kron(Q1.levelProjector(1), Q2.levelProjector(1))
systemParams.measurement = 0.5*np.kron(Q1.levelProjector(0), Q2.levelProjector(0)) + 0.67*np.kron(Q1.levelProjector(1), Q2.levelProjector(0)) + \
0.64*np.kron(Q1.levelProjector(0), Q2.levelProjector(1)) + 0.72*np.kron(Q1.levelProjector(0), Q2.levelProjector(2)) + \
0.75*np.kron(Q1.levelProjector(1), Q2.levelProjector(1)) + 0.78*np.kron(Q1.levelProjector(1), Q2.levelProjector(2))
#Add the T1 dissipators
systemParams.dissipators.append(Dissipator(systemParams.expand_operator('Q1', Q1.T1Dissipator)))
systemParams.dissipators.append(Dissipator(systemParams.expand_operator('Q2', Q2.T1Dissipator)))
#Setup the initial state as the ground state
rhoIn = np.zeros((systemParams.dim, systemParams.dim))
rhoIn[0,0] = 1
#First run 1D spectroscopy around the Bell-Rabi drive frequency
freqSweep = 1e9*np.linspace(5.02, 5.040, 20)
# freqSweep = [5.023e9]
ampSweep = np.linspace(-1,1,80)
x = np.linspace(-2,2,100)
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)] ''' Simple Rabi Driving We'll vary the Rabi power (but always keep the time to a calibrated pi pulse. We expect to see a maximum at some intermediate regime where we have a balance between selectivity and T1 decay ''' pulseSeqs = [] pulseTimes = 1e-9*np.arange(4,100, 2)
