#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 = 12.0/24
crossCoupling21 = 0.5/12
#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 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)
class TwoQubit(unittest.TestCase):
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 tearDown(self):
pass
def testZZGate(self):
'''Test whether the ZZ interaction performs as expected'''
#Take the bare Hamiltonian as the interaction Hamiltonian
H_int = Hamiltonian(self.systemParams.Hnat.matrix)
#First add a 2MHz ZZ interaction and add it to the system
self.systemParams.add_interaction('Q1', 'Q2', 'ZZ', 2e6)
self.systemParams.create_full_Ham()
#Setup the pulseSequences
delays = np.linspace(0, 4e-6, 100)
pulseSeqs = []
for delay in delays:
tmpPulseSeq = PulseSequence()
tmpPulseSeq.add_control_line(freq=-5.0e9, phase=0)
tmpPulseSeq.add_control_line(freq=-6.0e9, phase=0)
tmpPulseSeq.controlAmps = self.rabiFreq * np.array(
[[1, 0], [0, 0]], dtype=np.float64)
tmpPulseSeq.timeSteps = np.array([25e-9, delay])
tmpPulseSeq.maxTimeStep = np.Inf
tmpPulseSeq.H_int = H_int
pulseSeqs.append(tmpPulseSeq)
self.systemParams.measurement = np.kron(self.Q1.pauliX, self.Q2.pauliZ)
resultsXZ = simulate_sequence_stack(pulseSeqs,
self.systemParams,
self.rhoIn,
simType='unitary')[0]
self.systemParams.measurement = np.kron(self.Q1.pauliY, self.Q2.pauliZ)
resultsYZ = simulate_sequence_stack(pulseSeqs,
self.systemParams,
self.rhoIn,
simType='unitary')[0]
if plotResults:
plt.figure()
plt.plot(delays * 1e6, resultsXZ)
plt.plot(delays * 1e6, resultsYZ, 'g')
plt.legend(('XZ', 'YZ'))
plt.xlabel('Coupling Time')
plt.ylabel('Operator Expectation Value')
plt.title('ZZ Coupling Evolution After a X90 on Q1')
plt.show()
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)
class TwoQubit(unittest.TestCase):
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 tearDown(self):
pass
def testZZGate(self):
'''Test whether the ZZ interaction performs as expected'''
#Take the bare Hamiltonian as the interaction Hamiltonian
H_int = Hamiltonian(self.systemParams.Hnat.matrix)
#First add a 2MHz ZZ interaction and add it to the system
self.systemParams.add_interaction('Q1', 'Q2', 'ZZ', 2e6)
self.systemParams.create_full_Ham()
#Setup the pulseSequences
delays = np.linspace(0,4e-6,100)
pulseSeqs = []
for delay in delays:
tmpPulseSeq = PulseSequence()
tmpPulseSeq.add_control_line(freq=-5.0e9, phase=0)
tmpPulseSeq.add_control_line(freq=-6.0e9, phase=0)
tmpPulseSeq.controlAmps = self.rabiFreq*np.array([[1, 0], [0,0]], dtype=np.float64)
tmpPulseSeq.timeSteps = np.array([25e-9, delay])
tmpPulseSeq.maxTimeStep = np.Inf
tmpPulseSeq.H_int = H_int
pulseSeqs.append(tmpPulseSeq)
self.systemParams.measurement = np.kron(self.Q1.pauliX, self.Q2.pauliZ)
resultsXZ = simulate_sequence_stack(pulseSeqs, self.systemParams, self.rhoIn, simType='unitary')[0]
self.systemParams.measurement = np.kron(self.Q1.pauliY, self.Q2.pauliZ)
resultsYZ = simulate_sequence_stack(pulseSeqs, self.systemParams, self.rhoIn, simType='unitary')[0]
if plotResults:
plt.figure()
plt.plot(delays*1e6, resultsXZ)
plt.plot(delays*1e6, resultsYZ, 'g')
plt.legend(('XZ','YZ'))
plt.xlabel('Coupling Time')
plt.ylabel('Operator Expectation Value')
plt.title('ZZ Coupling Evolution After a X90 on Q1')
plt.show()
systemParams.add_interaction('Q1', 'Q2', 'FlipFlop', 4.3e6)
#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
crossCoupling12 = 0.67
crossCoupling21 = 0.67
#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 *
#Add a 2MHz ZZ interaction
systemParams.add_interaction('Q1', 'Q2', 'FlipFlop', 4.3e6)
#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
crossCoupling12 = 0.67
crossCoupling21 = 0.67
#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]))
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)
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 from Q1 drive to Q2
crossCoupling12 = 0.67
crossCoupling21 = 0.67
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)))
#Add the Q1 drive Hamiltonians
systemParams.add_control_ham(inphase=inPhaseHam, quadrature=quadratureHam)
systemParams.add_control_ham(inphase=inPhaseHam, quadrature=quadratureHam)
#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_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
#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