Tutorial¶

It is very simple to use CtrlQ for simulating a state-preparation on a Trasmon qubit device using analog pulses. This tutorial shows how to use CtrlQ and only consist of few steps:

from ctrlq import cvqe

# define a pulse using cvqe.pulse()
mypulse = cvqe.pulse()

# construct a device Hamiltonian using cvqe.transmon()
myham = cvqe.transmon(mham = molecule_hamiltonian) # see below for molecule_hamiltonian

# initialize control
myctrl = cvqe.control(mypulse, myham)

# perform a pulse optimization
myctrl.optimize()

Running CtrlQ consist of the following steps:

Construct molecular Hamiltonian in the qubit representation.

Define a pulse shape.

Construct a device Hamiltonian

Run ctrl-VQE.

Molecular Hamiltonian¶

Molecular Hamiltonian in the qubit representation can simply be supplied into cvqe.transmon() as a numpy.ndarray:

myham = cvqe.transmon(mham = MyMolecularHamilonian)

Qiskit package can be used to construct the molecular Hamiltonian. See the documentations for the package. If you have qiskit package installed, the molecular Hamiltonian for H ₂, HeH ⁺ and LiH molecular systems can be obtained from mole.molecule:

from mole import molecule

# set the bond distance in angstom using dist
# for H2
MyMolecularHamiltonian = molecule.h2(dist=0.75)

# for HeH+
MyMolecularHamiltonian = molecule.hehp(dist=1.0)

# for LiH
MyMolecularHamiltonian = molecule.lih(dist=1.5)

The molecular Hamiltonian of H ₂ and HeH ⁺ is mapped to two-qubits and LiH to four-qubits using the parity mapping and Z2Symmetries reduction.

Pulse shape¶

Pulse shapes can be defined using the cvqe.pulse class. Simply initialize as in the example above mypulse = cvqe.pulse(). The amplitudes, time segments and the frequencies are all random guess. To set the amplitudes, simply supply a list with the shape (No. of qubits, No. of time windows). To set the time segments, supply a list with shape (No. of qubits, No. of time windows - 1). And to set the frequencies, supply a list with shape (No. of qubits). As an example for a two-qubit case with four-time seqment square pulses:

from ctrlq import cvqe

# duration is the total pulse duration
mypulse = cvqe.pulse(nqubit = 2, nwindow = 4, duration = 10.0)

# set amplitudes
mypulse.amp = [[0.05, 0.04, 0.03, 0.02], # for qubit 1
               [0.03, 0.01, 0.05, 0.06]] # for qubit 2

# set time window
mypulse.tseq = [[2.3, 5.6, 6.1], # for qubit 1
                [1.0, 3.4, 5.6]] # for qubit 2

# set frequencies
mypulse.freq = [ 29.0, 31.0] # for two-qubits

Device Hamiltonian¶

The device Hamiltonian can be easily set using cvqe.transmon() as shown in the above example. Here, the molecular Hamiltonian mham is required as a numpy.ndarray. Furthermore, initial state other the default set by cvqe.transmon() can also be set:

from ctrq import cvqe
from mole.molecule import h2

# molecular Hamiltonian
cham = h2()

# pulse
mypulse = cvqe.pulse()

# construct a device Hamiltonian with 2-qubits and 3-levels
myham = cvqe.transmon(nqubit=2, nstate=3, mham=cham)

# use a non-default initial state of |1> |1>
myham.initialize_psi([1,1])

Run ctrl-VQE¶

To perform ctrl-VQE pulse optimization, use the cvqe.control() class. Set the time-evolution solver, either solver='ode' or solver='trotter' and also the time-step nstep=. The optimization can be then called using cvqe.control.optimize(). Also specify whether to use the normalize expectation value or an unnormalized one using normalize=True or normalize=False. To just achieve a state-preparation using a pulse and compute the expectation value of the molecular Hamiltonain, call cvqe.control.energy(). Here, again specify whether or not to return the normalize expectation value.

Now, we can run ctrl-VQE using a custom pulse shape:

from ctrlq import cvqe
from mole.molecule import h2

# molecular Hamiltonian
cham = h2()

# duration is the total pulse duration
mypulse = cvqe.pulse(nqubit = 2, nwindow = 4, duration = 10.0)

# set amplitudes
mypulse.amp = [[0.05, 0.04, 0.03, 0.02], # for qubit 1
               [0.03, 0.01, 0.05, 0.06]] # for qubit 2

# set time window
mypulse.tseq = [[2.3, 5.6, 6.1], # for qubit 1
                [1.0, 3.4, 5.6]] # for qubit 2

# set frequencies
mypulse.freq = [ 29.0, 31.0] # for two-qubits

# construct a device Hamiltonian with 2-qubits and 3-levels
myham = cvqe.transmon(nqubit=2, nstate=3, mham=cham)

# use a non-default initial state of |1> |1>
myham.initialize_psi([1,1])

# control class
myctrl = cvqe.control(mypulse, myham, nstep=1000, solver='trotter')

# measure the expectation value using mypulse
Energy, leakage = myctrl.energy(normalize=True)

# perform variational pulse optimization
Energy, leakage = myctrl.optimize(normalize=True)

Check /ctrlq/example for more examples.