Examples for OptPulseProcessor¶
Author: Boxi Li (etamin1201@gmail.com)
from numpy import pi
from qutip import basis, fidelity, identity, sigmax, sigmaz, tensor
from qutip_qip.circuit import QubitCircuit
from qutip_qip.device import OptPulseProcessor
from qutip_qip.operations import expand_operator, toffoli
from qutip.ipynbtools import version_table
import qutip_qip
The qutip.OptPulseProcessor is a noisy quantum device simulator integrated with the optimal pulse algorithm from the qutip.control module. It is a subclass of qutip.Processor and is equipped with a method to find the optimal pulse sequence (hence the name OptPulseProcessor) for a qutip.QubitCircuit or a list of qutip.Qobj. For the user guide of qutip.Processor, please refer to the introductory guide.
Single-qubit gate¶
Like in the parent class Processor, we need to first define the available Hamiltonians in the system. The OptPulseProcessor has one more parameter, the drift Hamiltonian, which has no time-dependent coefficients and thus won't be optimized.
num_qubits = 1
# Drift Hamiltonian
H_d = sigmaz()
# The (single) control Hamiltonian
H_c = sigmax()
processor = OptPulseProcessor(num_qubits, drift=H_d)
processor.add_control(H_c, 0)
The method load_circuit calls qutip.control.optimize_pulse_unitary and returns the pulse coefficients.
qc = QubitCircuit(num_qubits)
qc.add_gate("SNOT", 0)
# This method calls optimize_pulse_unitary
tlist, coeffs = processor.load_circuit(
qc, min_grad=1e-20, init_pulse_type="RND", num_tslots=6,
evo_time=1, verbose=True
)
processor.plot_pulses(
title="Control pulse for the Hadamard gate", use_control_latex=False
);
********** Gate 0 ********** Final fidelity error 1.1894929485833927e-12 Final gradient normal 5.607322257959282e-06 Terminated due to Goal achieved Number of iterations 10
Like the Processor, the simulation is calculated with a QuTiP solver. The method run_state calls mesolve and returns the result. One can also add noise to observe the change in the fidelity, e.g. the t1 decoherence time.
rho0 = basis(2, 1)
plus = (basis(2, 0) + basis(2, 1)).unit()
minus = (basis(2, 0) - basis(2, 1)).unit()
result = processor.run_state(init_state=rho0)
print("Fidelity:", fidelity(result.states[-1], minus))
# add noise
processor.t1 = 40.0
result = processor.run_state(init_state=rho0)
print("Fidelity with qubit relaxation:", fidelity(result.states[-1], minus))
Fidelity: 0.9999999997365874 Fidelity with qubit relaxation: 0.9933448562237688
Multi-qubit gate¶
In the following example, we use OptPulseProcessor to find the optimal control pulse of a multi-qubit circuit. For simplicity, the circuit contains only one Toffoli gate.
toffoli()
We have single-qubit control $\sigma_x$ and $\sigma_z$, with the argument cyclic_permutation=True, it creates 3 operators each targeted on one qubit.
N = 3
H_d = tensor([identity(2)] * 3)
test_processor = OptPulseProcessor(N, H_d)
test_processor.add_control(sigmaz(), cyclic_permutation=True)
test_processor.add_control(sigmax(), cyclic_permutation=True)
The interaction is generated by $\sigma_x\sigma_x$ between the qubit 0 & 1 and qubit 1 & 2. expand_operator can be used to expand the operator to a larger dimension with given target qubits.
sxsx = tensor([sigmax(), sigmax()])
sxsx01 = expand_operator(sxsx, 3, targets=[0, 1])
sxsx12 = expand_operator(sxsx, 3, targets=[1, 2])
test_processor.add_control(sxsx01)
test_processor.add_control(sxsx12)
/home/runner/work/qutip-tutorials/qutip-tutorials/qutip-qip/src/qutip_qip/operations/gates.py:1267: DeprecationWarning: The function expand_operator has been generalized to arbitrary subsystems instead of only qubit systems.Please use the new signature e.g. expand_operator(oper, dims=[2, 3, 2, 2], targets=2) warnings.warn( /home/runner/work/qutip-tutorials/qutip-tutorials/qutip-qip/src/qutip_qip/operations/gates.py:1267: DeprecationWarning: The function expand_operator has been generalized to arbitrary subsystems instead of only qubit systems.Please use the new signature e.g. expand_operator(oper, dims=[2, 3, 2, 2], targets=2) warnings.warn(
Use the above defined control Hamiltonians, we now find the optimal pulse for the Toffoli gate with 6 time slots. Instead of a QubitCircuit, a list of operators can also be given as an input.
def get_control_latex():
"""
Get the labels for each Hamiltonian.
It is used in the method``plot_pulses``.
It is a 2-d nested list, in the plot,
a different color will be used for each sublist.
"""
return [
[r"$\sigma_z^%d$" % n for n in range(test_processor.num_qubits)],
[r"$\sigma_x^%d$" % n for n in range(test_processor.num_qubits)],
[r"$g_01$", r"$g_12$"],
]
test_processor.model.get_control_latex = get_control_latex
test_processor.dims = [2, 2, 2]
test_processor.load_circuit([toffoli()], num_tslots=6,
evo_time=1, verbose=True)
test_processor.plot_pulses(title="Contorl pulse for toffoli gate");
********** Gate 0 ********** Final fidelity error 0.07611888216651441 Final gradient normal 6.568348259402249e-06 Terminated due to function converged Number of iterations 216
Merging a quantum circuit¶
If there are multiple gates in the circuit, we can choose if we want to first merge them and then find the pulse for the merged unitary.
qc = QubitCircuit(3)
qc.add_gate("CNOT", controls=0, targets=2)
qc.add_gate("RX", targets=2, arg_value=pi / 4)
qc.add_gate("RY", targets=1, arg_value=pi / 8)
setting_args = {
"CNOT": {"num_tslots": 20, "evo_time": 3},
"RX": {"num_tslots": 2, "evo_time": 1},
"RY": {"num_tslots": 2, "evo_time": 1},
}
test_processor.load_circuit(
qc, merge_gates=False, setting_args=setting_args, verbose=True
)
fig, axes = test_processor.plot_pulses(
title="Control pulse for a each gate in the circuit", show_axis=True
)
axes[-1].set_xlabel("time");
********** Gate 0 ********** Final fidelity error 9.147571052858794e-07 Final gradient normal 1.1771662064694905e-05 Terminated due to function converged Number of iterations 325 ********** Gate 1 ********** Final fidelity error 9.677536549901333e-11 Final gradient normal 1.0541405237792527e-05 Terminated due to Goal achieved Number of iterations 9 ********** Gate 2 ********** Final fidelity error 8.065152989900071e-10 Final gradient normal 3.773022028771336e-06 Terminated due to function converged Number of iterations 25
In the above figure, the pulses from $t=0$ to $t=3$ are for the CNOT gate while the rest for are the two single qubits gates. The difference in the frequency of change is merely a result of our choice of evo_time. Here we can see that the three gates are carried out in sequence.
qc = QubitCircuit(3)
qc.add_gate("CNOT", controls=0, targets=2)
qc.add_gate("RX", targets=2, arg_value=pi / 4)
qc.add_gate("RY", targets=1, arg_value=pi / 8)
test_processor.load_circuit(
qc, merge_gates=True, verbose=True, num_tslots=20, evo_time=5
)
test_processor.plot_pulses(title="Control pulse for a \
merged unitary evolution");
********** Gate 0 ********** Final fidelity error 4.2431395841369124e-07 Final gradient normal 6.371637221281897e-05 Terminated due to function converged Number of iterations 262
In this figure there are no different stages, the three gates are first merged and then the algorithm finds the optimal pulse for the resulting unitary evolution.
print("qutip-qip version:", qutip_qip.version.version)
version_table()
qutip-qip version: 0.3.0.dev0+fa929ff
| Software | Version |
|---|---|
| QuTiP | 4.7.1 |
| Numpy | 1.22.4 |
| SciPy | 1.8.1 |
| matplotlib | 3.5.2 |
| Cython | 0.29.33 |
| Number of CPUs | 2 |
| BLAS Info | Generic |
| IPython | 8.11.0 |
| Python | 3.10.4 | packaged by conda-forge | (main, Mar 24 2022, 17:39:04) [GCC 10.3.0] |
| OS | posix [linux] |
| Wed Mar 15 08:11:25 2023 UTC | |