Author: Boxi Li (etamin1201@gmail.com)
In [1]:
from numpy import pi
from qutip.qip.device import OptPulseProcessor
from qutip.qip.circuit import QubitCircuit
from qutip.qip.operations import expand_operator, toffoli
from qutip.operators import sigmaz, sigmax, identity
from qutip.states import basis
from qutip.metrics import fidelity
from qutip.tensor import tensor
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 notebook.
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.
In [2]:
N = 1
# Drift Hamiltonian
H_d = sigmaz()
# The (single) control Hamiltonian
H_c = sigmax()
processor = OptPulseProcessor(N, drift=H_d)
processor.add_control(H_c, 0)
The method load_circuit calls qutip.control.optimize_pulse_unitary and returns the pulse coefficients.
In [3]:
qc = QubitCircuit(N)
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");
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.
In [4]:
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))
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.
In [5]:
toffoli()
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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.
In [6]:
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.
In [7]:
sxsx = tensor([sigmax(),sigmax()])
sxsx01 = expand_operator(sxsx, N=3, targets=[0,1])
sxsx12 = expand_operator(sxsx, N=3, targets=[1,2])
test_processor.add_control(sxsx01)
test_processor.add_control(sxsx12)
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. Different color in the figure represents different control pulses.
In [8]:
test_processor.load_circuit([toffoli()], num_tslots=6, evo_time=1, verbose=True);
test_processor.plot_pulses(title="Contorl pulse for toffoli gate");
In [9]:
qc = QubitCircuit(N=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)
In [10]:
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);
test_processor.plot_pulses(title="Control pulse for a each gate in the circuit");
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.
In [11]:
qc = QubitCircuit(N=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");
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.
In [12]:
from qutip.ipynbtools import version_table
version_table()
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