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https://github.com/qiskit-community/qiskit-translations-staging
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qiskit-community
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from qiskit_nature.problems.second_quantization.lattice.lattices import LineLattice
from qiskit_nature.problems.second_quantization.lattice.models import FermiHubbardModel
line = LineLattice(2)
fermi = FermiHubbardModel.uniform_parameters(line, 2.0, 4.0, 3.0)
print(fermi.second_q_ops()) # Note: the trailing `s`
from qiskit_nature.second_q.hamiltonians.lattices import LineLattice
from qiskit_nature.second_q.hamiltonians import FermiHubbardModel
line = LineLattice(2)
fermi = FermiHubbardModel(line.uniform_parameters(2.0, 4.0), 3.0)
print(fermi.second_q_op()) # Note: NO trailing `s`
import numpy as np
from qiskit_nature.problems.second_quantization.lattice.models import FermiHubbardModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
fermi = FermiHubbardModel.from_parameters(interaction, 3.0)
print(fermi.second_q_ops()) # Note: the trailing `s`
import numpy as np
from qiskit_nature.second_q.hamiltonians.lattices import Lattice
from qiskit_nature.second_q.hamiltonians import FermiHubbardModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
lattice = Lattice.from_adjacency_matrix(interaction)
fermi = FermiHubbardModel(lattice, 3.0)
print(fermi.second_q_op()) # Note: NO trailing `s`
from qiskit_nature.problems.second_quantization.lattice.lattices import LineLattice
from qiskit_nature.problems.second_quantization.lattice.models import IsingModel
line = LineLattice(2)
ising = IsingModel.uniform_parameters(line, 2.0, 4.0)
print(ising.second_q_ops()) # Note: the trailing `s`
from qiskit_nature.second_q.hamiltonians.lattices import LineLattice
from qiskit_nature.second_q.hamiltonians import IsingModel
line = LineLattice(2)
ising = IsingModel(line.uniform_parameters(2.0, 4.0))
print(ising.second_q_op()) # Note: NO trailing `s`
import numpy as np
from qiskit_nature.problems.second_quantization.lattice.models import IsingModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
ising = IsingModel.from_parameters(interaction)
print(ising.second_q_ops()) # Note: the trailing `s`
import numpy as np
from qiskit_nature.second_q.hamiltonians.lattices import Lattice
from qiskit_nature.second_q.hamiltonians import IsingModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
lattice = Lattice.from_adjacency_matrix(interaction)
ising = IsingModel(lattice)
print(ising.second_q_op()) # Note: NO trailing `s`
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(
atom="H 0 0 0; H 0 0 0.735",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
problem = driver.run()
print(problem)
hamiltonian = problem.hamiltonian
coefficients = hamiltonian.electronic_integrals
print(coefficients.alpha)
second_q_op = hamiltonian.second_q_op()
print(second_q_op)
hamiltonian.nuclear_repulsion_energy # NOT included in the second_q_op above
problem.molecule
problem.reference_energy
problem.num_particles
problem.num_spatial_orbitals
problem.basis
problem.properties
problem.properties.particle_number
problem.properties.angular_momentum
problem.properties.magnetization
problem.properties.electronic_dipole_moment
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
from qiskit_nature.second_q.mappers import JordanWignerMapper
solver = GroundStateEigensolver(
JordanWignerMapper(),
NumPyMinimumEigensolver(),
)
result = solver.solve(problem)
print(result)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import GaussianForcesDriver
# if you ran Gaussian elsewhere and already have the output file
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
# if you want to run the Gaussian job from Qiskit
# driver = GaussianForcesDriver(
# ['#p B3LYP/6-31g Freq=(Anharm) Int=Ultrafine SCF=VeryTight',
# '',
# 'CO2 geometry optimization B3LYP/6-31g',
# '',
# '0 1',
# 'C -0.848629 2.067624 0.160992',
# 'O 0.098816 2.655801 -0.159738',
# 'O -1.796073 1.479446 0.481721',
# '',
# ''
from qiskit_nature.second_q.problems import HarmonicBasis
basis = HarmonicBasis([2, 2, 2, 2])
from qiskit_nature.second_q.problems import VibrationalStructureProblem
from qiskit_nature.second_q.mappers import DirectMapper
vibrational_problem = driver.run(basis=basis)
vibrational_problem.hamiltonian.truncation_order = 2
main_op, aux_ops = vibrational_problem.second_q_ops()
print(main_op)
qubit_mapper = DirectMapper()
qubit_op = qubit_mapper.map(main_op)
print(qubit_op)
basis = HarmonicBasis([3, 3, 3, 3])
vibrational_problem = driver.run(basis=basis)
vibrational_problem.hamiltonian.truncation_order = 2
main_op, aux_ops = vibrational_problem.second_q_ops()
qubit_mapper = DirectMapper()
qubit_op = qubit_mapper.map(main_op)
print(qubit_op)
# for simplicity, we will use the smaller basis again
vibrational_problem = driver.run(basis=HarmonicBasis([2, 2, 2, 2]))
vibrational_problem.hamiltonian.truncation_order = 2
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
solver = GroundStateEigensolver(
qubit_mapper,
NumPyMinimumEigensolver(filter_criterion=vibrational_problem.get_default_filter_criterion()),
)
result = solver.solve(vibrational_problem)
print(result)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(
atom="H 0 0 0; H 0 0 0.735",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
es_problem = driver.run()
from qiskit_nature.second_q.mappers import JordanWignerMapper
mapper = JordanWignerMapper()
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
numpy_solver = NumPyMinimumEigensolver()
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD
ansatz = UCCSD(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
initial_state=HartreeFock(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
),
)
vqe_solver = VQE(Estimator(), ansatz, SLSQP())
vqe_solver.initial_point = [0.0] * ansatz.num_parameters
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.circuit.library import TwoLocal
tl_circuit = TwoLocal(
rotation_blocks=["h", "rx"],
entanglement_blocks="cz",
entanglement="full",
reps=2,
parameter_prefix="y",
)
another_solver = VQE(Estimator(), tl_circuit, SLSQP())
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
calc = GroundStateEigensolver(mapper, vqe_solver)
res = calc.solve(es_problem)
print(res)
calc = GroundStateEigensolver(mapper, numpy_solver)
res = calc.solve(es_problem)
print(res)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.drivers import GaussianForcesDriver
from qiskit_nature.second_q.mappers import DirectMapper
from qiskit_nature.second_q.problems import HarmonicBasis
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
basis = HarmonicBasis([2, 2, 2, 2])
vib_problem = driver.run(basis=basis)
vib_problem.hamiltonian.truncation_order = 2
mapper = DirectMapper()
solver_without_filter = NumPyMinimumEigensolver()
solver_with_filter = NumPyMinimumEigensolver(
filter_criterion=vib_problem.get_default_filter_criterion()
)
gsc_wo = GroundStateEigensolver(mapper, solver_without_filter)
result_wo = gsc_wo.solve(vib_problem)
gsc_w = GroundStateEigensolver(mapper, solver_with_filter)
result_w = gsc_w.solve(vib_problem)
print(result_wo)
print("\n\n")
print(result_w)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(
atom="H 0 0 0; H 0 0 0.735",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
es_problem = driver.run()
from qiskit_nature.second_q.mappers import JordanWignerMapper
mapper = JordanWignerMapper()
from qiskit.algorithms.eigensolvers import NumPyEigensolver
numpy_solver = NumPyEigensolver(filter_criterion=es_problem.get_default_filter_criterion())
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.algorithms import GroundStateEigensolver, QEOM
from qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD
ansatz = UCCSD(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
initial_state=HartreeFock(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
),
)
estimator = Estimator()
# This first part sets the ground state solver
# see more about this part in the ground state calculation tutorial
solver = VQE(estimator, ansatz, SLSQP())
solver.initial_point = [0.0] * ansatz.num_parameters
gse = GroundStateEigensolver(mapper, solver)
# The qEOM algorithm is simply instantiated with the chosen ground state solver and Estimator primitive
qeom_excited_states_solver = QEOM(gse, estimator, "sd")
from qiskit_nature.second_q.algorithms import ExcitedStatesEigensolver
numpy_excited_states_solver = ExcitedStatesEigensolver(mapper, numpy_solver)
numpy_results = numpy_excited_states_solver.solve(es_problem)
qeom_results = qeom_excited_states_solver.solve(es_problem)
print(numpy_results)
print("\n\n")
print(qeom_results)
import numpy as np
def filter_criterion(eigenstate, eigenvalue, aux_values):
return np.isclose(aux_values["ParticleNumber"][0], 2.0)
new_numpy_solver = NumPyEigensolver(filter_criterion=filter_criterion)
new_numpy_excited_states_solver = ExcitedStatesEigensolver(mapper, new_numpy_solver)
new_numpy_results = new_numpy_excited_states_solver.solve(es_problem)
print(new_numpy_results)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.problems import ElectronicBasis
driver = PySCFDriver()
driver.run_pyscf()
ao_problem = driver.to_problem(basis=ElectronicBasis.AO)
print(ao_problem.basis)
ao_hamil = ao_problem.hamiltonian
print(ao_hamil.electronic_integrals.alpha)
from qiskit_nature.second_q.formats.qcschema_translator import get_ao_to_mo_from_qcschema
qcschema = driver.to_qcschema()
basis_transformer = get_ao_to_mo_from_qcschema(qcschema)
print(basis_transformer.initial_basis)
print(basis_transformer.final_basis)
mo_problem = basis_transformer.transform(ao_problem)
print(mo_problem.basis)
mo_hamil = mo_problem.hamiltonian
print(mo_hamil.electronic_integrals.alpha)
import numpy as np
from qiskit_nature.second_q.operators import ElectronicIntegrals
from qiskit_nature.second_q.problems import ElectronicBasis
from qiskit_nature.second_q.transformers import BasisTransformer
ao2mo_alpha = np.random.random((2, 2))
ao2mo_beta = np.random.random((2, 2))
basis_transformer = BasisTransformer(
ElectronicBasis.AO,
ElectronicBasis.MO,
ElectronicIntegrals.from_raw_integrals(ao2mo_alpha, h1_b=ao2mo_beta),
)
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(atom="Li 0 0 0; H 0 0 1.5")
full_problem = driver.run()
print(full_problem.molecule)
print(full_problem.num_particles)
print(full_problem.num_spatial_orbitals)
from qiskit_nature.second_q.transformers import FreezeCoreTransformer
fc_transformer = FreezeCoreTransformer()
fc_problem = fc_transformer.transform(full_problem)
print(fc_problem.num_particles)
print(fc_problem.num_spatial_orbitals)
print(fc_problem.hamiltonian.constants)
fc_transformer = FreezeCoreTransformer(remove_orbitals=[4, 5])
fc_problem = fc_transformer.transform(full_problem)
print(fc_problem.num_particles)
print(fc_problem.num_spatial_orbitals)
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(atom="Li 0 0 0; H 0 0 1.5")
full_problem = driver.run()
print(full_problem.num_particles)
print(full_problem.num_spatial_orbitals)
from qiskit_nature.second_q.transformers import ActiveSpaceTransformer
as_transformer = ActiveSpaceTransformer(2, 2)
as_problem = as_transformer.transform(full_problem)
print(as_problem.num_particles)
print(as_problem.num_spatial_orbitals)
print(as_problem.hamiltonian.electronic_integrals.alpha)
as_transformer = ActiveSpaceTransformer(2, 2, active_orbitals=[0, 4])
as_problem = as_transformer.transform(full_problem)
print(as_problem.num_particles)
print(as_problem.num_spatial_orbitals)
print(as_problem.hamiltonian.electronic_integrals.alpha)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver()
problem = driver.run()
fermionic_op = problem.hamiltonian.second_q_op()
from qiskit_nature.second_q.mappers import JordanWignerMapper
mapper = JordanWignerMapper()
qubit_jw_op = mapper.map(fermionic_op)
print(qubit_jw_op)
from qiskit_nature.second_q.mappers import ParityMapper
mapper = ParityMapper()
qubit_p_op = mapper.map(fermionic_op)
print(qubit_p_op)
mapper = ParityMapper(num_particles=problem.num_particles)
qubit_op = mapper.map(fermionic_op)
print(qubit_op)
tapered_mapper = problem.get_tapered_mapper(mapper)
print(type(tapered_mapper))
qubit_op = tapered_mapper.map(fermionic_op)
print(qubit_op)
from qiskit_nature.second_q.circuit.library import HartreeFock
hf_state = HartreeFock(2, (1, 1), JordanWignerMapper())
hf_state.draw()
from qiskit_nature.second_q.mappers import InterleavedQubitMapper
interleaved_mapper = InterleavedQubitMapper(JordanWignerMapper())
hf_state = HartreeFock(2, (1, 1), interleaved_mapper)
hf_state.draw()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.mappers import ParityMapper
from qiskit_nature.second_q.properties import ParticleNumber
from qiskit_nature.second_q.transformers import ActiveSpaceTransformer
bond_distance = 2.5 # in Angstrom
# specify driver
driver = PySCFDriver(
atom=f"Li 0 0 0; H 0 0 {bond_distance}",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
problem = driver.run()
# specify active space transformation
active_space_trafo = ActiveSpaceTransformer(
num_electrons=problem.num_particles, num_spatial_orbitals=3
)
# transform the electronic structure problem
problem = active_space_trafo.transform(problem)
# construct the parity mapper with 2-qubit reduction
qubit_mapper = ParityMapper(num_particles=problem.num_particles)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms.ground_state_solvers import GroundStateEigensolver
np_solver = NumPyMinimumEigensolver()
np_groundstate_solver = GroundStateEigensolver(qubit_mapper, np_solver)
np_result = np_groundstate_solver.solve(problem)
target_energy = np_result.total_energies[0]
print(np_result)
from qiskit.circuit.library import EfficientSU2
ansatz = EfficientSU2(num_qubits=4, reps=1, entanglement="linear", insert_barriers=True)
ansatz.decompose().draw("mpl", style="iqx")
import numpy as np
from qiskit.utils import algorithm_globals
# fix random seeds for reproducibility
np.random.seed(5)
algorithm_globals.random_seed = 5
from qiskit.algorithms.optimizers import SPSA
optimizer = SPSA(maxiter=100)
initial_point = np.random.random(ansatz.num_parameters)
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.primitives import Estimator
estimator = Estimator()
local_vqe = VQE(
estimator,
ansatz,
optimizer,
initial_point=initial_point,
)
local_vqe_groundstate_solver = GroundStateEigensolver(qubit_mapper, local_vqe)
local_vqe_result = local_vqe_groundstate_solver.solve(problem)
print(local_vqe_result)
from qiskit import IBMQ
IBMQ.load_account()
provider = IBMQ.get_provider(group="open") # replace by your runtime provider
backend = provider.get_backend("ibmq_qasm_simulator") # select a backend that supports the runtime
from qiskit_nature.runtime import VQEClient
runtime_vqe = VQEClient(
ansatz=ansatz,
optimizer=optimizer,
initial_point=initial_point,
provider=provider,
backend=backend,
shots=1024,
measurement_error_mitigation=True,
) # use a complete measurement fitter for error mitigation
runtime_vqe_groundstate_solver = GroundStateEigensolver(qubit_mapper, runtime_vqe)
runtime_vqe_result = runtime_vqe_groundstate_solver.solve(problem)
print(runtime_vqe_result)
runtime_result = runtime_vqe_result.raw_result
history = runtime_result.optimizer_history
loss = history["energy"]
import matplotlib.pyplot as plt
plt.rcParams["font.size"] = 14
# plot loss and reference value
plt.figure(figsize=(12, 6))
plt.plot(loss + runtime_vqe_result.nuclear_repulsion_energy, label="Runtime VQE")
plt.axhline(y=target_energy + 0.2, color="tab:red", ls=":", label="Target + 200mH")
plt.axhline(y=target_energy, color="tab:red", ls="--", label="Target")
plt.legend(loc="best")
plt.xlabel("Iteration")
plt.ylabel("Energy [H]")
plt.title("VQE energy");
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver()
problem = driver.run()
print(problem)
from qiskit_nature.second_q.problems import ElectronicBasis
driver.run_pyscf()
problem = driver.to_problem(basis=ElectronicBasis.MO, include_dipole=True)
print(problem.basis)
ao_problem = driver.to_problem(basis=ElectronicBasis.AO)
print(ao_problem.basis)
from qiskit_nature.second_q.formats.qcschema_translator import qcschema_to_problem
qcschema = driver.to_qcschema()
ao_problem = qcschema_to_problem(qcschema, basis=ElectronicBasis.AO)
from qiskit_nature.second_q.formats.qcschema_translator import get_ao_to_mo_from_qcschema
basis_transformer = get_ao_to_mo_from_qcschema(qcschema)
mo_problem = basis_transformer.transform(ao_problem)
print(mo_problem.basis)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.problems import BaseProblem
dummy_hamiltonian = None
base_problem = BaseProblem(dummy_hamiltonian)
print(base_problem.properties)
from qiskit_nature.second_q.properties import AngularMomentum
print("AngularMomentum is in problem.properties:", AngularMomentum in base_problem.properties)
print("Adding AngularMomentum to problem.properties...")
base_problem.properties.add(AngularMomentum(2))
print("AngularMomentum is in problem.properties:", AngularMomentum in base_problem.properties)
print("Discarding AngularMomentum from problem.properties...")
base_problem.properties.discard(AngularMomentum)
print("AngularMomentum is in problem.properties:", AngularMomentum in base_problem.properties)
from qiskit_nature.second_q.drivers import PySCFDriver
es_problem = PySCFDriver().run()
print(es_problem.properties.particle_number)
print(es_problem.properties.angular_momentum)
print(es_problem.properties.magnetization)
print(es_problem.properties.electronic_dipole_moment)
print(es_problem.properties.electronic_density)
from qiskit_nature.second_q.properties import ElectronicDensity
density = ElectronicDensity.from_orbital_occupation(
es_problem.orbital_occupations,
es_problem.orbital_occupations_b,
)
es_problem.properties.electronic_density = density
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from math import pi
import numpy as np
import rustworkx as rx
from qiskit_nature.second_q.hamiltonians.lattices import (
BoundaryCondition,
HyperCubicLattice,
Lattice,
LatticeDrawStyle,
LineLattice,
SquareLattice,
TriangularLattice,
)
from qiskit_nature.second_q.hamiltonians import FermiHubbardModel
num_nodes = 11
boundary_condition = BoundaryCondition.OPEN
line_lattice = LineLattice(num_nodes=num_nodes, boundary_condition=boundary_condition)
line_lattice.draw()
num_nodes = 11
boundary_condition = BoundaryCondition.PERIODIC
line_lattice = LineLattice(num_nodes=num_nodes, boundary_condition=boundary_condition)
line_lattice.draw()
line_lattice.draw_without_boundary()
num_nodes = 11
boundary_condition = BoundaryCondition.PERIODIC
edge_parameter = 1.0 + 1.0j
onsite_parameter = 1.0
line_lattice = LineLattice(
num_nodes=num_nodes,
edge_parameter=edge_parameter,
onsite_parameter=onsite_parameter,
boundary_condition=boundary_condition,
)
set(line_lattice.graph.weighted_edge_list())
line_lattice.to_adjacency_matrix()
line_lattice.to_adjacency_matrix(weighted=True)
rows = 5
cols = 4
boundary_condition = BoundaryCondition.OPEN
square_lattice = SquareLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
square_lattice.draw()
rows = 5
cols = 4
boundary_condition = (
BoundaryCondition.OPEN,
BoundaryCondition.PERIODIC,
) # open in the x-direction, periodic in the y-direction
square_lattice = SquareLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
square_lattice.draw()
rows = 5
cols = 4
edge_parameter = (1.0, 1.0 + 1.0j)
boundary_condition = (
BoundaryCondition.OPEN,
BoundaryCondition.PERIODIC,
) # open in the x-direction, periodic in the y-direction
onsite_parameter = 1.0
square_lattice = SquareLattice(
rows=rows,
cols=cols,
edge_parameter=edge_parameter,
onsite_parameter=onsite_parameter,
boundary_condition=boundary_condition,
)
set(square_lattice.graph.weighted_edge_list())
size = (3, 4, 5)
boundary_condition = (
BoundaryCondition.OPEN,
BoundaryCondition.OPEN,
BoundaryCondition.OPEN,
)
cubic_lattice = HyperCubicLattice(size=size, boundary_condition=boundary_condition)
# function for setting the positions
def indextocoord_3d(index: int, size: tuple, angle) -> list:
z = index // (size[0] * size[1])
a = index % (size[0] * size[1])
y = a // size[0]
x = a % size[0]
vec_x = np.array([1, 0])
vec_y = np.array([np.cos(angle), np.sin(angle)])
vec_z = np.array([0, 1])
return_coord = x * vec_x + y * vec_y + z * vec_z
return return_coord.tolist()
pos = dict([(index, indextocoord_3d(index, size, angle=pi / 4)) for index in range(np.prod(size))])
cubic_lattice.draw(style=LatticeDrawStyle(pos=pos))
rows = 4
cols = 3
boundary_condition = BoundaryCondition.OPEN
triangular_lattice = TriangularLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
triangular_lattice.draw()
rows = 4
cols = 3
boundary_condition = BoundaryCondition.PERIODIC
triangular_lattice = TriangularLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
triangular_lattice.draw()
graph = rx.PyGraph(multigraph=False) # multigraph shoud be False
graph.add_nodes_from(range(6))
weighted_edge_list = [
(0, 1, 1.0 + 1.0j),
(0, 2, -1.0),
(2, 3, 2.0),
(4, 2, -1.0 + 2.0j),
(4, 4, 3.0),
(2, 5, -1.0),
]
graph.add_edges_from(weighted_edge_list)
# make a lattice
general_lattice = Lattice(graph)
set(general_lattice.graph.weighted_edge_list())
general_lattice.draw()
general_lattice.draw(self_loop=True)
general_lattice.draw(self_loop=True, style=LatticeDrawStyle(with_labels=True))
square_lattice = SquareLattice(rows=5, cols=4, boundary_condition=BoundaryCondition.PERIODIC)
t = -1.0 # the interaction parameter
v = 0.0 # the onsite potential
u = 5.0 # the interaction parameter U
fhm = FermiHubbardModel(
square_lattice.uniform_parameters(
uniform_interaction=t,
uniform_onsite_potential=v,
),
onsite_interaction=u,
)
ham = fhm.second_q_op().simplify()
print(ham)
graph = rx.PyGraph(multigraph=False) # multiigraph shoud be False
graph.add_nodes_from(range(6))
weighted_edge_list = [
(0, 1, 1.0 + 1.0j),
(0, 2, -1.0),
(2, 3, 2.0),
(4, 2, -1.0 + 2.0j),
(4, 4, 3.0),
(2, 5, -1.0),
]
graph.add_edges_from(weighted_edge_list)
general_lattice = Lattice(graph) # the lattice whose weights are seen as the interaction matrix.
u = 5.0 # the interaction parameter U
fhm = FermiHubbardModel(lattice=general_lattice, onsite_interaction=u)
ham = fhm.second_q_op().simplify()
print(ham)
from qiskit_nature.second_q.problems import LatticeModelProblem
num_nodes = 4
boundary_condition = BoundaryCondition.OPEN
line_lattice = LineLattice(num_nodes=num_nodes, boundary_condition=boundary_condition)
fhm = FermiHubbardModel(
line_lattice.uniform_parameters(
uniform_interaction=t,
uniform_onsite_potential=v,
),
onsite_interaction=u,
)
lmp = LatticeModelProblem(fhm)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
from qiskit_nature.second_q.mappers import JordanWignerMapper
numpy_solver = NumPyMinimumEigensolver()
qubit_mapper = JordanWignerMapper()
calc = GroundStateEigensolver(qubit_mapper, numpy_solver)
res = calc.solve(lmp)
print(res)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
from qiskit_nature.second_q.hamiltonians import QuadraticHamiltonian
# create Hamiltonian
hermitian_part = np.array(
[
[1.0, 2.0, 0.0, 0.0],
[2.0, 1.0, 2.0, 0.0],
[0.0, 2.0, 1.0, 2.0],
[0.0, 0.0, 2.0, 1.0],
]
)
antisymmetric_part = np.array(
[
[0.0, 3.0, 0.0, 0.0],
[-3.0, 0.0, 3.0, 0.0],
[0.0, -3.0, 0.0, 3.0],
[0.0, 0.0, -3.0, 0.0],
]
)
constant = 4.0
hamiltonian = QuadraticHamiltonian(
hermitian_part=hermitian_part,
antisymmetric_part=antisymmetric_part,
constant=constant,
)
# convert it to a FermionicOp and print it
hamiltonian_ferm = hamiltonian.second_q_op()
print(hamiltonian_ferm)
# get the transformation matrix W and orbital energies {epsilon_j}
(
transformation_matrix,
orbital_energies,
transformed_constant,
) = hamiltonian.diagonalizing_bogoliubov_transform()
print(f"Shape of matrix W: {transformation_matrix.shape}")
print(f"Orbital energies: {orbital_energies}")
print(f"Transformed constant: {transformed_constant}")
from qiskit_nature.second_q.circuit.library import FermionicGaussianState
occupied_orbitals = (0, 2)
eig = np.sum(orbital_energies[list(occupied_orbitals)]) + transformed_constant
print(f"Eigenvalue: {eig}")
circuit = FermionicGaussianState(transformation_matrix, occupied_orbitals=occupied_orbitals)
circuit.draw("mpl")
from qiskit.quantum_info import Statevector
from qiskit_nature.second_q.mappers import JordanWignerMapper
# simulate the circuit to get the final state
state = np.array(Statevector(circuit))
# convert the Hamiltonian to a matrix
hamiltonian_jw = JordanWignerMapper().map(hamiltonian_ferm).to_matrix()
# check that the state is an eigenvector with the expected eigenvalue
np.testing.assert_allclose(hamiltonian_jw @ state, eig * state, atol=1e-8)
# create Hamiltonian
hermitian_part = np.array(
[
[1.0, 2.0, 0.0, 0.0],
[2.0, 1.0, 2.0, 0.0],
[0.0, 2.0, 1.0, 2.0],
[0.0, 0.0, 2.0, 1.0],
]
)
constant = 4.0
hamiltonian = QuadraticHamiltonian(
hermitian_part=hermitian_part,
constant=constant,
)
print(f"Hamiltonian conserves particle number: {hamiltonian.conserves_particle_number()}")
# get the transformation matrix W and orbital energies {epsilon_j}
(
transformation_matrix,
orbital_energies,
transformed_constant,
) = hamiltonian.diagonalizing_bogoliubov_transform()
print(f"Shape of matrix W: {transformation_matrix.shape}")
print(f"Orbital energies: {orbital_energies}")
print(f"Transformed constant: {transformed_constant}")
from qiskit_nature.second_q.circuit.library import SlaterDeterminant
occupied_orbitals = (0, 2)
eig = np.sum(orbital_energies[list(occupied_orbitals)]) + transformed_constant
print(f"Eigenvalue: {eig}")
circuit = SlaterDeterminant(transformation_matrix[list(occupied_orbitals)])
circuit.draw("mpl")
from qiskit_nature.second_q.circuit.library import BogoliubovTransform
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.quantum_info import random_hermitian, random_statevector, state_fidelity
from scipy.linalg import expm
# create Hamiltonian
n_modes = 5
hermitian_part = np.array(random_hermitian(n_modes))
hamiltonian = QuadraticHamiltonian(hermitian_part=hermitian_part)
# diagonalize Hamiltonian
(
transformation_matrix,
orbital_energies,
_,
) = hamiltonian.diagonalizing_bogoliubov_transform()
# set simulation time and construct time evolution circuit
time = 1.0
register = QuantumRegister(n_modes)
circuit = QuantumCircuit(register)
bog_circuit = BogoliubovTransform(transformation_matrix)
# change to the diagonal basis of the Hamiltonian
circuit.append(bog_circuit.inverse(), register)
# perform time evolution by applying z rotations
for q, energy in zip(register, orbital_energies):
circuit.rz(-energy * time, q)
# change back to the original basis
circuit.append(bog_circuit, register)
# simulate the circuit
initial_state = random_statevector(2**n_modes)
final_state = initial_state.evolve(circuit)
# compute the correct state by direct exponentiation
hamiltonian_jw = JordanWignerMapper().map(hamiltonian.second_q_op()).to_matrix()
exact_evolution_op = expm(-1j * time * hamiltonian_jw)
expected_state = exact_evolution_op @ np.array(initial_state)
# check that the simulated state is correct
fidelity = state_fidelity(final_state, expected_state)
np.testing.assert_allclose(fidelity, 1.0, atol=1e-8)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import display, clear_output
from qiskit.primitives import Estimator
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.observables_evaluator import estimate_observables
from qiskit.algorithms.optimizers import COBYLA, SLSQP
from qiskit.circuit import QuantumCircuit, Parameter
from qiskit.circuit.library import TwoLocal
from qiskit.quantum_info import Pauli, SparsePauliOp
from qiskit.utils import algorithm_globals
from qiskit_nature.second_q.operators import FermionicOp
from qiskit_nature.second_q.mappers import JordanWignerMapper
def kronecker_delta_function(n: int, m: int) -> int:
"""An implementation of the Kronecker delta function.
Args:
n (int): The first integer argument.
m (int): The second integer argument.
Returns:
Returns 1 if n = m, else returns 0.
"""
return int(n == m)
def create_deuteron_hamiltonian(
N: int, hbar_omega: float = 7.0, V_0: float = -5.68658111
) -> SparsePauliOp:
"""Creates a version of the Deuteron Hamiltonian as a qubit operator.
Args:
N (int): An integer number that represents the dimension of the
basis.
hbar_omega (float, optional): The value of the product of hbar and omega. Defaults to 7.0.
V_0 (float, optional): The value of the potential energy. Defaults to -5.68658111.
Returns:
SparsePauliOp: The qubit-space Hamiltonian that represents the Deuteron.
"""
hamiltonian_terms = {}
for m in range(N):
for n in range(N):
label = "+_{} -_{}".format(str(n), str(m))
coefficient_kinect = (hbar_omega / 2) * (
(2 * n + 3 / 2) * kronecker_delta_function(n, m)
- np.sqrt(n * (n + (1 / 2))) * kronecker_delta_function(n, m + 1)
- np.sqrt((n + 1) * (n + (3 / 2)) * kronecker_delta_function(n, m - 1))
)
hamiltonian_terms[label] = coefficient_kinect
coefficient_potential = (
V_0 * kronecker_delta_function(n, 0) * kronecker_delta_function(n, m)
)
hamiltonian_terms[label] += coefficient_potential
hamiltonian = FermionicOp(hamiltonian_terms, num_spin_orbitals=N)
mapper = JordanWignerMapper()
qubit_hamiltonian = mapper.map(hamiltonian)
if not isinstance(qubit_hamiltonian, SparsePauliOp):
qubit_hamiltonian = qubit_hamiltonian.primitive
return qubit_hamiltonian
deuteron_hamiltonians = [create_deuteron_hamiltonian(i) for i in range(1, 5)]
for i, hamiltonian in enumerate(deuteron_hamiltonians):
print("Deuteron Hamiltonian: H_{}".format(i + 1))
print(hamiltonian)
print("\n")
theta = Parameter(r"$\theta$")
eta = Parameter(r"$\eta$")
wavefunction = QuantumCircuit(1)
wavefunction.ry(theta, 0)
wavefunction.draw("mpl")
wavefunction2 = QuantumCircuit(2)
wavefunction2.x(0)
wavefunction2.ry(theta, 1)
wavefunction2.cx(1, 0)
wavefunction2.draw("mpl")
wavefunction3 = QuantumCircuit(3)
wavefunction3.x(0)
wavefunction3.ry(eta, 1)
wavefunction3.ry(theta, 2)
wavefunction3.cx(2, 0)
wavefunction3.cx(0, 1)
wavefunction3.ry(-eta, 1)
wavefunction3.cx(0, 1)
wavefunction3.cx(1, 0)
wavefunction3.draw("mpl")
ansatz = [wavefunction, wavefunction2, wavefunction3]
reference_values = []
print("Exact binding energies calculated through numpy.linalg.eigh \n")
for i, hamiltonian in enumerate(deuteron_hamiltonians):
eigenvalues, eigenstates = np.linalg.eigh(hamiltonian.to_matrix())
reference_values.append(eigenvalues[0])
print("Exact binding energy for H_{}: {}".format(i + 1, eigenvalues[0]))
print(
"Results using Estimator for H_1, H_2 and H_3 with the ansatz given in the reference paper \n"
)
for i in range(3):
seed = 42
algorithm_globals.random_seed = seed
vqe = VQE(Estimator(), ansatz=ansatz[i], optimizer=SLSQP())
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
binding_energy = vqe_result.optimal_value
print("Binding energy for H_{}: {} MeV".format(i + 1, binding_energy))
def callback(eval_count, parameters, mean, std):
# Overwrites the same line when printing
display("Evaluation: {}, Energy: {}, Std: {}".format(eval_count, mean, std))
clear_output(wait=True)
counts.append(eval_count)
values.append(mean)
params.append(parameters)
deviation.append(std)
plots = []
for i in range(3):
counts = []
values = []
params = []
deviation = []
seed = 42
algorithm_globals.random_seed = seed
vqe = VQE(Estimator(), ansatz=ansatz[i], optimizer=COBYLA(), callback=callback)
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
plots.append([counts, values])
fig, ax = plt.subplots(nrows=3, ncols=1)
fig.set_size_inches((12, 12))
for i, plot in enumerate(plots):
ax[i].plot(plot[0], plot[1], "o-", label="COBYLA")
ax[i].axhline(
y=reference_values[i],
color="k",
linestyle="--",
label=f"Reference Value: {reference_values[i]}",
)
ax[i].legend()
ax[i].set_xlabel("Cost Function Evaluations", fontsize=15)
ax[i].set_ylabel(r"$\langle H_{} \rangle$ - Energy (MeV)".format(i + 1), fontsize=15)
plt.show()
twolocal_ansatzes = []
for i in range(1, 5):
ansatz = TwoLocal(
deuteron_hamiltonians[i - 1].num_qubits,
["rz", "ry"],
"cx",
entanglement="full",
reps=i,
initial_state=None,
)
twolocal_ansatzes.append(ansatz)
print("Results using Estimator for H_1, H_2, H_3 and H_4 with TwoLocal ansatz \n")
seed = 42
algorithm_globals.random_seed = seed
for i in range(4):
vqe = VQE(Estimator(), ansatz=twolocal_ansatzes[i], optimizer=SLSQP())
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
binding_energy = vqe_result.optimal_value
print("Binding energy for H_{}:".format(i + 1), binding_energy, "MeV")
seed = 42
algorithm_globals.random_seed = seed
plots_tl = []
for i in range(4):
counts = []
values = []
params = []
deviation = []
vqe = VQE(
Estimator(),
ansatz=twolocal_ansatzes[i],
optimizer=SLSQP(),
callback=callback,
)
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
plots_tl.append([counts, values])
fig, ax = plt.subplots(nrows=4, ncols=1)
fig.set_size_inches((15, 15))
for i, plot in enumerate(plots_tl):
ax[i].plot(plot[0], plot[1], "o-", label="COBYLA")
ax[i].axhline(
y=reference_values[i],
color="k",
linestyle="--",
label=f"Reference Value: {reference_values[i]}",
)
ax[i].legend()
ax[i].set_xlabel("Cost Function Evaluations", fontsize=15)
ax[i].set_ylabel(r"$\langle H_{} \rangle$ - Energy (MeV)".format(i + 1), fontsize=15)
plt.show()
def calculate_observables_exp_values(
quantum_circuit: QuantumCircuit, observables: list, angles: list
) -> list:
"""Calculate the expectation value of an observable given the quantum
circuit that represents the wavefunction and a list of parameters.
Args:
quantum_circuit (QuantumCircuit): A parameterized quantum circuit
that represents the wavefunction of the system.
observables (list): A list containing the observables that we want
to know the expectation values.
angles (list): A list with the values that will be used in the
'bind_parameters' method.
Returns:
list_exp_values (list): A list containing the expectation values
of the observables given as input.
"""
list_exp_values = []
for observable in observables:
exp_values = []
for angle in angles:
qc = quantum_circuit.bind_parameters({theta: angle})
result = estimate_observables(
Estimator(),
quantum_state=qc,
observables=[observable],
)
exp_values.append(result[0][0])
list_exp_values.append(exp_values)
return list_exp_values
angles = list(np.linspace(-np.pi, np.pi, 100))
observables = [
Pauli("IZ"),
Pauli("ZI"),
Pauli("XX"),
Pauli("YY"),
deuteron_hamiltonians[1],
]
h2_observables_exp_values = calculate_observables_exp_values(wavefunction2, observables, angles)
fig, ax = plt.subplots(nrows=2, ncols=1)
fig.set_size_inches((12, 12))
ax[0].plot(angles, h2_observables_exp_values[0], "o", label=r"$Z_0$")
ax[0].plot(angles, h2_observables_exp_values[1], "o", label=r"$Z_1$")
ax[0].plot(angles, h2_observables_exp_values[2], "o", label=r"$X_0X_1$")
ax[0].plot(angles, h2_observables_exp_values[3], "o", label=r"$Y_0Y_1$")
ax[0].axhline(
y=1,
color="k",
linestyle="--",
)
ax[0].axhline(y=-1, color="k", linestyle="--")
ax[0].legend()
ax[0].set_xlabel(r"Theta - $\theta$", fontsize=15)
ax[0].set_ylabel(r"$\langle O \rangle $ - Operator Expectation Value", fontsize=15)
ax[0].set_xticks(
[-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi],
labels=[r"$-\pi$", r"$-\pi/2$", "0", r"$\pi/2$", r"$\pi$"],
)
ax[0].set_title(
r"Expectation value of the observables $Z_0$, $Z_1$, $X_0X_1$ and $Y_0Y_1$ when we vary $\theta$ in the ansatz.",
fontsize=15,
)
ax[1].plot(angles, h2_observables_exp_values[4], "o")
ax[1].axhline(
y=reference_values[1],
color="k",
linestyle="--",
label="Binding Energy: {} MeV".format(np.round(reference_values[1], 3)),
)
ax[1].legend()
ax[1].set_xlabel(r"Theta - $\theta$", fontsize=15)
ax[1].set_ylabel(r"$\langle H_2 \rangle $ - Energy (MeV)", fontsize=15)
ax[1].set_xticks(
[-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi],
labels=[r"$-\pi$", r"$-\pi/2$", "0", r"$\pi/2$", r"$\pi$"],
)
ax[1].set_title(
r"Behavior of the expectation value of $H_2$ when we vary $\theta$ in the ansatz.", fontsize=15
)
plt.show()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.mappers.second_quantization import LogarithmicMapper
mapper = LogarithmicMapper(2)
from qiskit_nature.second_q.mappers import LogarithmicMapper
mapper = LogarithmicMapper(2)
from qiskit_nature.second_q.mappers import LogarithmicMapper
mapper = LogarithmicMapper(padding=2)
from qiskit_nature.circuit.library import HartreeFock
from qiskit_nature.converters.second_quantization import QubitConverter
from qiskit_nature.mappers.second_quantization import JordanWignerMapper
converter = QubitConverter(JordanWignerMapper())
init_state = HartreeFock(num_spin_orbitals=6, num_particles=(2, 1), qubit_converter=converter)
print(init_state.draw())
from qiskit_nature.second_q.circuit.library import HartreeFock
from qiskit_nature.second_q.mappers import JordanWignerMapper, QubitConverter
converter = QubitConverter(JordanWignerMapper())
init_state = HartreeFock(num_spatial_orbitals=3, num_particles=(2, 1), qubit_converter=converter)
print(init_state.draw())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.circuit.library import UCCSD
ansatz = UCCSD()
ansatz.num_spin_orbitals = 10
from qiskit_nature.second_q.circuit.library import UCCSD
ansatz = UCCSD()
ansatz.num_spatial_orbitals = 5
from qiskit_nature.circuit.library import UCC, UVCC
ucc = UCC(qubit_converter=None, num_particles=None, num_spin_orbitals=None, excitations=None)
uvcc = UVCC(qubit_converter=None, num_modals=None, excitations=None)
from qiskit_nature.second_q.circuit.library import UCC, UVCC
ucc = UCC(num_spatial_orbitals=None, num_particles=None, excitations=None, qubit_converter=None)
uvcc = UVCC(num_modals=None, excitations=None, qubit_converter=None)
from qiskit_nature.circuit.library import HartreeFock, VSCF
from qiskit_nature.converters.second_quantization import QubitConverter
from qiskit_nature.mappers.second_quantization import DirectMapper, JordanWignerMapper
hf = HartreeFock(
num_spin_orbitals=4, num_particles=(1, 1), qubit_converter=QubitConverter(JordanWignerMapper())
)
vscf = VSCF(num_modals=[2, 2])
from qiskit_nature.second_q.circuit.library import HartreeFock, VSCF
from qiskit_nature.second_q.mappers import DirectMapper, JordanWignerMapper, QubitConverter
hf = HartreeFock()
hf.num_spatial_orbitals = 2
hf.num_particles = (1, 1)
hf.qubit_converter = QubitConverter(JordanWignerMapper())
vscf = VSCF()
vscf.num_modals = [2, 2]
from qiskit.providers.basicaer import BasicAer
from qiskit.utils import QuantumInstance
from qiskit_nature.algorithms.ground_state_solvers import VQEUCCFactory
quantum_instance = QuantumInstance(BasicAer.get_backend("statevector_simulator"))
vqe_factory = VQEUCCFactory(quantum_instance=quantum_instance)
from qiskit.algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.circuit.library import UCCSD
from qiskit_nature.second_q.algorithms.ground_state_solvers import VQEUCCFactory
estimator = Estimator()
ansatz = UCCSD()
optimizer = SLSQP()
vqe_factory = VQEUCCFactory(estimator, ansatz, optimizer)
from qiskit_nature.algorithms.ground_state_solvers import GroundStateEigensolver, VQEUCCFactory
from qiskit_nature.algorithms.excited_states_solvers import QEOM
from qiskit_nature.converters.second_quantization import QubitConverter
from qiskit_nature.mappers.second_quantization import JordanWignerMapper
vqe_factory = VQEUCCFactory()
converter = QubitConverter(JordanWignerMapper())
ground_state_solver = GroundStateEigensolver(converter, vqe_factory)
qeom = QEOM(ground_state_solver)
from qiskit.algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.circuit.library import UCCSD
from qiskit_nature.second_q.algorithms.ground_state_solvers import (
GroundStateEigensolver,
VQEUCCFactory,
)
from qiskit_nature.second_q.algorithms.excited_states_solvers import QEOM
from qiskit_nature.second_q.mappers import JordanWignerMapper, QubitConverter
estimator = Estimator()
ansatz = UCCSD()
optimizer = SLSQP()
vqe_factory = VQEUCCFactory(estimator, ansatz, optimizer)
converter = QubitConverter(JordanWignerMapper())
ground_state_solver = GroundStateEigensolver(converter, vqe_factory)
qeom = QEOM(ground_state_solver, estimator)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.drivers import Molecule
from qiskit_nature.drivers.second_quantization import (
ElectronicStructureDriverType,
ElectronicStructureMoleculeDriver,
PySCFDriver,
)
from qiskit_nature.problems.second_quantization import ElectronicStructureProblem
from qiskit_nature.transformers.second_quantization.electronic import FreezeCoreTransformer
from qiskit_nature.settings import settings
settings.dict_aux_operators = True
molecule = Molecule(
geometry=[["H", [0.0, 0.0, 0.0]], ["H", [0.0, 0.0, 0.735]]], charge=0, multiplicity=1
)
driver = ElectronicStructureMoleculeDriver(
molecule, basis="sto3g", driver_type=ElectronicStructureDriverType.PYSCF
)
# or equivalently:
driver = PySCFDriver.from_molecule(molecule, basis="sto3g")
transformer = FreezeCoreTransformer()
problem = ElectronicStructureProblem(driver, transformers=[transformer])
# Note: at this point, `driver.run()` has NOT been called yet. We can trigger this indirectly like so:
second_q_ops = problem.second_q_ops()
hamiltonian = second_q_ops["ElectronicEnergy"]
print(hamiltonian)
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.formats.molecule_info import MoleculeInfo
from qiskit_nature.second_q.transformers import FreezeCoreTransformer
molecule = MoleculeInfo(["H", "H"], [(0.0, 0.0, 0.0), (0.0, 0.0, 0.735)], charge=0, multiplicity=1)
driver = PySCFDriver.from_molecule(molecule, basis="sto3g")
# this is now done explicitly
problem = driver.run()
transformer = FreezeCoreTransformer()
# and you also apply transformers explicitly
problem = transformer.transform(problem)
hamiltonian = problem.hamiltonian.second_q_op()
print("\n".join(str(hamiltonian).splitlines()[:10] + ["..."]))
from qiskit_nature.drivers import Molecule
from qiskit_nature.drivers.second_quantization import PySCFDriver
molecule = Molecule(
geometry=[["H", [0.0, 0.0, 0.0]], ["H", [0.0, 0.0, 0.735]]], charge=0, multiplicity=1
)
driver = PySCFDriver.from_molecule(molecule)
result = driver.run()
print(type(result))
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.formats.molecule_info import MoleculeInfo
molecule = MoleculeInfo(["H", "H"], [(0.0, 0.0, 0.0), (0.0, 0.0, 0.735)], charge=0, multiplicity=1)
driver = PySCFDriver.from_molecule(molecule, basis="sto3g")
result = driver.run()
print(type(result))
from qiskit_nature.drivers.second_quantization import FCIDumpDriver
path_to_fcidump = "aux_files/h2.fcidump"
driver = FCIDumpDriver(path_to_fcidump)
result = driver.run()
print(type(result))
from qiskit_nature.second_q.formats.fcidump import FCIDump
path_to_fcidump = "aux_files/h2.fcidump"
fcidump = FCIDump.from_file(path_to_fcidump)
print(type(fcidump))
from qiskit_nature.second_q.formats.fcidump_translator import fcidump_to_problem
problem = fcidump_to_problem(fcidump)
print(type(problem))
from qiskit_nature.drivers.second_quantization import PySCFDriver
from qiskit_nature.transformers.second_quantization.electronic import FreezeCoreTransformer
transformer = FreezeCoreTransformer()
driver = PySCFDriver()
transformed_result = transformer.transform(driver.run())
print(type(transformed_result))
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.transformers import FreezeCoreTransformer
transformer = FreezeCoreTransformer()
driver = PySCFDriver()
transformed_result = transformer.transform(driver.run())
print(type(transformed_result))
from qiskit_nature.drivers.second_quantization import PySCFDriver
from qiskit_nature.problems.second_quantization.electronic import ElectronicStructureProblem
from qiskit_nature.transformers.second_quantization.electronic import FreezeCoreTransformer
driver = PySCFDriver()
transformer = FreezeCoreTransformer()
problem = ElectronicStructureProblem(driver, transformers=[transformer])
# we trigger driver.run() implicitly like so:
second_q_ops = problem.second_q_ops()
hamiltonian_op = second_q_ops.pop("ElectronicEnergy")
aux_ops = second_q_ops
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.transformers import FreezeCoreTransformer
driver = PySCFDriver()
problem = driver.run()
transformer = FreezeCoreTransformer()
problem = transformer.transform(problem)
hamiltonian_op, aux_ops = problem.second_q_ops()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.drivers.second_quantization import GaussianForcesDriver
from qiskit_nature.problems.second_quantization import VibrationalStructureProblem
from qiskit_nature.settings import settings
settings.dict_aux_operators = True
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
problem = VibrationalStructureProblem(driver, num_modals=[2, 2, 3, 4], truncation_order=2)
# Note: at this point, `driver.run()` has NOT been called yet. We can trigger this indirectly like so:
second_q_ops = problem.second_q_ops()
hamiltonian = second_q_ops["VibrationalEnergy"]
print("\n".join(str(hamiltonian).splitlines()[:10] + ["..."]))
from qiskit_nature.second_q.drivers import GaussianForcesDriver
from qiskit_nature.second_q.problems import HarmonicBasis
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
basis = HarmonicBasis(num_modals=[2, 2, 3, 4])
# this is now done explicitly and already requires the basis
problem = driver.run(basis=basis)
problem.hamiltonian.truncation_order = 2
hamiltonian = problem.hamiltonian.second_q_op()
print("\n".join(str(hamiltonian).splitlines()[:10] + ["..."]))
from qiskit_nature.drivers.second_quantization import GaussianLogResult
from qiskit_nature.properties.second_quantization.vibrational.bases import HarmonicBasis
from qiskit_nature.settings import settings
settings.dict_aux_operators = True
log_result = GaussianLogResult("aux_files/CO2_freq_B3LYP_631g.log")
hamiltonian = log_result.get_vibrational_energy()
print(hamiltonian)
hamiltonian.basis = HarmonicBasis([2, 2, 3, 4])
op = hamiltonian.second_q_ops()["VibrationalEnergy"]
print("\n".join(str(op).splitlines()[:10] + ["..."]))
from qiskit_nature.second_q.drivers import GaussianLogResult
from qiskit_nature.second_q.formats import watson_to_problem
from qiskit_nature.second_q.problems import HarmonicBasis
log_result = GaussianLogResult("aux_files/CO2_freq_B3LYP_631g.log")
watson = log_result.get_watson_hamiltonian()
print(watson)
basis = HarmonicBasis(num_modals=[2, 2, 3, 4])
problem = watson_to_problem(watson, basis)
hamiltonian = problem.hamiltonian.second_q_op()
print("\n".join(str(hamiltonian).splitlines()[:10] + ["..."]))
from qiskit_nature.drivers.second_quantization import GaussianForcesDriver
from qiskit_nature.problems.second_quantization import VibrationalStructureProblem
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
problem = VibrationalStructureProblem(driver, num_modals=[2, 2, 3, 4], truncation_order=2)
# we trigger driver.run() implicitly like so:
second_q_ops = problem.second_q_ops()
hamiltonian_op = second_q_ops.pop("VibrationalEnergy")
aux_ops = second_q_ops
from qiskit_nature.second_q.drivers import GaussianForcesDriver
from qiskit_nature.second_q.problems import HarmonicBasis
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
basis = HarmonicBasis(num_modals=[2, 2, 3, 4])
problem = driver.run(basis=basis)
problem.hamiltonian.truncation_order = 2
hamiltonian_op, aux_ops = problem.second_q_ops()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.problems.second_quantization.lattice.lattices import LineLattice
from qiskit_nature.problems.second_quantization.lattice.models import FermiHubbardModel
line = LineLattice(2)
fermi = FermiHubbardModel.uniform_parameters(line, 2.0, 4.0, 3.0)
print(fermi.second_q_ops()) # Note: the trailing `s`
from qiskit_nature.second_q.hamiltonians.lattices import LineLattice
from qiskit_nature.second_q.hamiltonians import FermiHubbardModel
line = LineLattice(2)
fermi = FermiHubbardModel(line.uniform_parameters(2.0, 4.0), 3.0)
print(fermi.second_q_op()) # Note: NO trailing `s`
import numpy as np
from qiskit_nature.problems.second_quantization.lattice.models import FermiHubbardModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
fermi = FermiHubbardModel.from_parameters(interaction, 3.0)
print(fermi.second_q_ops()) # Note: the trailing `s`
import numpy as np
from qiskit_nature.second_q.hamiltonians.lattices import Lattice
from qiskit_nature.second_q.hamiltonians import FermiHubbardModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
lattice = Lattice.from_adjacency_matrix(interaction)
fermi = FermiHubbardModel(lattice, 3.0)
print(fermi.second_q_op()) # Note: NO trailing `s`
from qiskit_nature.problems.second_quantization.lattice.lattices import LineLattice
from qiskit_nature.problems.second_quantization.lattice.models import IsingModel
line = LineLattice(2)
ising = IsingModel.uniform_parameters(line, 2.0, 4.0)
print(ising.second_q_ops()) # Note: the trailing `s`
from qiskit_nature.second_q.hamiltonians.lattices import LineLattice
from qiskit_nature.second_q.hamiltonians import IsingModel
line = LineLattice(2)
ising = IsingModel(line.uniform_parameters(2.0, 4.0))
print(ising.second_q_op()) # Note: NO trailing `s`
import numpy as np
from qiskit_nature.problems.second_quantization.lattice.models import IsingModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
ising = IsingModel.from_parameters(interaction)
print(ising.second_q_ops()) # Note: the trailing `s`
import numpy as np
from qiskit_nature.second_q.hamiltonians.lattices import Lattice
from qiskit_nature.second_q.hamiltonians import IsingModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
lattice = Lattice.from_adjacency_matrix(interaction)
ising = IsingModel(lattice)
print(ising.second_q_op()) # Note: NO trailing `s`
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(
atom="H 0 0 0; H 0 0 0.735",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
problem = driver.run()
print(problem)
hamiltonian = problem.hamiltonian
coefficients = hamiltonian.electronic_integrals
print(coefficients.alpha)
second_q_op = hamiltonian.second_q_op()
print(second_q_op)
hamiltonian.nuclear_repulsion_energy # NOT included in the second_q_op above
problem.molecule
problem.reference_energy
problem.num_particles
problem.num_spatial_orbitals
problem.basis
problem.properties
problem.properties.particle_number
problem.properties.angular_momentum
problem.properties.magnetization
problem.properties.electronic_dipole_moment
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
from qiskit_nature.second_q.mappers import JordanWignerMapper
solver = GroundStateEigensolver(
JordanWignerMapper(),
NumPyMinimumEigensolver(),
)
result = solver.solve(problem)
print(result)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import GaussianForcesDriver
# if you ran Gaussian elsewhere and already have the output file
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
# if you want to run the Gaussian job from Qiskit
# driver = GaussianForcesDriver(
# ['#p B3LYP/6-31g Freq=(Anharm) Int=Ultrafine SCF=VeryTight',
# '',
# 'CO2 geometry optimization B3LYP/6-31g',
# '',
# '0 1',
# 'C -0.848629 2.067624 0.160992',
# 'O 0.098816 2.655801 -0.159738',
# 'O -1.796073 1.479446 0.481721',
# '',
# ''
from qiskit_nature.second_q.problems import HarmonicBasis
basis = HarmonicBasis([2, 2, 2, 2])
from qiskit_nature.second_q.problems import VibrationalStructureProblem
from qiskit_nature.second_q.mappers import DirectMapper
vibrational_problem = driver.run(basis=basis)
vibrational_problem.hamiltonian.truncation_order = 2
main_op, aux_ops = vibrational_problem.second_q_ops()
print(main_op)
qubit_mapper = DirectMapper()
qubit_op = qubit_mapper.map(main_op)
print(qubit_op)
basis = HarmonicBasis([3, 3, 3, 3])
vibrational_problem = driver.run(basis=basis)
vibrational_problem.hamiltonian.truncation_order = 2
main_op, aux_ops = vibrational_problem.second_q_ops()
qubit_mapper = DirectMapper()
qubit_op = qubit_mapper.map(main_op)
print(qubit_op)
# for simplicity, we will use the smaller basis again
vibrational_problem = driver.run(basis=HarmonicBasis([2, 2, 2, 2]))
vibrational_problem.hamiltonian.truncation_order = 2
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
solver = GroundStateEigensolver(
qubit_mapper,
NumPyMinimumEigensolver(filter_criterion=vibrational_problem.get_default_filter_criterion()),
)
result = solver.solve(vibrational_problem)
print(result)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(
atom="H 0 0 0; H 0 0 0.735",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
es_problem = driver.run()
from qiskit_nature.second_q.mappers import JordanWignerMapper
mapper = JordanWignerMapper()
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
numpy_solver = NumPyMinimumEigensolver()
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD
ansatz = UCCSD(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
initial_state=HartreeFock(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
),
)
vqe_solver = VQE(Estimator(), ansatz, SLSQP())
vqe_solver.initial_point = [0.0] * ansatz.num_parameters
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.circuit.library import TwoLocal
tl_circuit = TwoLocal(
rotation_blocks=["h", "rx"],
entanglement_blocks="cz",
entanglement="full",
reps=2,
parameter_prefix="y",
)
another_solver = VQE(Estimator(), tl_circuit, SLSQP())
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
calc = GroundStateEigensolver(mapper, vqe_solver)
res = calc.solve(es_problem)
print(res)
calc = GroundStateEigensolver(mapper, numpy_solver)
res = calc.solve(es_problem)
print(res)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.drivers import GaussianForcesDriver
from qiskit_nature.second_q.mappers import DirectMapper
from qiskit_nature.second_q.problems import HarmonicBasis
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
basis = HarmonicBasis([2, 2, 2, 2])
vib_problem = driver.run(basis=basis)
vib_problem.hamiltonian.truncation_order = 2
mapper = DirectMapper()
solver_without_filter = NumPyMinimumEigensolver()
solver_with_filter = NumPyMinimumEigensolver(
filter_criterion=vib_problem.get_default_filter_criterion()
)
gsc_wo = GroundStateEigensolver(mapper, solver_without_filter)
result_wo = gsc_wo.solve(vib_problem)
gsc_w = GroundStateEigensolver(mapper, solver_with_filter)
result_w = gsc_w.solve(vib_problem)
print(result_wo)
print("\n\n")
print(result_w)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(
atom="H 0 0 0; H 0 0 0.735",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
es_problem = driver.run()
from qiskit_nature.second_q.mappers import JordanWignerMapper
mapper = JordanWignerMapper()
from qiskit.algorithms.eigensolvers import NumPyEigensolver
numpy_solver = NumPyEigensolver(filter_criterion=es_problem.get_default_filter_criterion())
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.algorithms import GroundStateEigensolver, QEOM
from qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD
ansatz = UCCSD(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
initial_state=HartreeFock(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
),
)
estimator = Estimator()
# This first part sets the ground state solver
# see more about this part in the ground state calculation tutorial
solver = VQE(estimator, ansatz, SLSQP())
solver.initial_point = [0.0] * ansatz.num_parameters
gse = GroundStateEigensolver(mapper, solver)
# The qEOM algorithm is simply instantiated with the chosen ground state solver and Estimator primitive
qeom_excited_states_solver = QEOM(gse, estimator, "sd")
from qiskit_nature.second_q.algorithms import ExcitedStatesEigensolver
numpy_excited_states_solver = ExcitedStatesEigensolver(mapper, numpy_solver)
numpy_results = numpy_excited_states_solver.solve(es_problem)
qeom_results = qeom_excited_states_solver.solve(es_problem)
print(numpy_results)
print("\n\n")
print(qeom_results)
import numpy as np
def filter_criterion(eigenstate, eigenvalue, aux_values):
return np.isclose(aux_values["ParticleNumber"][0], 2.0)
new_numpy_solver = NumPyEigensolver(filter_criterion=filter_criterion)
new_numpy_excited_states_solver = ExcitedStatesEigensolver(mapper, new_numpy_solver)
new_numpy_results = new_numpy_excited_states_solver.solve(es_problem)
print(new_numpy_results)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.problems import ElectronicBasis
driver = PySCFDriver()
driver.run_pyscf()
ao_problem = driver.to_problem(basis=ElectronicBasis.AO)
print(ao_problem.basis)
ao_hamil = ao_problem.hamiltonian
print(ao_hamil.electronic_integrals.alpha)
from qiskit_nature.second_q.formats.qcschema_translator import get_ao_to_mo_from_qcschema
qcschema = driver.to_qcschema()
basis_transformer = get_ao_to_mo_from_qcschema(qcschema)
print(basis_transformer.initial_basis)
print(basis_transformer.final_basis)
mo_problem = basis_transformer.transform(ao_problem)
print(mo_problem.basis)
mo_hamil = mo_problem.hamiltonian
print(mo_hamil.electronic_integrals.alpha)
import numpy as np
from qiskit_nature.second_q.operators import ElectronicIntegrals
from qiskit_nature.second_q.problems import ElectronicBasis
from qiskit_nature.second_q.transformers import BasisTransformer
ao2mo_alpha = np.random.random((2, 2))
ao2mo_beta = np.random.random((2, 2))
basis_transformer = BasisTransformer(
ElectronicBasis.AO,
ElectronicBasis.MO,
ElectronicIntegrals.from_raw_integrals(ao2mo_alpha, h1_b=ao2mo_beta),
)
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(atom="Li 0 0 0; H 0 0 1.5")
full_problem = driver.run()
print(full_problem.molecule)
print(full_problem.num_particles)
print(full_problem.num_spatial_orbitals)
from qiskit_nature.second_q.transformers import FreezeCoreTransformer
fc_transformer = FreezeCoreTransformer()
fc_problem = fc_transformer.transform(full_problem)
print(fc_problem.num_particles)
print(fc_problem.num_spatial_orbitals)
print(fc_problem.hamiltonian.constants)
fc_transformer = FreezeCoreTransformer(remove_orbitals=[4, 5])
fc_problem = fc_transformer.transform(full_problem)
print(fc_problem.num_particles)
print(fc_problem.num_spatial_orbitals)
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(atom="Li 0 0 0; H 0 0 1.5")
full_problem = driver.run()
print(full_problem.num_particles)
print(full_problem.num_spatial_orbitals)
from qiskit_nature.second_q.transformers import ActiveSpaceTransformer
as_transformer = ActiveSpaceTransformer(2, 2)
as_problem = as_transformer.transform(full_problem)
print(as_problem.num_particles)
print(as_problem.num_spatial_orbitals)
print(as_problem.hamiltonian.electronic_integrals.alpha)
as_transformer = ActiveSpaceTransformer(2, 2, active_orbitals=[0, 4])
as_problem = as_transformer.transform(full_problem)
print(as_problem.num_particles)
print(as_problem.num_spatial_orbitals)
print(as_problem.hamiltonian.electronic_integrals.alpha)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver()
problem = driver.run()
fermionic_op = problem.hamiltonian.second_q_op()
from qiskit_nature.second_q.mappers import JordanWignerMapper
mapper = JordanWignerMapper()
qubit_jw_op = mapper.map(fermionic_op)
print(qubit_jw_op)
from qiskit_nature.second_q.mappers import ParityMapper
mapper = ParityMapper()
qubit_p_op = mapper.map(fermionic_op)
print(qubit_p_op)
mapper = ParityMapper(num_particles=problem.num_particles)
qubit_op = mapper.map(fermionic_op)
print(qubit_op)
tapered_mapper = problem.get_tapered_mapper(mapper)
print(type(tapered_mapper))
qubit_op = tapered_mapper.map(fermionic_op)
print(qubit_op)
from qiskit_nature.second_q.circuit.library import HartreeFock
hf_state = HartreeFock(2, (1, 1), JordanWignerMapper())
hf_state.draw()
from qiskit_nature.second_q.mappers import InterleavedQubitMapper
interleaved_mapper = InterleavedQubitMapper(JordanWignerMapper())
hf_state = HartreeFock(2, (1, 1), interleaved_mapper)
hf_state.draw()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.mappers import ParityMapper
from qiskit_nature.second_q.properties import ParticleNumber
from qiskit_nature.second_q.transformers import ActiveSpaceTransformer
bond_distance = 2.5 # in Angstrom
# specify driver
driver = PySCFDriver(
atom=f"Li 0 0 0; H 0 0 {bond_distance}",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
problem = driver.run()
# specify active space transformation
active_space_trafo = ActiveSpaceTransformer(
num_electrons=problem.num_particles, num_spatial_orbitals=3
)
# transform the electronic structure problem
problem = active_space_trafo.transform(problem)
# construct the parity mapper with 2-qubit reduction
qubit_mapper = ParityMapper(num_particles=problem.num_particles)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms.ground_state_solvers import GroundStateEigensolver
np_solver = NumPyMinimumEigensolver()
np_groundstate_solver = GroundStateEigensolver(qubit_mapper, np_solver)
np_result = np_groundstate_solver.solve(problem)
target_energy = np_result.total_energies[0]
print(np_result)
from qiskit.circuit.library import EfficientSU2
ansatz = EfficientSU2(num_qubits=4, reps=1, entanglement="linear", insert_barriers=True)
ansatz.decompose().draw("mpl", style="iqx")
import numpy as np
from qiskit.utils import algorithm_globals
# fix random seeds for reproducibility
np.random.seed(5)
algorithm_globals.random_seed = 5
from qiskit.algorithms.optimizers import SPSA
optimizer = SPSA(maxiter=100)
initial_point = np.random.random(ansatz.num_parameters)
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.primitives import Estimator
estimator = Estimator()
local_vqe = VQE(
estimator,
ansatz,
optimizer,
initial_point=initial_point,
)
local_vqe_groundstate_solver = GroundStateEigensolver(qubit_mapper, local_vqe)
local_vqe_result = local_vqe_groundstate_solver.solve(problem)
print(local_vqe_result)
from qiskit import IBMQ
IBMQ.load_account()
provider = IBMQ.get_provider(group="open") # replace by your runtime provider
backend = provider.get_backend("ibmq_qasm_simulator") # select a backend that supports the runtime
from qiskit_nature.runtime import VQEClient
runtime_vqe = VQEClient(
ansatz=ansatz,
optimizer=optimizer,
initial_point=initial_point,
provider=provider,
backend=backend,
shots=1024,
measurement_error_mitigation=True,
) # use a complete measurement fitter for error mitigation
runtime_vqe_groundstate_solver = GroundStateEigensolver(qubit_mapper, runtime_vqe)
runtime_vqe_result = runtime_vqe_groundstate_solver.solve(problem)
print(runtime_vqe_result)
runtime_result = runtime_vqe_result.raw_result
history = runtime_result.optimizer_history
loss = history["energy"]
import matplotlib.pyplot as plt
plt.rcParams["font.size"] = 14
# plot loss and reference value
plt.figure(figsize=(12, 6))
plt.plot(loss + runtime_vqe_result.nuclear_repulsion_energy, label="Runtime VQE")
plt.axhline(y=target_energy + 0.2, color="tab:red", ls=":", label="Target + 200mH")
plt.axhline(y=target_energy, color="tab:red", ls="--", label="Target")
plt.legend(loc="best")
plt.xlabel("Iteration")
plt.ylabel("Energy [H]")
plt.title("VQE energy");
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver()
problem = driver.run()
print(problem)
from qiskit_nature.second_q.problems import ElectronicBasis
driver.run_pyscf()
problem = driver.to_problem(basis=ElectronicBasis.MO, include_dipole=True)
print(problem.basis)
ao_problem = driver.to_problem(basis=ElectronicBasis.AO)
print(ao_problem.basis)
from qiskit_nature.second_q.formats.qcschema_translator import qcschema_to_problem
qcschema = driver.to_qcschema()
ao_problem = qcschema_to_problem(qcschema, basis=ElectronicBasis.AO)
from qiskit_nature.second_q.formats.qcschema_translator import get_ao_to_mo_from_qcschema
basis_transformer = get_ao_to_mo_from_qcschema(qcschema)
mo_problem = basis_transformer.transform(ao_problem)
print(mo_problem.basis)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.problems import BaseProblem
dummy_hamiltonian = None
base_problem = BaseProblem(dummy_hamiltonian)
print(base_problem.properties)
from qiskit_nature.second_q.properties import AngularMomentum
print("AngularMomentum is in problem.properties:", AngularMomentum in base_problem.properties)
print("Adding AngularMomentum to problem.properties...")
base_problem.properties.add(AngularMomentum(2))
print("AngularMomentum is in problem.properties:", AngularMomentum in base_problem.properties)
print("Discarding AngularMomentum from problem.properties...")
base_problem.properties.discard(AngularMomentum)
print("AngularMomentum is in problem.properties:", AngularMomentum in base_problem.properties)
from qiskit_nature.second_q.drivers import PySCFDriver
es_problem = PySCFDriver().run()
print(es_problem.properties.particle_number)
print(es_problem.properties.angular_momentum)
print(es_problem.properties.magnetization)
print(es_problem.properties.electronic_dipole_moment)
print(es_problem.properties.electronic_density)
from qiskit_nature.second_q.properties import ElectronicDensity
density = ElectronicDensity.from_orbital_occupation(
es_problem.orbital_occupations,
es_problem.orbital_occupations_b,
)
es_problem.properties.electronic_density = density
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from math import pi
import numpy as np
import rustworkx as rx
from qiskit_nature.second_q.hamiltonians.lattices import (
BoundaryCondition,
HyperCubicLattice,
Lattice,
LatticeDrawStyle,
LineLattice,
SquareLattice,
TriangularLattice,
)
from qiskit_nature.second_q.hamiltonians import FermiHubbardModel
num_nodes = 11
boundary_condition = BoundaryCondition.OPEN
line_lattice = LineLattice(num_nodes=num_nodes, boundary_condition=boundary_condition)
line_lattice.draw()
num_nodes = 11
boundary_condition = BoundaryCondition.PERIODIC
line_lattice = LineLattice(num_nodes=num_nodes, boundary_condition=boundary_condition)
line_lattice.draw()
line_lattice.draw_without_boundary()
num_nodes = 11
boundary_condition = BoundaryCondition.PERIODIC
edge_parameter = 1.0 + 1.0j
onsite_parameter = 1.0
line_lattice = LineLattice(
num_nodes=num_nodes,
edge_parameter=edge_parameter,
onsite_parameter=onsite_parameter,
boundary_condition=boundary_condition,
)
set(line_lattice.graph.weighted_edge_list())
line_lattice.to_adjacency_matrix()
line_lattice.to_adjacency_matrix(weighted=True)
rows = 5
cols = 4
boundary_condition = BoundaryCondition.OPEN
square_lattice = SquareLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
square_lattice.draw()
rows = 5
cols = 4
boundary_condition = (
BoundaryCondition.OPEN,
BoundaryCondition.PERIODIC,
) # open in the x-direction, periodic in the y-direction
square_lattice = SquareLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
square_lattice.draw()
rows = 5
cols = 4
edge_parameter = (1.0, 1.0 + 1.0j)
boundary_condition = (
BoundaryCondition.OPEN,
BoundaryCondition.PERIODIC,
) # open in the x-direction, periodic in the y-direction
onsite_parameter = 1.0
square_lattice = SquareLattice(
rows=rows,
cols=cols,
edge_parameter=edge_parameter,
onsite_parameter=onsite_parameter,
boundary_condition=boundary_condition,
)
set(square_lattice.graph.weighted_edge_list())
size = (3, 4, 5)
boundary_condition = (
BoundaryCondition.OPEN,
BoundaryCondition.OPEN,
BoundaryCondition.OPEN,
)
cubic_lattice = HyperCubicLattice(size=size, boundary_condition=boundary_condition)
# function for setting the positions
def indextocoord_3d(index: int, size: tuple, angle) -> list:
z = index // (size[0] * size[1])
a = index % (size[0] * size[1])
y = a // size[0]
x = a % size[0]
vec_x = np.array([1, 0])
vec_y = np.array([np.cos(angle), np.sin(angle)])
vec_z = np.array([0, 1])
return_coord = x * vec_x + y * vec_y + z * vec_z
return return_coord.tolist()
pos = dict([(index, indextocoord_3d(index, size, angle=pi / 4)) for index in range(np.prod(size))])
cubic_lattice.draw(style=LatticeDrawStyle(pos=pos))
rows = 4
cols = 3
boundary_condition = BoundaryCondition.OPEN
triangular_lattice = TriangularLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
triangular_lattice.draw()
rows = 4
cols = 3
boundary_condition = BoundaryCondition.PERIODIC
triangular_lattice = TriangularLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
triangular_lattice.draw()
graph = rx.PyGraph(multigraph=False) # multigraph shoud be False
graph.add_nodes_from(range(6))
weighted_edge_list = [
(0, 1, 1.0 + 1.0j),
(0, 2, -1.0),
(2, 3, 2.0),
(4, 2, -1.0 + 2.0j),
(4, 4, 3.0),
(2, 5, -1.0),
]
graph.add_edges_from(weighted_edge_list)
# make a lattice
general_lattice = Lattice(graph)
set(general_lattice.graph.weighted_edge_list())
general_lattice.draw()
general_lattice.draw(self_loop=True)
general_lattice.draw(self_loop=True, style=LatticeDrawStyle(with_labels=True))
square_lattice = SquareLattice(rows=5, cols=4, boundary_condition=BoundaryCondition.PERIODIC)
t = -1.0 # the interaction parameter
v = 0.0 # the onsite potential
u = 5.0 # the interaction parameter U
fhm = FermiHubbardModel(
square_lattice.uniform_parameters(
uniform_interaction=t,
uniform_onsite_potential=v,
),
onsite_interaction=u,
)
ham = fhm.second_q_op().simplify()
print(ham)
graph = rx.PyGraph(multigraph=False) # multiigraph shoud be False
graph.add_nodes_from(range(6))
weighted_edge_list = [
(0, 1, 1.0 + 1.0j),
(0, 2, -1.0),
(2, 3, 2.0),
(4, 2, -1.0 + 2.0j),
(4, 4, 3.0),
(2, 5, -1.0),
]
graph.add_edges_from(weighted_edge_list)
general_lattice = Lattice(graph) # the lattice whose weights are seen as the interaction matrix.
u = 5.0 # the interaction parameter U
fhm = FermiHubbardModel(lattice=general_lattice, onsite_interaction=u)
ham = fhm.second_q_op().simplify()
print(ham)
from qiskit_nature.second_q.problems import LatticeModelProblem
num_nodes = 4
boundary_condition = BoundaryCondition.OPEN
line_lattice = LineLattice(num_nodes=num_nodes, boundary_condition=boundary_condition)
fhm = FermiHubbardModel(
line_lattice.uniform_parameters(
uniform_interaction=t,
uniform_onsite_potential=v,
),
onsite_interaction=u,
)
lmp = LatticeModelProblem(fhm)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
from qiskit_nature.second_q.mappers import JordanWignerMapper
numpy_solver = NumPyMinimumEigensolver()
qubit_mapper = JordanWignerMapper()
calc = GroundStateEigensolver(qubit_mapper, numpy_solver)
res = calc.solve(lmp)
print(res)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
from qiskit_nature.second_q.hamiltonians import QuadraticHamiltonian
# create Hamiltonian
hermitian_part = np.array(
[
[1.0, 2.0, 0.0, 0.0],
[2.0, 1.0, 2.0, 0.0],
[0.0, 2.0, 1.0, 2.0],
[0.0, 0.0, 2.0, 1.0],
]
)
antisymmetric_part = np.array(
[
[0.0, 3.0, 0.0, 0.0],
[-3.0, 0.0, 3.0, 0.0],
[0.0, -3.0, 0.0, 3.0],
[0.0, 0.0, -3.0, 0.0],
]
)
constant = 4.0
hamiltonian = QuadraticHamiltonian(
hermitian_part=hermitian_part,
antisymmetric_part=antisymmetric_part,
constant=constant,
)
# convert it to a FermionicOp and print it
hamiltonian_ferm = hamiltonian.second_q_op()
print(hamiltonian_ferm)
# get the transformation matrix W and orbital energies {epsilon_j}
(
transformation_matrix,
orbital_energies,
transformed_constant,
) = hamiltonian.diagonalizing_bogoliubov_transform()
print(f"Shape of matrix W: {transformation_matrix.shape}")
print(f"Orbital energies: {orbital_energies}")
print(f"Transformed constant: {transformed_constant}")
from qiskit_nature.second_q.circuit.library import FermionicGaussianState
occupied_orbitals = (0, 2)
eig = np.sum(orbital_energies[list(occupied_orbitals)]) + transformed_constant
print(f"Eigenvalue: {eig}")
circuit = FermionicGaussianState(transformation_matrix, occupied_orbitals=occupied_orbitals)
circuit.draw("mpl")
from qiskit.quantum_info import Statevector
from qiskit_nature.second_q.mappers import JordanWignerMapper
# simulate the circuit to get the final state
state = np.array(Statevector(circuit))
# convert the Hamiltonian to a matrix
hamiltonian_jw = JordanWignerMapper().map(hamiltonian_ferm).to_matrix()
# check that the state is an eigenvector with the expected eigenvalue
np.testing.assert_allclose(hamiltonian_jw @ state, eig * state, atol=1e-8)
# create Hamiltonian
hermitian_part = np.array(
[
[1.0, 2.0, 0.0, 0.0],
[2.0, 1.0, 2.0, 0.0],
[0.0, 2.0, 1.0, 2.0],
[0.0, 0.0, 2.0, 1.0],
]
)
constant = 4.0
hamiltonian = QuadraticHamiltonian(
hermitian_part=hermitian_part,
constant=constant,
)
print(f"Hamiltonian conserves particle number: {hamiltonian.conserves_particle_number()}")
# get the transformation matrix W and orbital energies {epsilon_j}
(
transformation_matrix,
orbital_energies,
transformed_constant,
) = hamiltonian.diagonalizing_bogoliubov_transform()
print(f"Shape of matrix W: {transformation_matrix.shape}")
print(f"Orbital energies: {orbital_energies}")
print(f"Transformed constant: {transformed_constant}")
from qiskit_nature.second_q.circuit.library import SlaterDeterminant
occupied_orbitals = (0, 2)
eig = np.sum(orbital_energies[list(occupied_orbitals)]) + transformed_constant
print(f"Eigenvalue: {eig}")
circuit = SlaterDeterminant(transformation_matrix[list(occupied_orbitals)])
circuit.draw("mpl")
from qiskit_nature.second_q.circuit.library import BogoliubovTransform
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.quantum_info import random_hermitian, random_statevector, state_fidelity
from scipy.linalg import expm
# create Hamiltonian
n_modes = 5
hermitian_part = np.array(random_hermitian(n_modes))
hamiltonian = QuadraticHamiltonian(hermitian_part=hermitian_part)
# diagonalize Hamiltonian
(
transformation_matrix,
orbital_energies,
_,
) = hamiltonian.diagonalizing_bogoliubov_transform()
# set simulation time and construct time evolution circuit
time = 1.0
register = QuantumRegister(n_modes)
circuit = QuantumCircuit(register)
bog_circuit = BogoliubovTransform(transformation_matrix)
# change to the diagonal basis of the Hamiltonian
circuit.append(bog_circuit.inverse(), register)
# perform time evolution by applying z rotations
for q, energy in zip(register, orbital_energies):
circuit.rz(-energy * time, q)
# change back to the original basis
circuit.append(bog_circuit, register)
# simulate the circuit
initial_state = random_statevector(2**n_modes)
final_state = initial_state.evolve(circuit)
# compute the correct state by direct exponentiation
hamiltonian_jw = JordanWignerMapper().map(hamiltonian.second_q_op()).to_matrix()
exact_evolution_op = expm(-1j * time * hamiltonian_jw)
expected_state = exact_evolution_op @ np.array(initial_state)
# check that the simulated state is correct
fidelity = state_fidelity(final_state, expected_state)
np.testing.assert_allclose(fidelity, 1.0, atol=1e-8)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import display, clear_output
from qiskit.primitives import Estimator
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.observables_evaluator import estimate_observables
from qiskit.algorithms.optimizers import COBYLA, SLSQP
from qiskit.circuit import QuantumCircuit, Parameter
from qiskit.circuit.library import TwoLocal
from qiskit.quantum_info import Pauli, SparsePauliOp
from qiskit.utils import algorithm_globals
from qiskit_nature.second_q.operators import FermionicOp
from qiskit_nature.second_q.mappers import JordanWignerMapper
def kronecker_delta_function(n: int, m: int) -> int:
"""An implementation of the Kronecker delta function.
Args:
n (int): The first integer argument.
m (int): The second integer argument.
Returns:
Returns 1 if n = m, else returns 0.
"""
return int(n == m)
def create_deuteron_hamiltonian(
N: int, hbar_omega: float = 7.0, V_0: float = -5.68658111
) -> SparsePauliOp:
"""Creates a version of the Deuteron Hamiltonian as a qubit operator.
Args:
N (int): An integer number that represents the dimension of the
basis.
hbar_omega (float, optional): The value of the product of hbar and omega. Defaults to 7.0.
V_0 (float, optional): The value of the potential energy. Defaults to -5.68658111.
Returns:
SparsePauliOp: The qubit-space Hamiltonian that represents the Deuteron.
"""
hamiltonian_terms = {}
for m in range(N):
for n in range(N):
label = "+_{} -_{}".format(str(n), str(m))
coefficient_kinect = (hbar_omega / 2) * (
(2 * n + 3 / 2) * kronecker_delta_function(n, m)
- np.sqrt(n * (n + (1 / 2))) * kronecker_delta_function(n, m + 1)
- np.sqrt((n + 1) * (n + (3 / 2)) * kronecker_delta_function(n, m - 1))
)
hamiltonian_terms[label] = coefficient_kinect
coefficient_potential = (
V_0 * kronecker_delta_function(n, 0) * kronecker_delta_function(n, m)
)
hamiltonian_terms[label] += coefficient_potential
hamiltonian = FermionicOp(hamiltonian_terms, num_spin_orbitals=N)
mapper = JordanWignerMapper()
qubit_hamiltonian = mapper.map(hamiltonian)
if not isinstance(qubit_hamiltonian, SparsePauliOp):
qubit_hamiltonian = qubit_hamiltonian.primitive
return qubit_hamiltonian
deuteron_hamiltonians = [create_deuteron_hamiltonian(i) for i in range(1, 5)]
for i, hamiltonian in enumerate(deuteron_hamiltonians):
print("Deuteron Hamiltonian: H_{}".format(i + 1))
print(hamiltonian)
print("\n")
theta = Parameter(r"$\theta$")
eta = Parameter(r"$\eta$")
wavefunction = QuantumCircuit(1)
wavefunction.ry(theta, 0)
wavefunction.draw("mpl")
wavefunction2 = QuantumCircuit(2)
wavefunction2.x(0)
wavefunction2.ry(theta, 1)
wavefunction2.cx(1, 0)
wavefunction2.draw("mpl")
wavefunction3 = QuantumCircuit(3)
wavefunction3.x(0)
wavefunction3.ry(eta, 1)
wavefunction3.ry(theta, 2)
wavefunction3.cx(2, 0)
wavefunction3.cx(0, 1)
wavefunction3.ry(-eta, 1)
wavefunction3.cx(0, 1)
wavefunction3.cx(1, 0)
wavefunction3.draw("mpl")
ansatz = [wavefunction, wavefunction2, wavefunction3]
reference_values = []
print("Exact binding energies calculated through numpy.linalg.eigh \n")
for i, hamiltonian in enumerate(deuteron_hamiltonians):
eigenvalues, eigenstates = np.linalg.eigh(hamiltonian.to_matrix())
reference_values.append(eigenvalues[0])
print("Exact binding energy for H_{}: {}".format(i + 1, eigenvalues[0]))
print(
"Results using Estimator for H_1, H_2 and H_3 with the ansatz given in the reference paper \n"
)
for i in range(3):
seed = 42
algorithm_globals.random_seed = seed
vqe = VQE(Estimator(), ansatz=ansatz[i], optimizer=SLSQP())
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
binding_energy = vqe_result.optimal_value
print("Binding energy for H_{}: {} MeV".format(i + 1, binding_energy))
def callback(eval_count, parameters, mean, std):
# Overwrites the same line when printing
display("Evaluation: {}, Energy: {}, Std: {}".format(eval_count, mean, std))
clear_output(wait=True)
counts.append(eval_count)
values.append(mean)
params.append(parameters)
deviation.append(std)
plots = []
for i in range(3):
counts = []
values = []
params = []
deviation = []
seed = 42
algorithm_globals.random_seed = seed
vqe = VQE(Estimator(), ansatz=ansatz[i], optimizer=COBYLA(), callback=callback)
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
plots.append([counts, values])
fig, ax = plt.subplots(nrows=3, ncols=1)
fig.set_size_inches((12, 12))
for i, plot in enumerate(plots):
ax[i].plot(plot[0], plot[1], "o-", label="COBYLA")
ax[i].axhline(
y=reference_values[i],
color="k",
linestyle="--",
label=f"Reference Value: {reference_values[i]}",
)
ax[i].legend()
ax[i].set_xlabel("Cost Function Evaluations", fontsize=15)
ax[i].set_ylabel(r"$\langle H_{} \rangle$ - Energy (MeV)".format(i + 1), fontsize=15)
plt.show()
twolocal_ansatzes = []
for i in range(1, 5):
ansatz = TwoLocal(
deuteron_hamiltonians[i - 1].num_qubits,
["rz", "ry"],
"cx",
entanglement="full",
reps=i,
initial_state=None,
)
twolocal_ansatzes.append(ansatz)
print("Results using Estimator for H_1, H_2, H_3 and H_4 with TwoLocal ansatz \n")
seed = 42
algorithm_globals.random_seed = seed
for i in range(4):
vqe = VQE(Estimator(), ansatz=twolocal_ansatzes[i], optimizer=SLSQP())
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
binding_energy = vqe_result.optimal_value
print("Binding energy for H_{}:".format(i + 1), binding_energy, "MeV")
seed = 42
algorithm_globals.random_seed = seed
plots_tl = []
for i in range(4):
counts = []
values = []
params = []
deviation = []
vqe = VQE(
Estimator(),
ansatz=twolocal_ansatzes[i],
optimizer=SLSQP(),
callback=callback,
)
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
plots_tl.append([counts, values])
fig, ax = plt.subplots(nrows=4, ncols=1)
fig.set_size_inches((15, 15))
for i, plot in enumerate(plots_tl):
ax[i].plot(plot[0], plot[1], "o-", label="COBYLA")
ax[i].axhline(
y=reference_values[i],
color="k",
linestyle="--",
label=f"Reference Value: {reference_values[i]}",
)
ax[i].legend()
ax[i].set_xlabel("Cost Function Evaluations", fontsize=15)
ax[i].set_ylabel(r"$\langle H_{} \rangle$ - Energy (MeV)".format(i + 1), fontsize=15)
plt.show()
def calculate_observables_exp_values(
quantum_circuit: QuantumCircuit, observables: list, angles: list
) -> list:
"""Calculate the expectation value of an observable given the quantum
circuit that represents the wavefunction and a list of parameters.
Args:
quantum_circuit (QuantumCircuit): A parameterized quantum circuit
that represents the wavefunction of the system.
observables (list): A list containing the observables that we want
to know the expectation values.
angles (list): A list with the values that will be used in the
'bind_parameters' method.
Returns:
list_exp_values (list): A list containing the expectation values
of the observables given as input.
"""
list_exp_values = []
for observable in observables:
exp_values = []
for angle in angles:
qc = quantum_circuit.bind_parameters({theta: angle})
result = estimate_observables(
Estimator(),
quantum_state=qc,
observables=[observable],
)
exp_values.append(result[0][0])
list_exp_values.append(exp_values)
return list_exp_values
angles = list(np.linspace(-np.pi, np.pi, 100))
observables = [
Pauli("IZ"),
Pauli("ZI"),
Pauli("XX"),
Pauli("YY"),
deuteron_hamiltonians[1],
]
h2_observables_exp_values = calculate_observables_exp_values(wavefunction2, observables, angles)
fig, ax = plt.subplots(nrows=2, ncols=1)
fig.set_size_inches((12, 12))
ax[0].plot(angles, h2_observables_exp_values[0], "o", label=r"$Z_0$")
ax[0].plot(angles, h2_observables_exp_values[1], "o", label=r"$Z_1$")
ax[0].plot(angles, h2_observables_exp_values[2], "o", label=r"$X_0X_1$")
ax[0].plot(angles, h2_observables_exp_values[3], "o", label=r"$Y_0Y_1$")
ax[0].axhline(
y=1,
color="k",
linestyle="--",
)
ax[0].axhline(y=-1, color="k", linestyle="--")
ax[0].legend()
ax[0].set_xlabel(r"Theta - $\theta$", fontsize=15)
ax[0].set_ylabel(r"$\langle O \rangle $ - Operator Expectation Value", fontsize=15)
ax[0].set_xticks(
[-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi],
labels=[r"$-\pi$", r"$-\pi/2$", "0", r"$\pi/2$", r"$\pi$"],
)
ax[0].set_title(
r"Expectation value of the observables $Z_0$, $Z_1$, $X_0X_1$ and $Y_0Y_1$ when we vary $\theta$ in the ansatz.",
fontsize=15,
)
ax[1].plot(angles, h2_observables_exp_values[4], "o")
ax[1].axhline(
y=reference_values[1],
color="k",
linestyle="--",
label="Binding Energy: {} MeV".format(np.round(reference_values[1], 3)),
)
ax[1].legend()
ax[1].set_xlabel(r"Theta - $\theta$", fontsize=15)
ax[1].set_ylabel(r"$\langle H_2 \rangle $ - Energy (MeV)", fontsize=15)
ax[1].set_xticks(
[-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi],
labels=[r"$-\pi$", r"$-\pi/2$", "0", r"$\pi/2$", r"$\pi$"],
)
ax[1].set_title(
r"Behavior of the expectation value of $H_2$ when we vary $\theta$ in the ansatz.", fontsize=15
)
plt.show()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.mappers.second_quantization import LogarithmicMapper
mapper = LogarithmicMapper(2)
from qiskit_nature.second_q.mappers import LogarithmicMapper
mapper = LogarithmicMapper(2)
from qiskit_nature.second_q.mappers import LogarithmicMapper
mapper = LogarithmicMapper(padding=2)
from qiskit_nature.circuit.library import HartreeFock
from qiskit_nature.converters.second_quantization import QubitConverter
from qiskit_nature.mappers.second_quantization import JordanWignerMapper
converter = QubitConverter(JordanWignerMapper())
init_state = HartreeFock(num_spin_orbitals=6, num_particles=(2, 1), qubit_converter=converter)
print(init_state.draw())
from qiskit_nature.second_q.circuit.library import HartreeFock
from qiskit_nature.second_q.mappers import JordanWignerMapper, QubitConverter
converter = QubitConverter(JordanWignerMapper())
init_state = HartreeFock(num_spatial_orbitals=3, num_particles=(2, 1), qubit_converter=converter)
print(init_state.draw())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.circuit.library import UCCSD
ansatz = UCCSD()
ansatz.num_spin_orbitals = 10
from qiskit_nature.second_q.circuit.library import UCCSD
ansatz = UCCSD()
ansatz.num_spatial_orbitals = 5
from qiskit_nature.circuit.library import UCC, UVCC
ucc = UCC(qubit_converter=None, num_particles=None, num_spin_orbitals=None, excitations=None)
uvcc = UVCC(qubit_converter=None, num_modals=None, excitations=None)
from qiskit_nature.second_q.circuit.library import UCC, UVCC
ucc = UCC(num_spatial_orbitals=None, num_particles=None, excitations=None, qubit_converter=None)
uvcc = UVCC(num_modals=None, excitations=None, qubit_converter=None)
from qiskit_nature.circuit.library import HartreeFock, VSCF
from qiskit_nature.converters.second_quantization import QubitConverter
from qiskit_nature.mappers.second_quantization import DirectMapper, JordanWignerMapper
hf = HartreeFock(
num_spin_orbitals=4, num_particles=(1, 1), qubit_converter=QubitConverter(JordanWignerMapper())
)
vscf = VSCF(num_modals=[2, 2])
from qiskit_nature.second_q.circuit.library import HartreeFock, VSCF
from qiskit_nature.second_q.mappers import DirectMapper, JordanWignerMapper, QubitConverter
hf = HartreeFock()
hf.num_spatial_orbitals = 2
hf.num_particles = (1, 1)
hf.qubit_converter = QubitConverter(JordanWignerMapper())
vscf = VSCF()
vscf.num_modals = [2, 2]
from qiskit.providers.basicaer import BasicAer
from qiskit.utils import QuantumInstance
from qiskit_nature.algorithms.ground_state_solvers import VQEUCCFactory
quantum_instance = QuantumInstance(BasicAer.get_backend("statevector_simulator"))
vqe_factory = VQEUCCFactory(quantum_instance=quantum_instance)
from qiskit.algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.circuit.library import UCCSD
from qiskit_nature.second_q.algorithms.ground_state_solvers import VQEUCCFactory
estimator = Estimator()
ansatz = UCCSD()
optimizer = SLSQP()
vqe_factory = VQEUCCFactory(estimator, ansatz, optimizer)
from qiskit_nature.algorithms.ground_state_solvers import GroundStateEigensolver, VQEUCCFactory
from qiskit_nature.algorithms.excited_states_solvers import QEOM
from qiskit_nature.converters.second_quantization import QubitConverter
from qiskit_nature.mappers.second_quantization import JordanWignerMapper
vqe_factory = VQEUCCFactory()
converter = QubitConverter(JordanWignerMapper())
ground_state_solver = GroundStateEigensolver(converter, vqe_factory)
qeom = QEOM(ground_state_solver)
from qiskit.algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.circuit.library import UCCSD
from qiskit_nature.second_q.algorithms.ground_state_solvers import (
GroundStateEigensolver,
VQEUCCFactory,
)
from qiskit_nature.second_q.algorithms.excited_states_solvers import QEOM
from qiskit_nature.second_q.mappers import JordanWignerMapper, QubitConverter
estimator = Estimator()
ansatz = UCCSD()
optimizer = SLSQP()
vqe_factory = VQEUCCFactory(estimator, ansatz, optimizer)
converter = QubitConverter(JordanWignerMapper())
ground_state_solver = GroundStateEigensolver(converter, vqe_factory)
qeom = QEOM(ground_state_solver, estimator)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.drivers import Molecule
from qiskit_nature.drivers.second_quantization import (
ElectronicStructureDriverType,
ElectronicStructureMoleculeDriver,
PySCFDriver,
)
from qiskit_nature.problems.second_quantization import ElectronicStructureProblem
from qiskit_nature.transformers.second_quantization.electronic import FreezeCoreTransformer
from qiskit_nature.settings import settings
settings.dict_aux_operators = True
molecule = Molecule(
geometry=[["H", [0.0, 0.0, 0.0]], ["H", [0.0, 0.0, 0.735]]], charge=0, multiplicity=1
)
driver = ElectronicStructureMoleculeDriver(
molecule, basis="sto3g", driver_type=ElectronicStructureDriverType.PYSCF
)
# or equivalently:
driver = PySCFDriver.from_molecule(molecule, basis="sto3g")
transformer = FreezeCoreTransformer()
problem = ElectronicStructureProblem(driver, transformers=[transformer])
# Note: at this point, `driver.run()` has NOT been called yet. We can trigger this indirectly like so:
second_q_ops = problem.second_q_ops()
hamiltonian = second_q_ops["ElectronicEnergy"]
print(hamiltonian)
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.formats.molecule_info import MoleculeInfo
from qiskit_nature.second_q.transformers import FreezeCoreTransformer
molecule = MoleculeInfo(["H", "H"], [(0.0, 0.0, 0.0), (0.0, 0.0, 0.735)], charge=0, multiplicity=1)
driver = PySCFDriver.from_molecule(molecule, basis="sto3g")
# this is now done explicitly
problem = driver.run()
transformer = FreezeCoreTransformer()
# and you also apply transformers explicitly
problem = transformer.transform(problem)
hamiltonian = problem.hamiltonian.second_q_op()
print("\n".join(str(hamiltonian).splitlines()[:10] + ["..."]))
from qiskit_nature.drivers import Molecule
from qiskit_nature.drivers.second_quantization import PySCFDriver
molecule = Molecule(
geometry=[["H", [0.0, 0.0, 0.0]], ["H", [0.0, 0.0, 0.735]]], charge=0, multiplicity=1
)
driver = PySCFDriver.from_molecule(molecule)
result = driver.run()
print(type(result))
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.formats.molecule_info import MoleculeInfo
molecule = MoleculeInfo(["H", "H"], [(0.0, 0.0, 0.0), (0.0, 0.0, 0.735)], charge=0, multiplicity=1)
driver = PySCFDriver.from_molecule(molecule, basis="sto3g")
result = driver.run()
print(type(result))
from qiskit_nature.drivers.second_quantization import FCIDumpDriver
path_to_fcidump = "aux_files/h2.fcidump"
driver = FCIDumpDriver(path_to_fcidump)
result = driver.run()
print(type(result))
from qiskit_nature.second_q.formats.fcidump import FCIDump
path_to_fcidump = "aux_files/h2.fcidump"
fcidump = FCIDump.from_file(path_to_fcidump)
print(type(fcidump))
from qiskit_nature.second_q.formats.fcidump_translator import fcidump_to_problem
problem = fcidump_to_problem(fcidump)
print(type(problem))
from qiskit_nature.drivers.second_quantization import PySCFDriver
from qiskit_nature.transformers.second_quantization.electronic import FreezeCoreTransformer
transformer = FreezeCoreTransformer()
driver = PySCFDriver()
transformed_result = transformer.transform(driver.run())
print(type(transformed_result))
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.transformers import FreezeCoreTransformer
transformer = FreezeCoreTransformer()
driver = PySCFDriver()
transformed_result = transformer.transform(driver.run())
print(type(transformed_result))
from qiskit_nature.drivers.second_quantization import PySCFDriver
from qiskit_nature.problems.second_quantization.electronic import ElectronicStructureProblem
from qiskit_nature.transformers.second_quantization.electronic import FreezeCoreTransformer
driver = PySCFDriver()
transformer = FreezeCoreTransformer()
problem = ElectronicStructureProblem(driver, transformers=[transformer])
# we trigger driver.run() implicitly like so:
second_q_ops = problem.second_q_ops()
hamiltonian_op = second_q_ops.pop("ElectronicEnergy")
aux_ops = second_q_ops
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.transformers import FreezeCoreTransformer
driver = PySCFDriver()
problem = driver.run()
transformer = FreezeCoreTransformer()
problem = transformer.transform(problem)
hamiltonian_op, aux_ops = problem.second_q_ops()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.drivers.second_quantization import GaussianForcesDriver
from qiskit_nature.problems.second_quantization import VibrationalStructureProblem
from qiskit_nature.settings import settings
settings.dict_aux_operators = True
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
problem = VibrationalStructureProblem(driver, num_modals=[2, 2, 3, 4], truncation_order=2)
# Note: at this point, `driver.run()` has NOT been called yet. We can trigger this indirectly like so:
second_q_ops = problem.second_q_ops()
hamiltonian = second_q_ops["VibrationalEnergy"]
print("\n".join(str(hamiltonian).splitlines()[:10] + ["..."]))
from qiskit_nature.second_q.drivers import GaussianForcesDriver
from qiskit_nature.second_q.problems import HarmonicBasis
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
basis = HarmonicBasis(num_modals=[2, 2, 3, 4])
# this is now done explicitly and already requires the basis
problem = driver.run(basis=basis)
problem.hamiltonian.truncation_order = 2
hamiltonian = problem.hamiltonian.second_q_op()
print("\n".join(str(hamiltonian).splitlines()[:10] + ["..."]))
from qiskit_nature.drivers.second_quantization import GaussianLogResult
from qiskit_nature.properties.second_quantization.vibrational.bases import HarmonicBasis
from qiskit_nature.settings import settings
settings.dict_aux_operators = True
log_result = GaussianLogResult("aux_files/CO2_freq_B3LYP_631g.log")
hamiltonian = log_result.get_vibrational_energy()
print(hamiltonian)
hamiltonian.basis = HarmonicBasis([2, 2, 3, 4])
op = hamiltonian.second_q_ops()["VibrationalEnergy"]
print("\n".join(str(op).splitlines()[:10] + ["..."]))
from qiskit_nature.second_q.drivers import GaussianLogResult
from qiskit_nature.second_q.formats import watson_to_problem
from qiskit_nature.second_q.problems import HarmonicBasis
log_result = GaussianLogResult("aux_files/CO2_freq_B3LYP_631g.log")
watson = log_result.get_watson_hamiltonian()
print(watson)
basis = HarmonicBasis(num_modals=[2, 2, 3, 4])
problem = watson_to_problem(watson, basis)
hamiltonian = problem.hamiltonian.second_q_op()
print("\n".join(str(hamiltonian).splitlines()[:10] + ["..."]))
from qiskit_nature.drivers.second_quantization import GaussianForcesDriver
from qiskit_nature.problems.second_quantization import VibrationalStructureProblem
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
problem = VibrationalStructureProblem(driver, num_modals=[2, 2, 3, 4], truncation_order=2)
# we trigger driver.run() implicitly like so:
second_q_ops = problem.second_q_ops()
hamiltonian_op = second_q_ops.pop("VibrationalEnergy")
aux_ops = second_q_ops
from qiskit_nature.second_q.drivers import GaussianForcesDriver
from qiskit_nature.second_q.problems import HarmonicBasis
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
basis = HarmonicBasis(num_modals=[2, 2, 3, 4])
problem = driver.run(basis=basis)
problem.hamiltonian.truncation_order = 2
hamiltonian_op, aux_ops = problem.second_q_ops()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.problems.second_quantization.lattice.lattices import LineLattice
from qiskit_nature.problems.second_quantization.lattice.models import FermiHubbardModel
line = LineLattice(2)
fermi = FermiHubbardModel.uniform_parameters(line, 2.0, 4.0, 3.0)
print(fermi.second_q_ops()) # Note: the trailing `s`
from qiskit_nature.second_q.hamiltonians.lattices import LineLattice
from qiskit_nature.second_q.hamiltonians import FermiHubbardModel
line = LineLattice(2)
fermi = FermiHubbardModel(line.uniform_parameters(2.0, 4.0), 3.0)
print(fermi.second_q_op()) # Note: NO trailing `s`
import numpy as np
from qiskit_nature.problems.second_quantization.lattice.models import FermiHubbardModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
fermi = FermiHubbardModel.from_parameters(interaction, 3.0)
print(fermi.second_q_ops()) # Note: the trailing `s`
import numpy as np
from qiskit_nature.second_q.hamiltonians.lattices import Lattice
from qiskit_nature.second_q.hamiltonians import FermiHubbardModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
lattice = Lattice.from_adjacency_matrix(interaction)
fermi = FermiHubbardModel(lattice, 3.0)
print(fermi.second_q_op()) # Note: NO trailing `s`
from qiskit_nature.problems.second_quantization.lattice.lattices import LineLattice
from qiskit_nature.problems.second_quantization.lattice.models import IsingModel
line = LineLattice(2)
ising = IsingModel.uniform_parameters(line, 2.0, 4.0)
print(ising.second_q_ops()) # Note: the trailing `s`
from qiskit_nature.second_q.hamiltonians.lattices import LineLattice
from qiskit_nature.second_q.hamiltonians import IsingModel
line = LineLattice(2)
ising = IsingModel(line.uniform_parameters(2.0, 4.0))
print(ising.second_q_op()) # Note: NO trailing `s`
import numpy as np
from qiskit_nature.problems.second_quantization.lattice.models import IsingModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
ising = IsingModel.from_parameters(interaction)
print(ising.second_q_ops()) # Note: the trailing `s`
import numpy as np
from qiskit_nature.second_q.hamiltonians.lattices import Lattice
from qiskit_nature.second_q.hamiltonians import IsingModel
interaction = np.array([[4.0, 2.0], [2.0, 4.0]])
lattice = Lattice.from_adjacency_matrix(interaction)
ising = IsingModel(lattice)
print(ising.second_q_op()) # Note: NO trailing `s`
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(
atom="H 0 0 0; H 0 0 0.735",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
problem = driver.run()
print(problem)
hamiltonian = problem.hamiltonian
coefficients = hamiltonian.electronic_integrals
print(coefficients.alpha)
second_q_op = hamiltonian.second_q_op()
print(second_q_op)
hamiltonian.nuclear_repulsion_energy # NOT included in the second_q_op above
problem.molecule
problem.reference_energy
problem.num_particles
problem.num_spatial_orbitals
problem.basis
problem.properties
problem.properties.particle_number
problem.properties.angular_momentum
problem.properties.magnetization
problem.properties.electronic_dipole_moment
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
from qiskit_nature.second_q.mappers import JordanWignerMapper
solver = GroundStateEigensolver(
JordanWignerMapper(),
NumPyMinimumEigensolver(),
)
result = solver.solve(problem)
print(result)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import GaussianForcesDriver
# if you ran Gaussian elsewhere and already have the output file
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
# if you want to run the Gaussian job from Qiskit
# driver = GaussianForcesDriver(
# ['#p B3LYP/6-31g Freq=(Anharm) Int=Ultrafine SCF=VeryTight',
# '',
# 'CO2 geometry optimization B3LYP/6-31g',
# '',
# '0 1',
# 'C -0.848629 2.067624 0.160992',
# 'O 0.098816 2.655801 -0.159738',
# 'O -1.796073 1.479446 0.481721',
# '',
# ''
from qiskit_nature.second_q.problems import HarmonicBasis
basis = HarmonicBasis([2, 2, 2, 2])
from qiskit_nature.second_q.problems import VibrationalStructureProblem
from qiskit_nature.second_q.mappers import DirectMapper
vibrational_problem = driver.run(basis=basis)
vibrational_problem.hamiltonian.truncation_order = 2
main_op, aux_ops = vibrational_problem.second_q_ops()
print(main_op)
qubit_mapper = DirectMapper()
qubit_op = qubit_mapper.map(main_op)
print(qubit_op)
basis = HarmonicBasis([3, 3, 3, 3])
vibrational_problem = driver.run(basis=basis)
vibrational_problem.hamiltonian.truncation_order = 2
main_op, aux_ops = vibrational_problem.second_q_ops()
qubit_mapper = DirectMapper()
qubit_op = qubit_mapper.map(main_op)
print(qubit_op)
# for simplicity, we will use the smaller basis again
vibrational_problem = driver.run(basis=HarmonicBasis([2, 2, 2, 2]))
vibrational_problem.hamiltonian.truncation_order = 2
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
solver = GroundStateEigensolver(
qubit_mapper,
NumPyMinimumEigensolver(filter_criterion=vibrational_problem.get_default_filter_criterion()),
)
result = solver.solve(vibrational_problem)
print(result)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(
atom="H 0 0 0; H 0 0 0.735",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
es_problem = driver.run()
from qiskit_nature.second_q.mappers import JordanWignerMapper
mapper = JordanWignerMapper()
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
numpy_solver = NumPyMinimumEigensolver()
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD
ansatz = UCCSD(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
initial_state=HartreeFock(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
),
)
vqe_solver = VQE(Estimator(), ansatz, SLSQP())
vqe_solver.initial_point = [0.0] * ansatz.num_parameters
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.circuit.library import TwoLocal
tl_circuit = TwoLocal(
rotation_blocks=["h", "rx"],
entanglement_blocks="cz",
entanglement="full",
reps=2,
parameter_prefix="y",
)
another_solver = VQE(Estimator(), tl_circuit, SLSQP())
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
calc = GroundStateEigensolver(mapper, vqe_solver)
res = calc.solve(es_problem)
print(res)
calc = GroundStateEigensolver(mapper, numpy_solver)
res = calc.solve(es_problem)
print(res)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.drivers import GaussianForcesDriver
from qiskit_nature.second_q.mappers import DirectMapper
from qiskit_nature.second_q.problems import HarmonicBasis
driver = GaussianForcesDriver(logfile="aux_files/CO2_freq_B3LYP_631g.log")
basis = HarmonicBasis([2, 2, 2, 2])
vib_problem = driver.run(basis=basis)
vib_problem.hamiltonian.truncation_order = 2
mapper = DirectMapper()
solver_without_filter = NumPyMinimumEigensolver()
solver_with_filter = NumPyMinimumEigensolver(
filter_criterion=vib_problem.get_default_filter_criterion()
)
gsc_wo = GroundStateEigensolver(mapper, solver_without_filter)
result_wo = gsc_wo.solve(vib_problem)
gsc_w = GroundStateEigensolver(mapper, solver_with_filter)
result_w = gsc_w.solve(vib_problem)
print(result_wo)
print("\n\n")
print(result_w)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(
atom="H 0 0 0; H 0 0 0.735",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
es_problem = driver.run()
from qiskit_nature.second_q.mappers import JordanWignerMapper
mapper = JordanWignerMapper()
from qiskit.algorithms.eigensolvers import NumPyEigensolver
numpy_solver = NumPyEigensolver(filter_criterion=es_problem.get_default_filter_criterion())
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.optimizers import SLSQP
from qiskit.primitives import Estimator
from qiskit_nature.second_q.algorithms import GroundStateEigensolver, QEOM
from qiskit_nature.second_q.circuit.library import HartreeFock, UCCSD
ansatz = UCCSD(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
initial_state=HartreeFock(
es_problem.num_spatial_orbitals,
es_problem.num_particles,
mapper,
),
)
estimator = Estimator()
# This first part sets the ground state solver
# see more about this part in the ground state calculation tutorial
solver = VQE(estimator, ansatz, SLSQP())
solver.initial_point = [0.0] * ansatz.num_parameters
gse = GroundStateEigensolver(mapper, solver)
# The qEOM algorithm is simply instantiated with the chosen ground state solver and Estimator primitive
qeom_excited_states_solver = QEOM(gse, estimator, "sd")
from qiskit_nature.second_q.algorithms import ExcitedStatesEigensolver
numpy_excited_states_solver = ExcitedStatesEigensolver(mapper, numpy_solver)
numpy_results = numpy_excited_states_solver.solve(es_problem)
qeom_results = qeom_excited_states_solver.solve(es_problem)
print(numpy_results)
print("\n\n")
print(qeom_results)
import numpy as np
def filter_criterion(eigenstate, eigenvalue, aux_values):
return np.isclose(aux_values["ParticleNumber"][0], 2.0)
new_numpy_solver = NumPyEigensolver(filter_criterion=filter_criterion)
new_numpy_excited_states_solver = ExcitedStatesEigensolver(mapper, new_numpy_solver)
new_numpy_results = new_numpy_excited_states_solver.solve(es_problem)
print(new_numpy_results)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.problems import ElectronicBasis
driver = PySCFDriver()
driver.run_pyscf()
ao_problem = driver.to_problem(basis=ElectronicBasis.AO)
print(ao_problem.basis)
ao_hamil = ao_problem.hamiltonian
print(ao_hamil.electronic_integrals.alpha)
from qiskit_nature.second_q.formats.qcschema_translator import get_ao_to_mo_from_qcschema
qcschema = driver.to_qcschema()
basis_transformer = get_ao_to_mo_from_qcschema(qcschema)
print(basis_transformer.initial_basis)
print(basis_transformer.final_basis)
mo_problem = basis_transformer.transform(ao_problem)
print(mo_problem.basis)
mo_hamil = mo_problem.hamiltonian
print(mo_hamil.electronic_integrals.alpha)
import numpy as np
from qiskit_nature.second_q.operators import ElectronicIntegrals
from qiskit_nature.second_q.problems import ElectronicBasis
from qiskit_nature.second_q.transformers import BasisTransformer
ao2mo_alpha = np.random.random((2, 2))
ao2mo_beta = np.random.random((2, 2))
basis_transformer = BasisTransformer(
ElectronicBasis.AO,
ElectronicBasis.MO,
ElectronicIntegrals.from_raw_integrals(ao2mo_alpha, h1_b=ao2mo_beta),
)
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(atom="Li 0 0 0; H 0 0 1.5")
full_problem = driver.run()
print(full_problem.molecule)
print(full_problem.num_particles)
print(full_problem.num_spatial_orbitals)
from qiskit_nature.second_q.transformers import FreezeCoreTransformer
fc_transformer = FreezeCoreTransformer()
fc_problem = fc_transformer.transform(full_problem)
print(fc_problem.num_particles)
print(fc_problem.num_spatial_orbitals)
print(fc_problem.hamiltonian.constants)
fc_transformer = FreezeCoreTransformer(remove_orbitals=[4, 5])
fc_problem = fc_transformer.transform(full_problem)
print(fc_problem.num_particles)
print(fc_problem.num_spatial_orbitals)
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver(atom="Li 0 0 0; H 0 0 1.5")
full_problem = driver.run()
print(full_problem.num_particles)
print(full_problem.num_spatial_orbitals)
from qiskit_nature.second_q.transformers import ActiveSpaceTransformer
as_transformer = ActiveSpaceTransformer(2, 2)
as_problem = as_transformer.transform(full_problem)
print(as_problem.num_particles)
print(as_problem.num_spatial_orbitals)
print(as_problem.hamiltonian.electronic_integrals.alpha)
as_transformer = ActiveSpaceTransformer(2, 2, active_orbitals=[0, 4])
as_problem = as_transformer.transform(full_problem)
print(as_problem.num_particles)
print(as_problem.num_spatial_orbitals)
print(as_problem.hamiltonian.electronic_integrals.alpha)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver()
problem = driver.run()
fermionic_op = problem.hamiltonian.second_q_op()
from qiskit_nature.second_q.mappers import JordanWignerMapper
mapper = JordanWignerMapper()
qubit_jw_op = mapper.map(fermionic_op)
print(qubit_jw_op)
from qiskit_nature.second_q.mappers import ParityMapper
mapper = ParityMapper()
qubit_p_op = mapper.map(fermionic_op)
print(qubit_p_op)
mapper = ParityMapper(num_particles=problem.num_particles)
qubit_op = mapper.map(fermionic_op)
print(qubit_op)
tapered_mapper = problem.get_tapered_mapper(mapper)
print(type(tapered_mapper))
qubit_op = tapered_mapper.map(fermionic_op)
print(qubit_op)
from qiskit_nature.second_q.circuit.library import HartreeFock
hf_state = HartreeFock(2, (1, 1), JordanWignerMapper())
hf_state.draw()
from qiskit_nature.second_q.mappers import InterleavedQubitMapper
interleaved_mapper = InterleavedQubitMapper(JordanWignerMapper())
hf_state = HartreeFock(2, (1, 1), interleaved_mapper)
hf_state.draw()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver
from qiskit_nature.second_q.mappers import ParityMapper
from qiskit_nature.second_q.properties import ParticleNumber
from qiskit_nature.second_q.transformers import ActiveSpaceTransformer
bond_distance = 2.5 # in Angstrom
# specify driver
driver = PySCFDriver(
atom=f"Li 0 0 0; H 0 0 {bond_distance}",
basis="sto3g",
charge=0,
spin=0,
unit=DistanceUnit.ANGSTROM,
)
problem = driver.run()
# specify active space transformation
active_space_trafo = ActiveSpaceTransformer(
num_electrons=problem.num_particles, num_spatial_orbitals=3
)
# transform the electronic structure problem
problem = active_space_trafo.transform(problem)
# construct the parity mapper with 2-qubit reduction
qubit_mapper = ParityMapper(num_particles=problem.num_particles)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms.ground_state_solvers import GroundStateEigensolver
np_solver = NumPyMinimumEigensolver()
np_groundstate_solver = GroundStateEigensolver(qubit_mapper, np_solver)
np_result = np_groundstate_solver.solve(problem)
target_energy = np_result.total_energies[0]
print(np_result)
from qiskit.circuit.library import EfficientSU2
ansatz = EfficientSU2(num_qubits=4, reps=1, entanglement="linear", insert_barriers=True)
ansatz.decompose().draw("mpl", style="iqx")
import numpy as np
from qiskit.utils import algorithm_globals
# fix random seeds for reproducibility
np.random.seed(5)
algorithm_globals.random_seed = 5
from qiskit.algorithms.optimizers import SPSA
optimizer = SPSA(maxiter=100)
initial_point = np.random.random(ansatz.num_parameters)
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.primitives import Estimator
estimator = Estimator()
local_vqe = VQE(
estimator,
ansatz,
optimizer,
initial_point=initial_point,
)
local_vqe_groundstate_solver = GroundStateEigensolver(qubit_mapper, local_vqe)
local_vqe_result = local_vqe_groundstate_solver.solve(problem)
print(local_vqe_result)
from qiskit import IBMQ
IBMQ.load_account()
provider = IBMQ.get_provider(group="open") # replace by your runtime provider
backend = provider.get_backend("ibmq_qasm_simulator") # select a backend that supports the runtime
from qiskit_nature.runtime import VQEClient
runtime_vqe = VQEClient(
ansatz=ansatz,
optimizer=optimizer,
initial_point=initial_point,
provider=provider,
backend=backend,
shots=1024,
measurement_error_mitigation=True,
) # use a complete measurement fitter for error mitigation
runtime_vqe_groundstate_solver = GroundStateEigensolver(qubit_mapper, runtime_vqe)
runtime_vqe_result = runtime_vqe_groundstate_solver.solve(problem)
print(runtime_vqe_result)
runtime_result = runtime_vqe_result.raw_result
history = runtime_result.optimizer_history
loss = history["energy"]
import matplotlib.pyplot as plt
plt.rcParams["font.size"] = 14
# plot loss and reference value
plt.figure(figsize=(12, 6))
plt.plot(loss + runtime_vqe_result.nuclear_repulsion_energy, label="Runtime VQE")
plt.axhline(y=target_energy + 0.2, color="tab:red", ls=":", label="Target + 200mH")
plt.axhline(y=target_energy, color="tab:red", ls="--", label="Target")
plt.legend(loc="best")
plt.xlabel("Iteration")
plt.ylabel("Energy [H]")
plt.title("VQE energy");
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.drivers import PySCFDriver
driver = PySCFDriver()
problem = driver.run()
print(problem)
from qiskit_nature.second_q.problems import ElectronicBasis
driver.run_pyscf()
problem = driver.to_problem(basis=ElectronicBasis.MO, include_dipole=True)
print(problem.basis)
ao_problem = driver.to_problem(basis=ElectronicBasis.AO)
print(ao_problem.basis)
from qiskit_nature.second_q.formats.qcschema_translator import qcschema_to_problem
qcschema = driver.to_qcschema()
ao_problem = qcschema_to_problem(qcschema, basis=ElectronicBasis.AO)
from qiskit_nature.second_q.formats.qcschema_translator import get_ao_to_mo_from_qcschema
basis_transformer = get_ao_to_mo_from_qcschema(qcschema)
mo_problem = basis_transformer.transform(ao_problem)
print(mo_problem.basis)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_nature.second_q.problems import BaseProblem
dummy_hamiltonian = None
base_problem = BaseProblem(dummy_hamiltonian)
print(base_problem.properties)
from qiskit_nature.second_q.properties import AngularMomentum
print("AngularMomentum is in problem.properties:", AngularMomentum in base_problem.properties)
print("Adding AngularMomentum to problem.properties...")
base_problem.properties.add(AngularMomentum(2))
print("AngularMomentum is in problem.properties:", AngularMomentum in base_problem.properties)
print("Discarding AngularMomentum from problem.properties...")
base_problem.properties.discard(AngularMomentum)
print("AngularMomentum is in problem.properties:", AngularMomentum in base_problem.properties)
from qiskit_nature.second_q.drivers import PySCFDriver
es_problem = PySCFDriver().run()
print(es_problem.properties.particle_number)
print(es_problem.properties.angular_momentum)
print(es_problem.properties.magnetization)
print(es_problem.properties.electronic_dipole_moment)
print(es_problem.properties.electronic_density)
from qiskit_nature.second_q.properties import ElectronicDensity
density = ElectronicDensity.from_orbital_occupation(
es_problem.orbital_occupations,
es_problem.orbital_occupations_b,
)
es_problem.properties.electronic_density = density
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from math import pi
import numpy as np
import rustworkx as rx
from qiskit_nature.second_q.hamiltonians.lattices import (
BoundaryCondition,
HyperCubicLattice,
Lattice,
LatticeDrawStyle,
LineLattice,
SquareLattice,
TriangularLattice,
)
from qiskit_nature.second_q.hamiltonians import FermiHubbardModel
num_nodes = 11
boundary_condition = BoundaryCondition.OPEN
line_lattice = LineLattice(num_nodes=num_nodes, boundary_condition=boundary_condition)
line_lattice.draw()
num_nodes = 11
boundary_condition = BoundaryCondition.PERIODIC
line_lattice = LineLattice(num_nodes=num_nodes, boundary_condition=boundary_condition)
line_lattice.draw()
line_lattice.draw_without_boundary()
num_nodes = 11
boundary_condition = BoundaryCondition.PERIODIC
edge_parameter = 1.0 + 1.0j
onsite_parameter = 1.0
line_lattice = LineLattice(
num_nodes=num_nodes,
edge_parameter=edge_parameter,
onsite_parameter=onsite_parameter,
boundary_condition=boundary_condition,
)
set(line_lattice.graph.weighted_edge_list())
line_lattice.to_adjacency_matrix()
line_lattice.to_adjacency_matrix(weighted=True)
rows = 5
cols = 4
boundary_condition = BoundaryCondition.OPEN
square_lattice = SquareLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
square_lattice.draw()
rows = 5
cols = 4
boundary_condition = (
BoundaryCondition.OPEN,
BoundaryCondition.PERIODIC,
) # open in the x-direction, periodic in the y-direction
square_lattice = SquareLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
square_lattice.draw()
rows = 5
cols = 4
edge_parameter = (1.0, 1.0 + 1.0j)
boundary_condition = (
BoundaryCondition.OPEN,
BoundaryCondition.PERIODIC,
) # open in the x-direction, periodic in the y-direction
onsite_parameter = 1.0
square_lattice = SquareLattice(
rows=rows,
cols=cols,
edge_parameter=edge_parameter,
onsite_parameter=onsite_parameter,
boundary_condition=boundary_condition,
)
set(square_lattice.graph.weighted_edge_list())
size = (3, 4, 5)
boundary_condition = (
BoundaryCondition.OPEN,
BoundaryCondition.OPEN,
BoundaryCondition.OPEN,
)
cubic_lattice = HyperCubicLattice(size=size, boundary_condition=boundary_condition)
# function for setting the positions
def indextocoord_3d(index: int, size: tuple, angle) -> list:
z = index // (size[0] * size[1])
a = index % (size[0] * size[1])
y = a // size[0]
x = a % size[0]
vec_x = np.array([1, 0])
vec_y = np.array([np.cos(angle), np.sin(angle)])
vec_z = np.array([0, 1])
return_coord = x * vec_x + y * vec_y + z * vec_z
return return_coord.tolist()
pos = dict([(index, indextocoord_3d(index, size, angle=pi / 4)) for index in range(np.prod(size))])
cubic_lattice.draw(style=LatticeDrawStyle(pos=pos))
rows = 4
cols = 3
boundary_condition = BoundaryCondition.OPEN
triangular_lattice = TriangularLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
triangular_lattice.draw()
rows = 4
cols = 3
boundary_condition = BoundaryCondition.PERIODIC
triangular_lattice = TriangularLattice(rows=rows, cols=cols, boundary_condition=boundary_condition)
triangular_lattice.draw()
graph = rx.PyGraph(multigraph=False) # multigraph shoud be False
graph.add_nodes_from(range(6))
weighted_edge_list = [
(0, 1, 1.0 + 1.0j),
(0, 2, -1.0),
(2, 3, 2.0),
(4, 2, -1.0 + 2.0j),
(4, 4, 3.0),
(2, 5, -1.0),
]
graph.add_edges_from(weighted_edge_list)
# make a lattice
general_lattice = Lattice(graph)
set(general_lattice.graph.weighted_edge_list())
general_lattice.draw()
general_lattice.draw(self_loop=True)
general_lattice.draw(self_loop=True, style=LatticeDrawStyle(with_labels=True))
square_lattice = SquareLattice(rows=5, cols=4, boundary_condition=BoundaryCondition.PERIODIC)
t = -1.0 # the interaction parameter
v = 0.0 # the onsite potential
u = 5.0 # the interaction parameter U
fhm = FermiHubbardModel(
square_lattice.uniform_parameters(
uniform_interaction=t,
uniform_onsite_potential=v,
),
onsite_interaction=u,
)
ham = fhm.second_q_op().simplify()
print(ham)
graph = rx.PyGraph(multigraph=False) # multiigraph shoud be False
graph.add_nodes_from(range(6))
weighted_edge_list = [
(0, 1, 1.0 + 1.0j),
(0, 2, -1.0),
(2, 3, 2.0),
(4, 2, -1.0 + 2.0j),
(4, 4, 3.0),
(2, 5, -1.0),
]
graph.add_edges_from(weighted_edge_list)
general_lattice = Lattice(graph) # the lattice whose weights are seen as the interaction matrix.
u = 5.0 # the interaction parameter U
fhm = FermiHubbardModel(lattice=general_lattice, onsite_interaction=u)
ham = fhm.second_q_op().simplify()
print(ham)
from qiskit_nature.second_q.problems import LatticeModelProblem
num_nodes = 4
boundary_condition = BoundaryCondition.OPEN
line_lattice = LineLattice(num_nodes=num_nodes, boundary_condition=boundary_condition)
fhm = FermiHubbardModel(
line_lattice.uniform_parameters(
uniform_interaction=t,
uniform_onsite_potential=v,
),
onsite_interaction=u,
)
lmp = LatticeModelProblem(fhm)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_nature.second_q.algorithms import GroundStateEigensolver
from qiskit_nature.second_q.mappers import JordanWignerMapper
numpy_solver = NumPyMinimumEigensolver()
qubit_mapper = JordanWignerMapper()
calc = GroundStateEigensolver(qubit_mapper, numpy_solver)
res = calc.solve(lmp)
print(res)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
from qiskit_nature.second_q.hamiltonians import QuadraticHamiltonian
# create Hamiltonian
hermitian_part = np.array(
[
[1.0, 2.0, 0.0, 0.0],
[2.0, 1.0, 2.0, 0.0],
[0.0, 2.0, 1.0, 2.0],
[0.0, 0.0, 2.0, 1.0],
]
)
antisymmetric_part = np.array(
[
[0.0, 3.0, 0.0, 0.0],
[-3.0, 0.0, 3.0, 0.0],
[0.0, -3.0, 0.0, 3.0],
[0.0, 0.0, -3.0, 0.0],
]
)
constant = 4.0
hamiltonian = QuadraticHamiltonian(
hermitian_part=hermitian_part,
antisymmetric_part=antisymmetric_part,
constant=constant,
)
# convert it to a FermionicOp and print it
hamiltonian_ferm = hamiltonian.second_q_op()
print(hamiltonian_ferm)
# get the transformation matrix W and orbital energies {epsilon_j}
(
transformation_matrix,
orbital_energies,
transformed_constant,
) = hamiltonian.diagonalizing_bogoliubov_transform()
print(f"Shape of matrix W: {transformation_matrix.shape}")
print(f"Orbital energies: {orbital_energies}")
print(f"Transformed constant: {transformed_constant}")
from qiskit_nature.second_q.circuit.library import FermionicGaussianState
occupied_orbitals = (0, 2)
eig = np.sum(orbital_energies[list(occupied_orbitals)]) + transformed_constant
print(f"Eigenvalue: {eig}")
circuit = FermionicGaussianState(transformation_matrix, occupied_orbitals=occupied_orbitals)
circuit.draw("mpl")
from qiskit.quantum_info import Statevector
from qiskit_nature.second_q.mappers import JordanWignerMapper
# simulate the circuit to get the final state
state = np.array(Statevector(circuit))
# convert the Hamiltonian to a matrix
hamiltonian_jw = JordanWignerMapper().map(hamiltonian_ferm).to_matrix()
# check that the state is an eigenvector with the expected eigenvalue
np.testing.assert_allclose(hamiltonian_jw @ state, eig * state, atol=1e-8)
# create Hamiltonian
hermitian_part = np.array(
[
[1.0, 2.0, 0.0, 0.0],
[2.0, 1.0, 2.0, 0.0],
[0.0, 2.0, 1.0, 2.0],
[0.0, 0.0, 2.0, 1.0],
]
)
constant = 4.0
hamiltonian = QuadraticHamiltonian(
hermitian_part=hermitian_part,
constant=constant,
)
print(f"Hamiltonian conserves particle number: {hamiltonian.conserves_particle_number()}")
# get the transformation matrix W and orbital energies {epsilon_j}
(
transformation_matrix,
orbital_energies,
transformed_constant,
) = hamiltonian.diagonalizing_bogoliubov_transform()
print(f"Shape of matrix W: {transformation_matrix.shape}")
print(f"Orbital energies: {orbital_energies}")
print(f"Transformed constant: {transformed_constant}")
from qiskit_nature.second_q.circuit.library import SlaterDeterminant
occupied_orbitals = (0, 2)
eig = np.sum(orbital_energies[list(occupied_orbitals)]) + transformed_constant
print(f"Eigenvalue: {eig}")
circuit = SlaterDeterminant(transformation_matrix[list(occupied_orbitals)])
circuit.draw("mpl")
from qiskit_nature.second_q.circuit.library import BogoliubovTransform
from qiskit import QuantumCircuit, QuantumRegister
from qiskit.quantum_info import random_hermitian, random_statevector, state_fidelity
from scipy.linalg import expm
# create Hamiltonian
n_modes = 5
hermitian_part = np.array(random_hermitian(n_modes))
hamiltonian = QuadraticHamiltonian(hermitian_part=hermitian_part)
# diagonalize Hamiltonian
(
transformation_matrix,
orbital_energies,
_,
) = hamiltonian.diagonalizing_bogoliubov_transform()
# set simulation time and construct time evolution circuit
time = 1.0
register = QuantumRegister(n_modes)
circuit = QuantumCircuit(register)
bog_circuit = BogoliubovTransform(transformation_matrix)
# change to the diagonal basis of the Hamiltonian
circuit.append(bog_circuit.inverse(), register)
# perform time evolution by applying z rotations
for q, energy in zip(register, orbital_energies):
circuit.rz(-energy * time, q)
# change back to the original basis
circuit.append(bog_circuit, register)
# simulate the circuit
initial_state = random_statevector(2**n_modes)
final_state = initial_state.evolve(circuit)
# compute the correct state by direct exponentiation
hamiltonian_jw = JordanWignerMapper().map(hamiltonian.second_q_op()).to_matrix()
exact_evolution_op = expm(-1j * time * hamiltonian_jw)
expected_state = exact_evolution_op @ np.array(initial_state)
# check that the simulated state is correct
fidelity = state_fidelity(final_state, expected_state)
np.testing.assert_allclose(fidelity, 1.0, atol=1e-8)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import display, clear_output
from qiskit.primitives import Estimator
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.observables_evaluator import estimate_observables
from qiskit.algorithms.optimizers import COBYLA, SLSQP
from qiskit.circuit import QuantumCircuit, Parameter
from qiskit.circuit.library import TwoLocal
from qiskit.quantum_info import Pauli, SparsePauliOp
from qiskit.utils import algorithm_globals
from qiskit_nature.second_q.operators import FermionicOp
from qiskit_nature.second_q.mappers import JordanWignerMapper
def kronecker_delta_function(n: int, m: int) -> int:
"""An implementation of the Kronecker delta function.
Args:
n (int): The first integer argument.
m (int): The second integer argument.
Returns:
Returns 1 if n = m, else returns 0.
"""
return int(n == m)
def create_deuteron_hamiltonian(
N: int, hbar_omega: float = 7.0, V_0: float = -5.68658111
) -> SparsePauliOp:
"""Creates a version of the Deuteron Hamiltonian as a qubit operator.
Args:
N (int): An integer number that represents the dimension of the
basis.
hbar_omega (float, optional): The value of the product of hbar and omega. Defaults to 7.0.
V_0 (float, optional): The value of the potential energy. Defaults to -5.68658111.
Returns:
SparsePauliOp: The qubit-space Hamiltonian that represents the Deuteron.
"""
hamiltonian_terms = {}
for m in range(N):
for n in range(N):
label = "+_{} -_{}".format(str(n), str(m))
coefficient_kinect = (hbar_omega / 2) * (
(2 * n + 3 / 2) * kronecker_delta_function(n, m)
- np.sqrt(n * (n + (1 / 2))) * kronecker_delta_function(n, m + 1)
- np.sqrt((n + 1) * (n + (3 / 2)) * kronecker_delta_function(n, m - 1))
)
hamiltonian_terms[label] = coefficient_kinect
coefficient_potential = (
V_0 * kronecker_delta_function(n, 0) * kronecker_delta_function(n, m)
)
hamiltonian_terms[label] += coefficient_potential
hamiltonian = FermionicOp(hamiltonian_terms, num_spin_orbitals=N)
mapper = JordanWignerMapper()
qubit_hamiltonian = mapper.map(hamiltonian)
if not isinstance(qubit_hamiltonian, SparsePauliOp):
qubit_hamiltonian = qubit_hamiltonian.primitive
return qubit_hamiltonian
deuteron_hamiltonians = [create_deuteron_hamiltonian(i) for i in range(1, 5)]
for i, hamiltonian in enumerate(deuteron_hamiltonians):
print("Deuteron Hamiltonian: H_{}".format(i + 1))
print(hamiltonian)
print("\n")
theta = Parameter(r"$\theta$")
eta = Parameter(r"$\eta$")
wavefunction = QuantumCircuit(1)
wavefunction.ry(theta, 0)
wavefunction.draw("mpl")
wavefunction2 = QuantumCircuit(2)
wavefunction2.x(0)
wavefunction2.ry(theta, 1)
wavefunction2.cx(1, 0)
wavefunction2.draw("mpl")
wavefunction3 = QuantumCircuit(3)
wavefunction3.x(0)
wavefunction3.ry(eta, 1)
wavefunction3.ry(theta, 2)
wavefunction3.cx(2, 0)
wavefunction3.cx(0, 1)
wavefunction3.ry(-eta, 1)
wavefunction3.cx(0, 1)
wavefunction3.cx(1, 0)
wavefunction3.draw("mpl")
ansatz = [wavefunction, wavefunction2, wavefunction3]
reference_values = []
print("Exact binding energies calculated through numpy.linalg.eigh \n")
for i, hamiltonian in enumerate(deuteron_hamiltonians):
eigenvalues, eigenstates = np.linalg.eigh(hamiltonian.to_matrix())
reference_values.append(eigenvalues[0])
print("Exact binding energy for H_{}: {}".format(i + 1, eigenvalues[0]))
print(
"Results using Estimator for H_1, H_2 and H_3 with the ansatz given in the reference paper \n"
)
for i in range(3):
seed = 42
algorithm_globals.random_seed = seed
vqe = VQE(Estimator(), ansatz=ansatz[i], optimizer=SLSQP())
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
binding_energy = vqe_result.optimal_value
print("Binding energy for H_{}: {} MeV".format(i + 1, binding_energy))
def callback(eval_count, parameters, mean, std):
# Overwrites the same line when printing
display("Evaluation: {}, Energy: {}, Std: {}".format(eval_count, mean, std))
clear_output(wait=True)
counts.append(eval_count)
values.append(mean)
params.append(parameters)
deviation.append(std)
plots = []
for i in range(3):
counts = []
values = []
params = []
deviation = []
seed = 42
algorithm_globals.random_seed = seed
vqe = VQE(Estimator(), ansatz=ansatz[i], optimizer=COBYLA(), callback=callback)
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
plots.append([counts, values])
fig, ax = plt.subplots(nrows=3, ncols=1)
fig.set_size_inches((12, 12))
for i, plot in enumerate(plots):
ax[i].plot(plot[0], plot[1], "o-", label="COBYLA")
ax[i].axhline(
y=reference_values[i],
color="k",
linestyle="--",
label=f"Reference Value: {reference_values[i]}",
)
ax[i].legend()
ax[i].set_xlabel("Cost Function Evaluations", fontsize=15)
ax[i].set_ylabel(r"$\langle H_{} \rangle$ - Energy (MeV)".format(i + 1), fontsize=15)
plt.show()
twolocal_ansatzes = []
for i in range(1, 5):
ansatz = TwoLocal(
deuteron_hamiltonians[i - 1].num_qubits,
["rz", "ry"],
"cx",
entanglement="full",
reps=i,
initial_state=None,
)
twolocal_ansatzes.append(ansatz)
print("Results using Estimator for H_1, H_2, H_3 and H_4 with TwoLocal ansatz \n")
seed = 42
algorithm_globals.random_seed = seed
for i in range(4):
vqe = VQE(Estimator(), ansatz=twolocal_ansatzes[i], optimizer=SLSQP())
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
binding_energy = vqe_result.optimal_value
print("Binding energy for H_{}:".format(i + 1), binding_energy, "MeV")
seed = 42
algorithm_globals.random_seed = seed
plots_tl = []
for i in range(4):
counts = []
values = []
params = []
deviation = []
vqe = VQE(
Estimator(),
ansatz=twolocal_ansatzes[i],
optimizer=SLSQP(),
callback=callback,
)
vqe_result = vqe.compute_minimum_eigenvalue(deuteron_hamiltonians[i])
plots_tl.append([counts, values])
fig, ax = plt.subplots(nrows=4, ncols=1)
fig.set_size_inches((15, 15))
for i, plot in enumerate(plots_tl):
ax[i].plot(plot[0], plot[1], "o-", label="COBYLA")
ax[i].axhline(
y=reference_values[i],
color="k",
linestyle="--",
label=f"Reference Value: {reference_values[i]}",
)
ax[i].legend()
ax[i].set_xlabel("Cost Function Evaluations", fontsize=15)
ax[i].set_ylabel(r"$\langle H_{} \rangle$ - Energy (MeV)".format(i + 1), fontsize=15)
plt.show()
def calculate_observables_exp_values(
quantum_circuit: QuantumCircuit, observables: list, angles: list
) -> list:
"""Calculate the expectation value of an observable given the quantum
circuit that represents the wavefunction and a list of parameters.
Args:
quantum_circuit (QuantumCircuit): A parameterized quantum circuit
that represents the wavefunction of the system.
observables (list): A list containing the observables that we want
to know the expectation values.
angles (list): A list with the values that will be used in the
'bind_parameters' method.
Returns:
list_exp_values (list): A list containing the expectation values
of the observables given as input.
"""
list_exp_values = []
for observable in observables:
exp_values = []
for angle in angles:
qc = quantum_circuit.bind_parameters({theta: angle})
result = estimate_observables(
Estimator(),
quantum_state=qc,
observables=[observable],
)
exp_values.append(result[0][0])
list_exp_values.append(exp_values)
return list_exp_values
angles = list(np.linspace(-np.pi, np.pi, 100))
observables = [
Pauli("IZ"),
Pauli("ZI"),
Pauli("XX"),
Pauli("YY"),
deuteron_hamiltonians[1],
]
h2_observables_exp_values = calculate_observables_exp_values(wavefunction2, observables, angles)
fig, ax = plt.subplots(nrows=2, ncols=1)
fig.set_size_inches((12, 12))
ax[0].plot(angles, h2_observables_exp_values[0], "o", label=r"$Z_0$")
ax[0].plot(angles, h2_observables_exp_values[1], "o", label=r"$Z_1$")
ax[0].plot(angles, h2_observables_exp_values[2], "o", label=r"$X_0X_1$")
ax[0].plot(angles, h2_observables_exp_values[3], "o", label=r"$Y_0Y_1$")
ax[0].axhline(
y=1,
color="k",
linestyle="--",
)
ax[0].axhline(y=-1, color="k", linestyle="--")
ax[0].legend()
ax[0].set_xlabel(r"Theta - $\theta$", fontsize=15)
ax[0].set_ylabel(r"$\langle O \rangle $ - Operator Expectation Value", fontsize=15)
ax[0].set_xticks(
[-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi],
labels=[r"$-\pi$", r"$-\pi/2$", "0", r"$\pi/2$", r"$\pi$"],
)
ax[0].set_title(
r"Expectation value of the observables $Z_0$, $Z_1$, $X_0X_1$ and $Y_0Y_1$ when we vary $\theta$ in the ansatz.",
fontsize=15,
)
ax[1].plot(angles, h2_observables_exp_values[4], "o")
ax[1].axhline(
y=reference_values[1],
color="k",
linestyle="--",
label="Binding Energy: {} MeV".format(np.round(reference_values[1], 3)),
)
ax[1].legend()
ax[1].set_xlabel(r"Theta - $\theta$", fontsize=15)
ax[1].set_ylabel(r"$\langle H_2 \rangle $ - Energy (MeV)", fontsize=15)
ax[1].set_xticks(
[-np.pi, -np.pi / 2, 0, np.pi / 2, np.pi],
labels=[r"$-\pi$", r"$-\pi/2$", "0", r"$\pi/2$", r"$\pi$"],
)
ax[1].set_title(
r"Behavior of the expectation value of $H_2$ when we vary $\theta$ in the ansatz.", fontsize=15
)
plt.show()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
problem = QuadraticProgram("sample")
problem.binary_var("x")
problem.binary_var("y")
problem.maximize(linear={"x": 1, "y": -2})
print(problem.prettyprint())
from qiskit.algorithms import NumPyMinimumEigensolver
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = NumPyMinimumEigensolver()
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = NumPyMinimumEigensolver()
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import MinimumEigenOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
mes = QAOA(optimizer=COBYLA(), quantum_instance=qins)
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
shots = 1000
mes = QAOA(sampler=Sampler(), optimizer=COBYLA())
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms import VQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import MinimumEigenOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
mes = VQE(ansatz=RealAmplitudes(), optimizer=COBYLA(), quantum_instance=qins)
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = SamplingVQE(sampler=Sampler(), ansatz=RealAmplitudes(), optimizer=COBYLA())
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Estimator
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = VQE(estimator=Estimator(), ansatz=RealAmplitudes(), optimizer=COBYLA())
try:
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
except TypeError as ex:
print(ex)
from qiskit import BasicAer
from qiskit.algorithms import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer, SlsqpOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
qaoa = QAOA(optimizer=COBYLA(), quantum_instance=qins)
optimizer = WarmStartQAOAOptimizer(
pre_solver=SlsqpOptimizer(), relax_for_pre_solver=True, qaoa=qaoa, epsilon=0.25
)
result = optimizer.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer, SlsqpOptimizer
qaoa = QAOA(sampler=Sampler(), optimizer=COBYLA())
optimizer = WarmStartQAOAOptimizer(
pre_solver=SlsqpOptimizer(), relax_for_pre_solver=True, qaoa=qaoa, epsilon=0.25
)
result = optimizer.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import GroverOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
optimizer = GroverOptimizer(num_value_qubits=3, num_iterations=3, quantum_instance=qins)
result = optimizer.solve(problem)
print(result)
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer
optimizer = GroverOptimizer(num_value_qubits=3, num_iterations=3, sampler=Sampler())
result = optimizer.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
try:
optimizer = GroverOptimizer(
num_value_qubits=3, num_iterations=3, quantum_instance=qins, sampler=Sampler()
)
# raises an error because both quantum_instance and sampler are set.
except ValueError as ex:
print(ex)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.translators import from_docplex_mp
# Make a Docplex model
from docplex.mp.model import Model
mdl = Model("docplex model")
x = mdl.binary_var("x")
y = mdl.integer_var(lb=-1, ub=5, name="y")
mdl.minimize(x + 2 * y)
mdl.add_constraint(x - y == 3)
mdl.add_constraint((x + y) * (x - y) <= 1)
print(mdl.export_as_lp_string())
# load from a Docplex model
mod = from_docplex_mp(mdl)
print(type(mod))
print()
print(mod.prettyprint())
# make an empty problem
mod = QuadraticProgram("my problem")
print(mod.prettyprint())
# Add variables
mod.binary_var(name="x")
mod.integer_var(name="y", lowerbound=-1, upperbound=5)
mod.continuous_var(name="z", lowerbound=-1, upperbound=5)
print(mod.prettyprint())
# Add objective function using dictionaries
mod.minimize(constant=3, linear={"x": 1}, quadratic={("x", "y"): 2, ("z", "z"): -1})
print(mod.prettyprint())
# Add objective function using lists/arrays
mod.minimize(constant=3, linear=[1, 0, 0], quadratic=[[0, 1, 0], [1, 0, 0], [0, 0, -1]])
print(mod.prettyprint())
print("constant:\t\t\t", mod.objective.constant)
print("linear dict:\t\t\t", mod.objective.linear.to_dict())
print("linear array:\t\t\t", mod.objective.linear.to_array())
print("linear array as sparse matrix:\n", mod.objective.linear.coefficients, "\n")
print("quadratic dict w/ index:\t", mod.objective.quadratic.to_dict())
print("quadratic dict w/ name:\t\t", mod.objective.quadratic.to_dict(use_name=True))
print(
"symmetric quadratic dict w/ name:\t",
mod.objective.quadratic.to_dict(use_name=True, symmetric=True),
)
print("quadratic matrix:\n", mod.objective.quadratic.to_array(), "\n")
print("symmetric quadratic matrix:\n", mod.objective.quadratic.to_array(symmetric=True), "\n")
print("quadratic matrix as sparse matrix:\n", mod.objective.quadratic.coefficients)
# Add linear constraints
mod.linear_constraint(linear={"x": 1, "y": 2}, sense="==", rhs=3, name="lin_eq")
mod.linear_constraint(linear={"x": 1, "y": 2}, sense="<=", rhs=3, name="lin_leq")
mod.linear_constraint(linear={"x": 1, "y": 2}, sense=">=", rhs=3, name="lin_geq")
print(mod.prettyprint())
# Add quadratic constraints
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense="==",
rhs=1,
name="quad_eq",
)
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense="<=",
rhs=1,
name="quad_leq",
)
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense=">=",
rhs=1,
name="quad_geq",
)
print(mod.prettyprint())
lin_geq = mod.get_linear_constraint("lin_geq")
print("lin_geq:", lin_geq.linear.to_dict(use_name=True), lin_geq.sense, lin_geq.rhs)
quad_geq = mod.get_quadratic_constraint("quad_geq")
print(
"quad_geq:",
quad_geq.linear.to_dict(use_name=True),
quad_geq.quadratic.to_dict(use_name=True),
quad_geq.sense,
lin_geq.rhs,
)
# Remove constraints
mod.remove_linear_constraint("lin_eq")
mod.remove_quadratic_constraint("quad_leq")
print(mod.prettyprint())
sub = mod.substitute_variables(constants={"x": 0}, variables={"y": ("z", -1)})
print(sub.prettyprint())
sub = mod.substitute_variables(constants={"x": -1})
print(sub.status)
from qiskit_optimization import QiskitOptimizationError
try:
sub = mod.substitute_variables(constants={"x": -1}, variables={"y": ("x", 1)})
except QiskitOptimizationError as e:
print("Error: {}".format(e))
mod = QuadraticProgram()
mod.binary_var(name="e")
mod.binary_var(name="f")
mod.continuous_var(name="g")
mod.minimize(linear=[1, 2, 3])
print(mod.export_as_lp_string())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
qp = QuadraticProgram()
qp.binary_var("x")
qp.binary_var("y")
qp.integer_var(lowerbound=0, upperbound=7, name="z")
qp.maximize(linear={"x": 2, "y": 1, "z": 1})
qp.linear_constraint(linear={"x": 1, "y": 1, "z": 1}, sense="LE", rhs=5.5, name="xyz_leq")
qp.linear_constraint(linear={"x": 1, "y": 1, "z": 1}, sense="GE", rhs=2.5, name="xyz_geq")
print(qp.prettyprint())
from qiskit_optimization.converters import InequalityToEquality
ineq2eq = InequalityToEquality()
qp_eq = ineq2eq.convert(qp)
print(qp_eq.prettyprint())
print(qp_eq.prettyprint())
from qiskit_optimization.converters import IntegerToBinary
int2bin = IntegerToBinary()
qp_eq_bin = int2bin.convert(qp_eq)
print(qp_eq_bin.prettyprint())
print(qp_eq_bin.prettyprint())
from qiskit_optimization.converters import LinearEqualityToPenalty
lineq2penalty = LinearEqualityToPenalty()
qubo = lineq2penalty.convert(qp_eq_bin)
print(qubo.prettyprint())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import (
MinimumEigenOptimizer,
RecursiveMinimumEigenOptimizer,
SolutionSample,
OptimizationResultStatus,
)
from qiskit_optimization import QuadraticProgram
from qiskit.visualization import plot_histogram
from typing import List, Tuple
import numpy as np
# create a QUBO
qubo = QuadraticProgram()
qubo.binary_var("x")
qubo.binary_var("y")
qubo.binary_var("z")
qubo.minimize(linear=[1, -2, 3], quadratic={("x", "y"): 1, ("x", "z"): -1, ("y", "z"): 2})
print(qubo.prettyprint())
op, offset = qubo.to_ising()
print("offset: {}".format(offset))
print("operator:")
print(op)
qp = QuadraticProgram()
qp.from_ising(op, offset, linear=True)
print(qp.prettyprint())
algorithm_globals.random_seed = 10598
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 0.0])
exact_mes = NumPyMinimumEigensolver()
qaoa = MinimumEigenOptimizer(qaoa_mes) # using QAOA
exact = MinimumEigenOptimizer(exact_mes) # using the exact classical numpy minimum eigen solver
exact_result = exact.solve(qubo)
print(exact_result.prettyprint())
qaoa_result = qaoa.solve(qubo)
print(qaoa_result.prettyprint())
print("variable order:", [var.name for var in qaoa_result.variables])
for s in qaoa_result.samples:
print(s)
def get_filtered_samples(
samples: List[SolutionSample],
threshold: float = 0,
allowed_status: Tuple[OptimizationResultStatus] = (OptimizationResultStatus.SUCCESS,),
):
res = []
for s in samples:
if s.status in allowed_status and s.probability > threshold:
res.append(s)
return res
filtered_samples = get_filtered_samples(
qaoa_result.samples, threshold=0.005, allowed_status=(OptimizationResultStatus.SUCCESS,)
)
for s in filtered_samples:
print(s)
fvals = [s.fval for s in qaoa_result.samples]
probabilities = [s.probability for s in qaoa_result.samples]
np.mean(fvals)
np.std(fvals)
samples_for_plot = {
" ".join(f"{qaoa_result.variables[i].name}={int(v)}" for i, v in enumerate(s.x)): s.probability
for s in filtered_samples
}
samples_for_plot
plot_histogram(samples_for_plot)
rqaoa = RecursiveMinimumEigenOptimizer(qaoa, min_num_vars=1, min_num_vars_optimizer=exact)
rqaoa_result = rqaoa.solve(qubo)
print(rqaoa_result.prettyprint())
filtered_samples = get_filtered_samples(
rqaoa_result.samples, threshold=0.005, allowed_status=(OptimizationResultStatus.SUCCESS,)
)
samples_for_plot = {
" ".join(f"{rqaoa_result.variables[i].name}={int(v)}" for i, v in enumerate(s.x)): s.probability
for s in filtered_samples
}
samples_for_plot
plot_histogram(samples_for_plot)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer, MinimumEigenOptimizer
from qiskit_optimization.translators import from_docplex_mp
from docplex.mp.model import Model
model = Model()
x0 = model.binary_var(name="x0")
x1 = model.binary_var(name="x1")
x2 = model.binary_var(name="x2")
model.minimize(-x0 + 2 * x1 - 3 * x2 - 2 * x0 * x2 - 1 * x1 * x2)
qp = from_docplex_mp(model)
print(qp.prettyprint())
grover_optimizer = GroverOptimizer(6, num_iterations=10, sampler=Sampler())
results = grover_optimizer.solve(qp)
print(results.prettyprint())
exact_solver = MinimumEigenOptimizer(NumPyMinimumEigensolver())
exact_result = exact_solver.solve(qp)
print(exact_result.prettyprint())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import matplotlib.pyplot as plt
from docplex.mp.model import Model
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import CobylaOptimizer, MinimumEigenOptimizer
from qiskit_optimization.algorithms.admm_optimizer import ADMMParameters, ADMMOptimizer
from qiskit_optimization.translators import from_docplex_mp
# If CPLEX is installed, you can uncomment this line to import the CplexOptimizer.
# CPLEX can be used in this tutorial to solve the convex continuous problem,
# but also as a reference to solve the QUBO, or even the full problem.
#
# from qiskit.optimization.algorithms import CplexOptimizer
# define COBYLA optimizer to handle convex continuous problems.
cobyla = CobylaOptimizer()
# define QAOA via the minimum eigen optimizer
qaoa = MinimumEigenOptimizer(QAOA(sampler=Sampler(), optimizer=COBYLA()))
# exact QUBO solver as classical benchmark
exact = MinimumEigenOptimizer(NumPyMinimumEigensolver()) # to solve QUBOs
# in case CPLEX is installed it can also be used for the convex problems, the QUBO,
# or as a benchmark for the full problem.
#
# cplex = CplexOptimizer()
# construct model using docplex
mdl = Model("ex6")
v = mdl.binary_var(name="v")
w = mdl.binary_var(name="w")
t = mdl.binary_var(name="t")
u = mdl.continuous_var(name="u")
mdl.minimize(v + w + t + 5 * (u - 2) ** 2)
mdl.add_constraint(v + 2 * w + t + u <= 3, "cons1")
mdl.add_constraint(v + w + t >= 1, "cons2")
mdl.add_constraint(v + w == 1, "cons3")
# load quadratic program from docplex model
qp = from_docplex_mp(mdl)
print(qp.prettyprint())
admm_params = ADMMParameters(
rho_initial=1001, beta=1000, factor_c=900, maxiter=100, three_block=True, tol=1.0e-6
)
# define QUBO optimizer
qubo_optimizer = exact
# qubo_optimizer = cplex # uncomment to use CPLEX instead
# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex # uncomment to use CPLEX instead
# initialize ADMM with classical QUBO and convex optimizer
admm = ADMMOptimizer(
params=admm_params, qubo_optimizer=qubo_optimizer, continuous_optimizer=convex_optimizer
)
# run ADMM to solve problem
result = admm.solve(qp)
print(result.prettyprint())
plt.plot(result.state.residuals)
plt.xlabel("Iterations")
plt.ylabel("Residuals")
plt.show()
# define QUBO optimizer
qubo_optimizer = qaoa
# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex # uncomment to use CPLEX instead
# initialize ADMM with quantum QUBO optimizer and classical convex optimizer
admm_q = ADMMOptimizer(
params=admm_params, qubo_optimizer=qubo_optimizer, continuous_optimizer=convex_optimizer
)
# run ADMM to solve problem
result_q = admm_q.solve(qp)
print(result.prettyprint())
plt.clf()
plt.plot(result_q.state.residuals)
plt.xlabel("Iterations")
plt.ylabel("Residuals")
plt.show()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
# useful additional packages
import matplotlib.pyplot as plt
import numpy as np
import networkx as nx
from qiskit_aer import Aer
from qiskit.tools.visualization import plot_histogram
from qiskit.circuit.library import TwoLocal
from qiskit_optimization.applications import Maxcut, Tsp
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import SPSA
from qiskit.utils import algorithm_globals
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
# Generating a graph of 4 nodes
n = 4 # Number of nodes in graph
G = nx.Graph()
G.add_nodes_from(np.arange(0, n, 1))
elist = [(0, 1, 1.0), (0, 2, 1.0), (0, 3, 1.0), (1, 2, 1.0), (2, 3, 1.0)]
# tuple is (i,j,weight) where (i,j) is the edge
G.add_weighted_edges_from(elist)
colors = ["r" for node in G.nodes()]
pos = nx.spring_layout(G)
def draw_graph(G, colors, pos):
default_axes = plt.axes(frameon=True)
nx.draw_networkx(G, node_color=colors, node_size=600, alpha=0.8, ax=default_axes, pos=pos)
edge_labels = nx.get_edge_attributes(G, "weight")
nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels)
draw_graph(G, colors, pos)
# Computing the weight matrix from the random graph
w = np.zeros([n, n])
for i in range(n):
for j in range(n):
temp = G.get_edge_data(i, j, default=0)
if temp != 0:
w[i, j] = temp["weight"]
print(w)
best_cost_brute = 0
for b in range(2**n):
x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]
cost = 0
for i in range(n):
for j in range(n):
cost = cost + w[i, j] * x[i] * (1 - x[j])
if best_cost_brute < cost:
best_cost_brute = cost
xbest_brute = x
print("case = " + str(x) + " cost = " + str(cost))
colors = ["r" if xbest_brute[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
print("\nBest solution = " + str(xbest_brute) + " cost = " + str(best_cost_brute))
max_cut = Maxcut(w)
qp = max_cut.to_quadratic_program()
print(qp.prettyprint())
qubitOp, offset = qp.to_ising()
print("Offset:", offset)
print("Ising Hamiltonian:")
print(str(qubitOp))
# solving Quadratic Program using exact classical eigensolver
exact = MinimumEigenOptimizer(NumPyMinimumEigensolver())
result = exact.solve(qp)
print(result.prettyprint())
# Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector
ee = NumPyMinimumEigensolver()
result = ee.compute_minimum_eigenvalue(qubitOp)
x = max_cut.sample_most_likely(result.eigenstate)
print("energy:", result.eigenvalue.real)
print("max-cut objective:", result.eigenvalue.real + offset)
print("solution:", x)
print("solution objective:", qp.objective.evaluate(x))
colors = ["r" if x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
# construct SamplingVQE
optimizer = SPSA(maxiter=300)
ry = TwoLocal(qubitOp.num_qubits, "ry", "cz", reps=5, entanglement="linear")
vqe = SamplingVQE(sampler=Sampler(), ansatz=ry, optimizer=optimizer)
# run SamplingVQE
result = vqe.compute_minimum_eigenvalue(qubitOp)
# print results
x = max_cut.sample_most_likely(result.eigenstate)
print("energy:", result.eigenvalue.real)
print("time:", result.optimizer_time)
print("max-cut objective:", result.eigenvalue.real + offset)
print("solution:", x)
print("solution objective:", qp.objective.evaluate(x))
# plot results
colors = ["r" if x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
# create minimum eigen optimizer based on SamplingVQE
vqe_optimizer = MinimumEigenOptimizer(vqe)
# solve quadratic program
result = vqe_optimizer.solve(qp)
print(result.prettyprint())
colors = ["r" if result.x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
# Generating a graph of 3 nodes
n = 3
num_qubits = n**2
tsp = Tsp.create_random_instance(n, seed=123)
adj_matrix = nx.to_numpy_array(tsp.graph)
print("distance\n", adj_matrix)
colors = ["r" for node in tsp.graph.nodes]
pos = [tsp.graph.nodes[node]["pos"] for node in tsp.graph.nodes]
draw_graph(tsp.graph, colors, pos)
from itertools import permutations
def brute_force_tsp(w, N):
a = list(permutations(range(1, N)))
last_best_distance = 1e10
for i in a:
distance = 0
pre_j = 0
for j in i:
distance = distance + w[j, pre_j]
pre_j = j
distance = distance + w[pre_j, 0]
order = (0,) + i
if distance < last_best_distance:
best_order = order
last_best_distance = distance
print("order = " + str(order) + " Distance = " + str(distance))
return last_best_distance, best_order
best_distance, best_order = brute_force_tsp(adj_matrix, n)
print(
"Best order from brute force = "
+ str(best_order)
+ " with total distance = "
+ str(best_distance)
)
def draw_tsp_solution(G, order, colors, pos):
G2 = nx.DiGraph()
G2.add_nodes_from(G)
n = len(order)
for i in range(n):
j = (i + 1) % n
G2.add_edge(order[i], order[j], weight=G[order[i]][order[j]]["weight"])
default_axes = plt.axes(frameon=True)
nx.draw_networkx(
G2, node_color=colors, edge_color="b", node_size=600, alpha=0.8, ax=default_axes, pos=pos
)
edge_labels = nx.get_edge_attributes(G2, "weight")
nx.draw_networkx_edge_labels(G2, pos, font_color="b", edge_labels=edge_labels)
draw_tsp_solution(tsp.graph, best_order, colors, pos)
qp = tsp.to_quadratic_program()
print(qp.prettyprint())
from qiskit_optimization.converters import QuadraticProgramToQubo
qp2qubo = QuadraticProgramToQubo()
qubo = qp2qubo.convert(qp)
qubitOp, offset = qubo.to_ising()
print("Offset:", offset)
print("Ising Hamiltonian:")
print(str(qubitOp))
result = exact.solve(qubo)
print(result.prettyprint())
# Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector
ee = NumPyMinimumEigensolver()
result = ee.compute_minimum_eigenvalue(qubitOp)
print("energy:", result.eigenvalue.real)
print("tsp objective:", result.eigenvalue.real + offset)
x = tsp.sample_most_likely(result.eigenstate)
print("feasible:", qubo.is_feasible(x))
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
optimizer = SPSA(maxiter=300)
ry = TwoLocal(qubitOp.num_qubits, "ry", "cz", reps=5, entanglement="linear")
vqe = SamplingVQE(sampler=Sampler(), ansatz=ry, optimizer=optimizer)
result = vqe.compute_minimum_eigenvalue(qubitOp)
print("energy:", result.eigenvalue.real)
print("time:", result.optimizer_time)
x = tsp.sample_most_likely(result.eigenstate)
print("feasible:", qubo.is_feasible(x))
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
# create minimum eigen optimizer based on SamplingVQE
vqe_optimizer = MinimumEigenOptimizer(vqe)
# solve quadratic program
result = vqe_optimizer.solve(qp)
print(result.prettyprint())
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import matplotlib.pyplot as plt
try:
import cplex
from cplex.exceptions import CplexError
except:
print("Warning: Cplex not found.")
import math
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE
from qiskit.algorithms.optimizers import SPSA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Sampler
# Initialize the problem by defining the parameters
n = 3 # number of nodes + depot (n+1)
K = 2 # number of vehicles
# Get the data
class Initializer:
def __init__(self, n):
self.n = n
def generate_instance(self):
n = self.n
# np.random.seed(33)
np.random.seed(1543)
xc = (np.random.rand(n) - 0.5) * 10
yc = (np.random.rand(n) - 0.5) * 10
instance = np.zeros([n, n])
for ii in range(0, n):
for jj in range(ii + 1, n):
instance[ii, jj] = (xc[ii] - xc[jj]) ** 2 + (yc[ii] - yc[jj]) ** 2
instance[jj, ii] = instance[ii, jj]
return xc, yc, instance
# Initialize the problem by randomly generating the instance
initializer = Initializer(n)
xc, yc, instance = initializer.generate_instance()
class ClassicalOptimizer:
def __init__(self, instance, n, K):
self.instance = instance
self.n = n # number of nodes
self.K = K # number of vehicles
def compute_allowed_combinations(self):
f = math.factorial
return f(self.n) / f(self.K) / f(self.n - self.K)
def cplex_solution(self):
# refactoring
instance = self.instance
n = self.n
K = self.K
my_obj = list(instance.reshape(1, n**2)[0]) + [0.0 for x in range(0, n - 1)]
my_ub = [1 for x in range(0, n**2 + n - 1)]
my_lb = [0 for x in range(0, n**2)] + [0.1 for x in range(0, n - 1)]
my_ctype = "".join(["I" for x in range(0, n**2)]) + "".join(
["C" for x in range(0, n - 1)]
)
my_rhs = (
2 * ([K] + [1 for x in range(0, n - 1)])
+ [1 - 0.1 for x in range(0, (n - 1) ** 2 - (n - 1))]
+ [0 for x in range(0, n)]
)
my_sense = (
"".join(["E" for x in range(0, 2 * n)])
+ "".join(["L" for x in range(0, (n - 1) ** 2 - (n - 1))])
+ "".join(["E" for x in range(0, n)])
)
try:
my_prob = cplex.Cplex()
self.populatebyrow(my_prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs)
my_prob.solve()
except CplexError as exc:
print(exc)
return
x = my_prob.solution.get_values()
x = np.array(x)
cost = my_prob.solution.get_objective_value()
return x, cost
def populatebyrow(self, prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs):
n = self.n
prob.objective.set_sense(prob.objective.sense.minimize)
prob.variables.add(obj=my_obj, lb=my_lb, ub=my_ub, types=my_ctype)
prob.set_log_stream(None)
prob.set_error_stream(None)
prob.set_warning_stream(None)
prob.set_results_stream(None)
rows = []
for ii in range(0, n):
col = [x for x in range(0 + n * ii, n + n * ii)]
coef = [1 for x in range(0, n)]
rows.append([col, coef])
for ii in range(0, n):
col = [x for x in range(0 + ii, n**2, n)]
coef = [1 for x in range(0, n)]
rows.append([col, coef])
# Sub-tour elimination constraints:
for ii in range(0, n):
for jj in range(0, n):
if (ii != jj) and (ii * jj > 0):
col = [ii + (jj * n), n**2 + ii - 1, n**2 + jj - 1]
coef = [1, 1, -1]
rows.append([col, coef])
for ii in range(0, n):
col = [(ii) * (n + 1)]
coef = [1]
rows.append([col, coef])
prob.linear_constraints.add(lin_expr=rows, senses=my_sense, rhs=my_rhs)
# Instantiate the classical optimizer class
classical_optimizer = ClassicalOptimizer(instance, n, K)
# Print number of feasible solutions
print("Number of feasible solutions = " + str(classical_optimizer.compute_allowed_combinations()))
# Solve the problem in a classical fashion via CPLEX
x = None
z = None
try:
x, classical_cost = classical_optimizer.cplex_solution()
# Put the solution in the z variable
z = [x[ii] for ii in range(n**2) if ii // n != ii % n]
# Print the solution
print(z)
except:
print("CPLEX may be missing.")
# Visualize the solution
def visualize_solution(xc, yc, x, C, n, K, title_str):
plt.figure()
plt.scatter(xc, yc, s=200)
for i in range(len(xc)):
plt.annotate(i, (xc[i] + 0.15, yc[i]), size=16, color="r")
plt.plot(xc[0], yc[0], "r*", ms=20)
plt.grid()
for ii in range(0, n**2):
if x[ii] > 0:
ix = ii // n
iy = ii % n
plt.arrow(
xc[ix],
yc[ix],
xc[iy] - xc[ix],
yc[iy] - yc[ix],
length_includes_head=True,
head_width=0.25,
)
plt.title(title_str + " cost = " + str(int(C * 100) / 100.0))
plt.show()
if x is not None:
visualize_solution(xc, yc, x, classical_cost, n, K, "Classical")
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.algorithms import MinimumEigenOptimizer
class QuantumOptimizer:
def __init__(self, instance, n, K):
self.instance = instance
self.n = n
self.K = K
def binary_representation(self, x_sol=0):
instance = self.instance
n = self.n
K = self.K
A = np.max(instance) * 100 # A parameter of cost function
# Determine the weights w
instance_vec = instance.reshape(n**2)
w_list = [instance_vec[x] for x in range(n**2) if instance_vec[x] > 0]
w = np.zeros(n * (n - 1))
for ii in range(len(w_list)):
w[ii] = w_list[ii]
# Some variables I will use
Id_n = np.eye(n)
Im_n_1 = np.ones([n - 1, n - 1])
Iv_n_1 = np.ones(n)
Iv_n_1[0] = 0
Iv_n = np.ones(n - 1)
neg_Iv_n_1 = np.ones(n) - Iv_n_1
v = np.zeros([n, n * (n - 1)])
for ii in range(n):
count = ii - 1
for jj in range(n * (n - 1)):
if jj // (n - 1) == ii:
count = ii
if jj // (n - 1) != ii and jj % (n - 1) == count:
v[ii][jj] = 1.0
vn = np.sum(v[1:], axis=0)
# Q defines the interactions between variables
Q = A * (np.kron(Id_n, Im_n_1) + np.dot(v.T, v))
# g defines the contribution from the individual variables
g = (
w
- 2 * A * (np.kron(Iv_n_1, Iv_n) + vn.T)
- 2 * A * K * (np.kron(neg_Iv_n_1, Iv_n) + v[0].T)
)
# c is the constant offset
c = 2 * A * (n - 1) + 2 * A * (K**2)
try:
max(x_sol)
# Evaluates the cost distance from a binary representation of a path
fun = (
lambda x: np.dot(np.around(x), np.dot(Q, np.around(x)))
+ np.dot(g, np.around(x))
+ c
)
cost = fun(x_sol)
except:
cost = 0
return Q, g, c, cost
def construct_problem(self, Q, g, c) -> QuadraticProgram:
qp = QuadraticProgram()
for i in range(n * (n - 1)):
qp.binary_var(str(i))
qp.objective.quadratic = Q
qp.objective.linear = g
qp.objective.constant = c
return qp
def solve_problem(self, qp):
algorithm_globals.random_seed = 10598
vqe = SamplingVQE(sampler=Sampler(), optimizer=SPSA(), ansatz=RealAmplitudes())
optimizer = MinimumEigenOptimizer(min_eigen_solver=vqe)
result = optimizer.solve(qp)
# compute cost of the obtained result
_, _, _, level = self.binary_representation(x_sol=result.x)
return result.x, level
# Instantiate the quantum optimizer class with parameters:
quantum_optimizer = QuantumOptimizer(instance, n, K)
# Check if the binary representation is correct
try:
if z is not None:
Q, g, c, binary_cost = quantum_optimizer.binary_representation(x_sol=z)
print("Binary cost:", binary_cost, "classical cost:", classical_cost)
if np.abs(binary_cost - classical_cost) < 0.01:
print("Binary formulation is correct")
else:
print("Error in the binary formulation")
else:
print("Could not verify the correctness, due to CPLEX solution being unavailable.")
Q, g, c, binary_cost = quantum_optimizer.binary_representation()
print("Binary cost:", binary_cost)
except NameError as e:
print("Warning: Please run the cells above first.")
print(e)
qp = quantum_optimizer.construct_problem(Q, g, c)
quantum_solution, quantum_cost = quantum_optimizer.solve_problem(qp)
print(quantum_solution, quantum_cost)
# Put the solution in a way that is compatible with the classical variables
x_quantum = np.zeros(n**2)
kk = 0
for ii in range(n**2):
if ii // n != ii % n:
x_quantum[ii] = quantum_solution[kk]
kk += 1
# visualize the solution
visualize_solution(xc, yc, x_quantum, quantum_cost, n, K, "Quantum")
# and visualize the classical for comparison
if x is not None:
visualize_solution(xc, yc, x, classical_cost, n, K, "Classical")
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.circuit.library import RealAmplitudes
from qiskit.algorithms.optimizers import COBYLA
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver, SamplingVQE
from qiskit.primitives import Sampler
from qiskit_optimization.converters import LinearEqualityToPenalty
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_optimization.translators import from_docplex_mp
from qiskit.utils import algorithm_globals
import numpy as np
import matplotlib.pyplot as plt
from docplex.mp.model import Model
algorithm_globals.random_seed = 123456
# prepare problem instance
n = 6 # number of assets
q = 0.5 # risk factor
budget = n // 2 # budget
penalty = 2 * n # scaling of penalty term
# instance from [1]
mu = np.array([0.7313, 0.9893, 0.2725, 0.8750, 0.7667, 0.3622])
sigma = np.array(
[
[0.7312, -0.6233, 0.4689, -0.5452, -0.0082, -0.3809],
[-0.6233, 2.4732, -0.7538, 2.4659, -0.0733, 0.8945],
[0.4689, -0.7538, 1.1543, -1.4095, 0.0007, -0.4301],
[-0.5452, 2.4659, -1.4095, 3.5067, 0.2012, 1.0922],
[-0.0082, -0.0733, 0.0007, 0.2012, 0.6231, 0.1509],
[-0.3809, 0.8945, -0.4301, 1.0922, 0.1509, 0.8992],
]
)
# or create random instance
# mu, sigma = portfolio.random_model(n, seed=123) # expected returns and covariance matrix
# create docplex model
mdl = Model("portfolio_optimization")
x = mdl.binary_var_list(range(n), name="x")
objective = mdl.sum([mu[i] * x[i] for i in range(n)])
objective -= q * mdl.sum([sigma[i, j] * x[i] * x[j] for i in range(n) for j in range(n)])
mdl.maximize(objective)
mdl.add_constraint(mdl.sum(x[i] for i in range(n)) == budget)
# case to
qp = from_docplex_mp(mdl)
# solve classically as reference
opt_result = MinimumEigenOptimizer(NumPyMinimumEigensolver()).solve(qp)
print(opt_result.prettyprint())
# we convert the problem to an unconstrained problem for further analysis,
# otherwise this would not be necessary as the MinimumEigenSolver would do this
# translation automatically
linear2penalty = LinearEqualityToPenalty(penalty=penalty)
qp = linear2penalty.convert(qp)
_, offset = qp.to_ising()
# set classical optimizer
maxiter = 100
optimizer = COBYLA(maxiter=maxiter)
# set variational ansatz
ansatz = RealAmplitudes(n, reps=1)
m = ansatz.num_parameters
# set sampler
sampler = Sampler()
# run variational optimization for different values of alpha
alphas = [1.0, 0.50, 0.25] # confidence levels to be evaluated
# dictionaries to store optimization progress and results
objectives = {alpha: [] for alpha in alphas} # set of tested objective functions w.r.t. alpha
results = {} # results of minimum eigensolver w.r.t alpha
# callback to store intermediate results
def callback(i, params, obj, stddev, alpha):
# we translate the objective from the internal Ising representation
# to the original optimization problem
objectives[alpha].append(np.real_if_close(-(obj + offset)))
# loop over all given alpha values
for alpha in alphas:
# initialize SamplingVQE using CVaR
vqe = SamplingVQE(
sampler=sampler,
ansatz=ansatz,
optimizer=optimizer,
aggregation=alpha,
callback=lambda i, params, obj, stddev: callback(i, params, obj, stddev, alpha),
)
# initialize optimization algorithm based on CVaR-SamplingVQE
opt_alg = MinimumEigenOptimizer(vqe)
# solve problem
results[alpha] = opt_alg.solve(qp)
# print results
print("alpha = {}:".format(alpha))
print(results[alpha].prettyprint())
print()
# plot resulting history of objective values
plt.figure(figsize=(10, 5))
plt.plot([0, maxiter], [opt_result.fval, opt_result.fval], "r--", linewidth=2, label="optimum")
for alpha in alphas:
plt.plot(objectives[alpha], label="alpha = %.2f" % alpha, linewidth=2)
plt.legend(loc="lower right", fontsize=14)
plt.xlim(0, maxiter)
plt.xticks(fontsize=14)
plt.xlabel("iterations", fontsize=14)
plt.yticks(fontsize=14)
plt.ylabel("objective value", fontsize=14)
plt.show()
# evaluate and sort all objective values
objective_values = np.zeros(2**n)
for i in range(2**n):
x_bin = ("{0:0%sb}" % n).format(i)
x = [0 if x_ == "0" else 1 for x_ in reversed(x_bin)]
objective_values[i] = qp.objective.evaluate(x)
ind = np.argsort(objective_values)
# evaluate final optimal probability for each alpha
for alpha in alphas:
probabilities = np.fromiter(
results[alpha].min_eigen_solver_result.eigenstate.binary_probabilities().values(),
dtype=float,
)
print("optimal probability (alpha = %.2f): %.4f" % (alpha, probabilities[ind][-1:]))
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.applications.vertex_cover import VertexCover
import networkx as nx
seed = 123
algorithm_globals.random_seed = seed
graph = nx.random_regular_graph(d=3, n=6, seed=seed)
pos = nx.spring_layout(graph, seed=seed)
prob = VertexCover(graph)
prob.draw(pos=pos)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# Numpy Eigensolver
meo = MinimumEigenOptimizer(min_eigen_solver=NumPyMinimumEigensolver())
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
prob.draw(result, pos=pos)
# QAOA
meo = MinimumEigenOptimizer(min_eigen_solver=QAOA(reps=1, sampler=Sampler(), optimizer=COBYLA()))
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
print("\ntime:", result.min_eigen_solver_result.optimizer_time)
prob.draw(result, pos=pos)
from qiskit_optimization.applications import Knapsack
prob = Knapsack(values=[3, 4, 5, 6, 7], weights=[2, 3, 4, 5, 6], max_weight=10)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# Numpy Eigensolver
meo = MinimumEigenOptimizer(min_eigen_solver=NumPyMinimumEigensolver())
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
# QAOA
meo = MinimumEigenOptimizer(min_eigen_solver=QAOA(reps=1, sampler=Sampler(), optimizer=COBYLA()))
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
print("\ntime:", result.min_eigen_solver_result.optimizer_time)
from qiskit_optimization.converters import QuadraticProgramToQubo
# the same knapsack problem instance as in the previous section
prob = Knapsack(values=[3, 4, 5, 6, 7], weights=[2, 3, 4, 5, 6], max_weight=10)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# intermediate QUBO form of the optimization problem
conv = QuadraticProgramToQubo()
qubo = conv.convert(qp)
print(qubo.prettyprint())
# qubit Hamiltonian and offset
op, offset = qubo.to_ising()
print(f"num qubits: {op.num_qubits}, offset: {offset}\n")
print(op)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import copy
# Problem modelling imports
from docplex.mp.model import Model
# Qiskit imports
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit.utils.algorithm_globals import algorithm_globals
from qiskit_optimization.algorithms import MinimumEigenOptimizer, CplexOptimizer
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.problems.variable import VarType
from qiskit_optimization.converters.quadratic_program_to_qubo import QuadraticProgramToQubo
from qiskit_optimization.translators import from_docplex_mp
def create_problem(mu: np.array, sigma: np.array, total: int = 3) -> QuadraticProgram:
"""Solve the quadratic program using docplex."""
mdl = Model()
x = [mdl.binary_var("x%s" % i) for i in range(len(sigma))]
objective = mdl.sum([mu[i] * x[i] for i in range(len(mu))])
objective -= 2 * mdl.sum(
[sigma[i, j] * x[i] * x[j] for i in range(len(mu)) for j in range(len(mu))]
)
mdl.maximize(objective)
cost = mdl.sum(x)
mdl.add_constraint(cost == total)
qp = from_docplex_mp(mdl)
return qp
def relax_problem(problem) -> QuadraticProgram:
"""Change all variables to continuous."""
relaxed_problem = copy.deepcopy(problem)
for variable in relaxed_problem.variables:
variable.vartype = VarType.CONTINUOUS
return relaxed_problem
mu = np.array([3.418, 2.0913, 6.2415, 4.4436, 10.892, 3.4051])
sigma = np.array(
[
[1.07978412, 0.00768914, 0.11227606, -0.06842969, -0.01016793, -0.00839765],
[0.00768914, 0.10922887, -0.03043424, -0.0020045, 0.00670929, 0.0147937],
[0.11227606, -0.03043424, 0.985353, 0.02307313, -0.05249785, 0.00904119],
[-0.06842969, -0.0020045, 0.02307313, 0.6043817, 0.03740115, -0.00945322],
[-0.01016793, 0.00670929, -0.05249785, 0.03740115, 0.79839634, 0.07616951],
[-0.00839765, 0.0147937, 0.00904119, -0.00945322, 0.07616951, 1.08464544],
]
)
qubo = create_problem(mu, sigma)
print(qubo.prettyprint())
result = CplexOptimizer().solve(qubo)
print(result.prettyprint())
qp = relax_problem(QuadraticProgramToQubo().convert(qubo))
print(qp.prettyprint())
sol = CplexOptimizer().solve(qp)
print(sol.prettyprint())
c_stars = sol.samples[0].x
print(c_stars)
algorithm_globals.random_seed = 12345
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 1.0])
exact_mes = NumPyMinimumEigensolver()
qaoa = MinimumEigenOptimizer(qaoa_mes)
qaoa_result = qaoa.solve(qubo)
print(qaoa_result.prettyprint())
from qiskit import QuantumCircuit
thetas = [2 * np.arcsin(np.sqrt(c_star)) for c_star in c_stars]
init_qc = QuantumCircuit(len(sigma))
for idx, theta in enumerate(thetas):
init_qc.ry(theta, idx)
init_qc.draw(output="mpl")
from qiskit.circuit import Parameter
beta = Parameter("β")
ws_mixer = QuantumCircuit(len(sigma))
for idx, theta in enumerate(thetas):
ws_mixer.ry(-theta, idx)
ws_mixer.rz(-2 * beta, idx)
ws_mixer.ry(theta, idx)
ws_mixer.draw(output="mpl")
ws_qaoa_mes = QAOA(
sampler=Sampler(),
optimizer=COBYLA(),
initial_state=init_qc,
mixer=ws_mixer,
initial_point=[0.0, 1.0],
)
ws_qaoa = MinimumEigenOptimizer(ws_qaoa_mes)
ws_qaoa_result = ws_qaoa.solve(qubo)
print(ws_qaoa_result.prettyprint())
def format_qaoa_samples(samples, max_len: int = 10):
qaoa_res = []
for s in samples:
if sum(s.x) == 3:
qaoa_res.append(("".join([str(int(_)) for _ in s.x]), s.fval, s.probability))
res = sorted(qaoa_res, key=lambda x: -x[1])[0:max_len]
return [(_[0] + f": value: {_[1]:.3f}, probability: {1e2*_[2]:.1f}%") for _ in res]
format_qaoa_samples(qaoa_result.samples)
format_qaoa_samples(ws_qaoa_result.samples)
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 1.0])
ws_qaoa = WarmStartQAOAOptimizer(
pre_solver=CplexOptimizer(), relax_for_pre_solver=True, qaoa=qaoa_mes, epsilon=0.0
)
ws_result = ws_qaoa.solve(qubo)
print(ws_result.prettyprint())
format_qaoa_samples(ws_result.samples)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization.problems import QuadraticProgram
# define a problem
qp = QuadraticProgram()
qp.binary_var("x")
qp.integer_var(name="y", lowerbound=-1, upperbound=4)
qp.maximize(quadratic={("x", "y"): 1})
qp.linear_constraint({"x": 1, "y": -1}, "<=", 0)
print(qp.prettyprint())
from qiskit_optimization.algorithms import CplexOptimizer, GurobiOptimizer
cplex_result = CplexOptimizer().solve(qp)
gurobi_result = GurobiOptimizer().solve(qp)
print("cplex")
print(cplex_result.prettyprint())
print()
print("gurobi")
print(gurobi_result.prettyprint())
result = CplexOptimizer(disp=True, cplex_parameters={"threads": 1, "timelimit": 0.1}).solve(qp)
print(result.prettyprint())
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_aer import Aer
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
meo = MinimumEigenOptimizer(QAOA(sampler=Sampler(), optimizer=COBYLA(maxiter=100)))
result = meo.solve(qp)
print(result.prettyprint())
print("\ndisplay the best 5 solution samples")
for sample in result.samples[:5]:
print(sample)
# docplex model
from docplex.mp.model import Model
docplex_model = Model("docplex")
x = docplex_model.binary_var("x")
y = docplex_model.integer_var(-1, 4, "y")
docplex_model.maximize(x * y)
docplex_model.add_constraint(x <= y)
docplex_model.prettyprint()
# gurobi model
import gurobipy as gp
gurobipy_model = gp.Model("gurobi")
x = gurobipy_model.addVar(vtype=gp.GRB.BINARY, name="x")
y = gurobipy_model.addVar(vtype=gp.GRB.INTEGER, lb=-1, ub=4, name="y")
gurobipy_model.setObjective(x * y, gp.GRB.MAXIMIZE)
gurobipy_model.addConstr(x - y <= 0)
gurobipy_model.update()
gurobipy_model.display()
from qiskit_optimization.translators import from_docplex_mp, from_gurobipy
qp = from_docplex_mp(docplex_model)
print("QuadraticProgram obtained from docpblex")
print(qp.prettyprint())
print("-------------")
print("QuadraticProgram obtained from gurobipy")
qp2 = from_gurobipy(gurobipy_model)
print(qp2.prettyprint())
from qiskit_optimization.translators import to_gurobipy, to_docplex_mp
gmod = to_gurobipy(from_docplex_mp(docplex_model))
print("convert docplex to gurobipy via QuadraticProgram")
gmod.display()
dmod = to_docplex_mp(from_gurobipy(gurobipy_model))
print("\nconvert gurobipy to docplex via QuadraticProgram")
print(dmod.export_as_lp_string())
ind_mod = Model("docplex")
x = ind_mod.binary_var("x")
y = ind_mod.integer_var(-1, 2, "y")
z = ind_mod.integer_var(-1, 2, "z")
ind_mod.maximize(3 * x + y - z)
ind_mod.add_indicator(x, y >= z, 1)
print(ind_mod.export_as_lp_string())
qp = from_docplex_mp(ind_mod)
result = meo.solve(qp) # apply QAOA to QuadraticProgram
print("QAOA")
print(result.prettyprint())
print("-----\nCPLEX")
print(ind_mod.solve()) # apply CPLEX directly to the Docplex model
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit import IBMQ
IBMQ.load_account()
provider = IBMQ.get_provider(hub="ibm-q", group="open", project="main")
program_id = "qaoa"
qaoa_program = provider.runtime.program(program_id)
print(f"Program name: {qaoa_program.name}, Program id: {qaoa_program.program_id}")
print(qaoa_program.parameters())
import numpy as np
from qiskit.tools import job_monitor
from qiskit.opflow import PauliSumOp, Z, I
from qiskit.algorithms.optimizers import SPSA
# Define the cost operator to run.
op = (
(Z ^ Z ^ I ^ I ^ I)
- (I ^ I ^ Z ^ Z ^ I)
+ (I ^ I ^ Z ^ I ^ Z)
- (Z ^ I ^ Z ^ I ^ I)
- (I ^ Z ^ Z ^ I ^ I)
+ (I ^ Z ^ I ^ Z ^ I)
+ (I ^ I ^ I ^ Z ^ Z)
)
# SPSA helps deal with noisy environments.
optimizer = SPSA(maxiter=100)
# We will run a depth two QAOA.
reps = 2
# The initial point for the optimization, chosen at random.
initial_point = np.random.random(2 * reps)
# The backend that will run the programm.
options = {"backend_name": "ibmq_qasm_simulator"}
# The inputs of the program as described above.
runtime_inputs = {
"operator": op,
"reps": reps,
"optimizer": optimizer,
"initial_point": initial_point,
"shots": 2**13,
# Set to True when running on real backends to reduce circuit
# depth by leveraging swap strategies. If False the
# given optimization_level (default is 1) will be used.
"use_swap_strategies": False,
# Set to True when optimizing sparse problems.
"use_initial_mapping": False,
# Set to true when using echoed-cross-resonance hardware.
"use_pulse_efficient": False,
}
job = provider.runtime.run(
program_id=program_id,
options=options,
inputs=runtime_inputs,
)
job_monitor(job)
print(f"Job id: {job.job_id()}")
print(f"Job status: {job.status()}")
result = job.result()
from collections import defaultdict
def op_adj_mat(op: PauliSumOp) -> np.array:
"""Extract the adjacency matrix from the op."""
adj_mat = np.zeros((op.num_qubits, op.num_qubits))
for pauli, coeff in op.primitive.to_list():
idx = tuple([i for i, c in enumerate(pauli[::-1]) if c == "Z"]) # index of Z
adj_mat[idx[0], idx[1]], adj_mat[idx[1], idx[0]] = np.real(coeff), np.real(coeff)
return adj_mat
def get_cost(bit_str: str, adj_mat: np.array) -> float:
"""Return the cut value of the bit string."""
n, x = len(bit_str), [int(bit) for bit in bit_str[::-1]]
cost = 0
for i in range(n):
for j in range(n):
cost += adj_mat[i, j] * x[i] * (1 - x[j])
return cost
def get_cut_distribution(result) -> dict:
"""Extract the cut distribution from the result.
Returns:
A dict of cut value: probability.
"""
adj_mat = op_adj_mat(PauliSumOp.from_list(result["inputs"]["operator"]))
state_results = []
for bit_str, amp in result["eigenstate"].items():
state_results.append((bit_str, get_cost(bit_str, adj_mat), amp**2 * 100))
vals = defaultdict(int)
for res in state_results:
vals[res[1]] += res[2]
return dict(vals)
import matplotlib.pyplot as plt
cut_vals = get_cut_distribution(result)
fig, axs = plt.subplots(1, 2, figsize=(14, 5))
axs[0].plot(result["optimizer_history"]["energy"])
axs[1].bar(list(cut_vals.keys()), list(cut_vals.values()))
axs[0].set_xlabel("Energy evaluation number")
axs[0].set_ylabel("Energy")
axs[1].set_xlabel("Cut value")
axs[1].set_ylabel("Probability")
from qiskit_optimization.runtime import QAOAClient
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_optimization import QuadraticProgram
qubo = QuadraticProgram()
qubo.binary_var("x")
qubo.binary_var("y")
qubo.binary_var("z")
qubo.minimize(linear=[1, -2, 3], quadratic={("x", "y"): 1, ("x", "z"): -1, ("y", "z"): 2})
print(qubo.prettyprint())
qaoa_mes = QAOAClient(
provider=provider, backend=provider.get_backend("ibmq_qasm_simulator"), reps=2, alpha=0.75
)
qaoa = MinimumEigenOptimizer(qaoa_mes)
result = qaoa.solve(qubo)
print(result.prettyprint())
from qiskit.transpiler import PassManager
from qiskit.circuit.library.standard_gates.equivalence_library import (
StandardEquivalenceLibrary as std_eqlib,
)
from qiskit.transpiler.passes import (
Collect2qBlocks,
ConsolidateBlocks,
UnrollCustomDefinitions,
BasisTranslator,
Optimize1qGatesDecomposition,
)
from qiskit.transpiler.passes.calibration.builders import RZXCalibrationBuilderNoEcho
from qiskit.transpiler.passes.optimization.echo_rzx_weyl_decomposition import (
EchoRZXWeylDecomposition,
)
from qiskit.test.mock import FakeBelem
backend = FakeBelem()
inst_map = backend.defaults().instruction_schedule_map
channel_map = backend.configuration().qubit_channel_mapping
rzx_basis = ["rzx", "rz", "x", "sx"]
pulse_efficient = PassManager(
[
# Consolidate consecutive two-qubit operations.
Collect2qBlocks(),
ConsolidateBlocks(basis_gates=["rz", "sx", "x", "rxx"]),
# Rewrite circuit in terms of Weyl-decomposed echoed RZX gates.
EchoRZXWeylDecomposition(backend.defaults().instruction_schedule_map),
# Attach scaled CR pulse schedules to the RZX gates.
RZXCalibrationBuilderNoEcho(
instruction_schedule_map=inst_map, qubit_channel_mapping=channel_map
),
# Simplify single-qubit gates.
UnrollCustomDefinitions(std_eqlib, rzx_basis),
BasisTranslator(std_eqlib, rzx_basis),
Optimize1qGatesDecomposition(rzx_basis),
]
)
from qiskit import QuantumCircuit
circ = QuantumCircuit(3)
circ.h([0, 1, 2])
circ.rzx(0.5, 0, 1)
circ.swap(0, 1)
circ.cx(2, 1)
circ.rz(0.4, 1)
circ.cx(2, 1)
circ.rx(1.23, 2)
circ.cx(2, 1)
circ.draw("mpl")
pulse_efficient.run(circ).draw("mpl", fold=False)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
problem = QuadraticProgram("sample")
problem.binary_var("x")
problem.binary_var("y")
problem.maximize(linear={"x": 1, "y": -2})
print(problem.prettyprint())
from qiskit.algorithms import NumPyMinimumEigensolver
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = NumPyMinimumEigensolver()
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = NumPyMinimumEigensolver()
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import MinimumEigenOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
mes = QAOA(optimizer=COBYLA(), quantum_instance=qins)
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
shots = 1000
mes = QAOA(sampler=Sampler(), optimizer=COBYLA())
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms import VQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import MinimumEigenOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
mes = VQE(ansatz=RealAmplitudes(), optimizer=COBYLA(), quantum_instance=qins)
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = SamplingVQE(sampler=Sampler(), ansatz=RealAmplitudes(), optimizer=COBYLA())
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Estimator
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = VQE(estimator=Estimator(), ansatz=RealAmplitudes(), optimizer=COBYLA())
try:
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
except TypeError as ex:
print(ex)
from qiskit import BasicAer
from qiskit.algorithms import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer, SlsqpOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
qaoa = QAOA(optimizer=COBYLA(), quantum_instance=qins)
optimizer = WarmStartQAOAOptimizer(
pre_solver=SlsqpOptimizer(), relax_for_pre_solver=True, qaoa=qaoa, epsilon=0.25
)
result = optimizer.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer, SlsqpOptimizer
qaoa = QAOA(sampler=Sampler(), optimizer=COBYLA())
optimizer = WarmStartQAOAOptimizer(
pre_solver=SlsqpOptimizer(), relax_for_pre_solver=True, qaoa=qaoa, epsilon=0.25
)
result = optimizer.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import GroverOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
optimizer = GroverOptimizer(num_value_qubits=3, num_iterations=3, quantum_instance=qins)
result = optimizer.solve(problem)
print(result)
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer
optimizer = GroverOptimizer(num_value_qubits=3, num_iterations=3, sampler=Sampler())
result = optimizer.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
try:
optimizer = GroverOptimizer(
num_value_qubits=3, num_iterations=3, quantum_instance=qins, sampler=Sampler()
)
# raises an error because both quantum_instance and sampler are set.
except ValueError as ex:
print(ex)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.translators import from_docplex_mp
# Make a Docplex model
from docplex.mp.model import Model
mdl = Model("docplex model")
x = mdl.binary_var("x")
y = mdl.integer_var(lb=-1, ub=5, name="y")
mdl.minimize(x + 2 * y)
mdl.add_constraint(x - y == 3)
mdl.add_constraint((x + y) * (x - y) <= 1)
print(mdl.export_as_lp_string())
# load from a Docplex model
mod = from_docplex_mp(mdl)
print(type(mod))
print()
print(mod.prettyprint())
# make an empty problem
mod = QuadraticProgram("my problem")
print(mod.prettyprint())
# Add variables
mod.binary_var(name="x")
mod.integer_var(name="y", lowerbound=-1, upperbound=5)
mod.continuous_var(name="z", lowerbound=-1, upperbound=5)
print(mod.prettyprint())
# Add objective function using dictionaries
mod.minimize(constant=3, linear={"x": 1}, quadratic={("x", "y"): 2, ("z", "z"): -1})
print(mod.prettyprint())
# Add objective function using lists/arrays
mod.minimize(constant=3, linear=[1, 0, 0], quadratic=[[0, 1, 0], [1, 0, 0], [0, 0, -1]])
print(mod.prettyprint())
print("constant:\t\t\t", mod.objective.constant)
print("linear dict:\t\t\t", mod.objective.linear.to_dict())
print("linear array:\t\t\t", mod.objective.linear.to_array())
print("linear array as sparse matrix:\n", mod.objective.linear.coefficients, "\n")
print("quadratic dict w/ index:\t", mod.objective.quadratic.to_dict())
print("quadratic dict w/ name:\t\t", mod.objective.quadratic.to_dict(use_name=True))
print(
"symmetric quadratic dict w/ name:\t",
mod.objective.quadratic.to_dict(use_name=True, symmetric=True),
)
print("quadratic matrix:\n", mod.objective.quadratic.to_array(), "\n")
print("symmetric quadratic matrix:\n", mod.objective.quadratic.to_array(symmetric=True), "\n")
print("quadratic matrix as sparse matrix:\n", mod.objective.quadratic.coefficients)
# Add linear constraints
mod.linear_constraint(linear={"x": 1, "y": 2}, sense="==", rhs=3, name="lin_eq")
mod.linear_constraint(linear={"x": 1, "y": 2}, sense="<=", rhs=3, name="lin_leq")
mod.linear_constraint(linear={"x": 1, "y": 2}, sense=">=", rhs=3, name="lin_geq")
print(mod.prettyprint())
# Add quadratic constraints
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense="==",
rhs=1,
name="quad_eq",
)
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense="<=",
rhs=1,
name="quad_leq",
)
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense=">=",
rhs=1,
name="quad_geq",
)
print(mod.prettyprint())
lin_geq = mod.get_linear_constraint("lin_geq")
print("lin_geq:", lin_geq.linear.to_dict(use_name=True), lin_geq.sense, lin_geq.rhs)
quad_geq = mod.get_quadratic_constraint("quad_geq")
print(
"quad_geq:",
quad_geq.linear.to_dict(use_name=True),
quad_geq.quadratic.to_dict(use_name=True),
quad_geq.sense,
lin_geq.rhs,
)
# Remove constraints
mod.remove_linear_constraint("lin_eq")
mod.remove_quadratic_constraint("quad_leq")
print(mod.prettyprint())
sub = mod.substitute_variables(constants={"x": 0}, variables={"y": ("z", -1)})
print(sub.prettyprint())
sub = mod.substitute_variables(constants={"x": -1})
print(sub.status)
from qiskit_optimization import QiskitOptimizationError
try:
sub = mod.substitute_variables(constants={"x": -1}, variables={"y": ("x", 1)})
except QiskitOptimizationError as e:
print("Error: {}".format(e))
mod = QuadraticProgram()
mod.binary_var(name="e")
mod.binary_var(name="f")
mod.continuous_var(name="g")
mod.minimize(linear=[1, 2, 3])
print(mod.export_as_lp_string())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
qp = QuadraticProgram()
qp.binary_var("x")
qp.binary_var("y")
qp.integer_var(lowerbound=0, upperbound=7, name="z")
qp.maximize(linear={"x": 2, "y": 1, "z": 1})
qp.linear_constraint(linear={"x": 1, "y": 1, "z": 1}, sense="LE", rhs=5.5, name="xyz_leq")
qp.linear_constraint(linear={"x": 1, "y": 1, "z": 1}, sense="GE", rhs=2.5, name="xyz_geq")
print(qp.prettyprint())
from qiskit_optimization.converters import InequalityToEquality
ineq2eq = InequalityToEquality()
qp_eq = ineq2eq.convert(qp)
print(qp_eq.prettyprint())
print(qp_eq.prettyprint())
from qiskit_optimization.converters import IntegerToBinary
int2bin = IntegerToBinary()
qp_eq_bin = int2bin.convert(qp_eq)
print(qp_eq_bin.prettyprint())
print(qp_eq_bin.prettyprint())
from qiskit_optimization.converters import LinearEqualityToPenalty
lineq2penalty = LinearEqualityToPenalty()
qubo = lineq2penalty.convert(qp_eq_bin)
print(qubo.prettyprint())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import (
MinimumEigenOptimizer,
RecursiveMinimumEigenOptimizer,
SolutionSample,
OptimizationResultStatus,
)
from qiskit_optimization import QuadraticProgram
from qiskit.visualization import plot_histogram
from typing import List, Tuple
import numpy as np
# create a QUBO
qubo = QuadraticProgram()
qubo.binary_var("x")
qubo.binary_var("y")
qubo.binary_var("z")
qubo.minimize(linear=[1, -2, 3], quadratic={("x", "y"): 1, ("x", "z"): -1, ("y", "z"): 2})
print(qubo.prettyprint())
op, offset = qubo.to_ising()
print("offset: {}".format(offset))
print("operator:")
print(op)
qp = QuadraticProgram()
qp.from_ising(op, offset, linear=True)
print(qp.prettyprint())
algorithm_globals.random_seed = 10598
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 0.0])
exact_mes = NumPyMinimumEigensolver()
qaoa = MinimumEigenOptimizer(qaoa_mes) # using QAOA
exact = MinimumEigenOptimizer(exact_mes) # using the exact classical numpy minimum eigen solver
exact_result = exact.solve(qubo)
print(exact_result.prettyprint())
qaoa_result = qaoa.solve(qubo)
print(qaoa_result.prettyprint())
print("variable order:", [var.name for var in qaoa_result.variables])
for s in qaoa_result.samples:
print(s)
def get_filtered_samples(
samples: List[SolutionSample],
threshold: float = 0,
allowed_status: Tuple[OptimizationResultStatus] = (OptimizationResultStatus.SUCCESS,),
):
res = []
for s in samples:
if s.status in allowed_status and s.probability > threshold:
res.append(s)
return res
filtered_samples = get_filtered_samples(
qaoa_result.samples, threshold=0.005, allowed_status=(OptimizationResultStatus.SUCCESS,)
)
for s in filtered_samples:
print(s)
fvals = [s.fval for s in qaoa_result.samples]
probabilities = [s.probability for s in qaoa_result.samples]
np.mean(fvals)
np.std(fvals)
samples_for_plot = {
" ".join(f"{qaoa_result.variables[i].name}={int(v)}" for i, v in enumerate(s.x)): s.probability
for s in filtered_samples
}
samples_for_plot
plot_histogram(samples_for_plot)
rqaoa = RecursiveMinimumEigenOptimizer(qaoa, min_num_vars=1, min_num_vars_optimizer=exact)
rqaoa_result = rqaoa.solve(qubo)
print(rqaoa_result.prettyprint())
filtered_samples = get_filtered_samples(
rqaoa_result.samples, threshold=0.005, allowed_status=(OptimizationResultStatus.SUCCESS,)
)
samples_for_plot = {
" ".join(f"{rqaoa_result.variables[i].name}={int(v)}" for i, v in enumerate(s.x)): s.probability
for s in filtered_samples
}
samples_for_plot
plot_histogram(samples_for_plot)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer, MinimumEigenOptimizer
from qiskit_optimization.translators import from_docplex_mp
from docplex.mp.model import Model
model = Model()
x0 = model.binary_var(name="x0")
x1 = model.binary_var(name="x1")
x2 = model.binary_var(name="x2")
model.minimize(-x0 + 2 * x1 - 3 * x2 - 2 * x0 * x2 - 1 * x1 * x2)
qp = from_docplex_mp(model)
print(qp.prettyprint())
grover_optimizer = GroverOptimizer(6, num_iterations=10, sampler=Sampler())
results = grover_optimizer.solve(qp)
print(results.prettyprint())
exact_solver = MinimumEigenOptimizer(NumPyMinimumEigensolver())
exact_result = exact_solver.solve(qp)
print(exact_result.prettyprint())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import matplotlib.pyplot as plt
from docplex.mp.model import Model
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import CobylaOptimizer, MinimumEigenOptimizer
from qiskit_optimization.algorithms.admm_optimizer import ADMMParameters, ADMMOptimizer
from qiskit_optimization.translators import from_docplex_mp
# If CPLEX is installed, you can uncomment this line to import the CplexOptimizer.
# CPLEX can be used in this tutorial to solve the convex continuous problem,
# but also as a reference to solve the QUBO, or even the full problem.
#
# from qiskit.optimization.algorithms import CplexOptimizer
# define COBYLA optimizer to handle convex continuous problems.
cobyla = CobylaOptimizer()
# define QAOA via the minimum eigen optimizer
qaoa = MinimumEigenOptimizer(QAOA(sampler=Sampler(), optimizer=COBYLA()))
# exact QUBO solver as classical benchmark
exact = MinimumEigenOptimizer(NumPyMinimumEigensolver()) # to solve QUBOs
# in case CPLEX is installed it can also be used for the convex problems, the QUBO,
# or as a benchmark for the full problem.
#
# cplex = CplexOptimizer()
# construct model using docplex
mdl = Model("ex6")
v = mdl.binary_var(name="v")
w = mdl.binary_var(name="w")
t = mdl.binary_var(name="t")
u = mdl.continuous_var(name="u")
mdl.minimize(v + w + t + 5 * (u - 2) ** 2)
mdl.add_constraint(v + 2 * w + t + u <= 3, "cons1")
mdl.add_constraint(v + w + t >= 1, "cons2")
mdl.add_constraint(v + w == 1, "cons3")
# load quadratic program from docplex model
qp = from_docplex_mp(mdl)
print(qp.prettyprint())
admm_params = ADMMParameters(
rho_initial=1001, beta=1000, factor_c=900, maxiter=100, three_block=True, tol=1.0e-6
)
# define QUBO optimizer
qubo_optimizer = exact
# qubo_optimizer = cplex # uncomment to use CPLEX instead
# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex # uncomment to use CPLEX instead
# initialize ADMM with classical QUBO and convex optimizer
admm = ADMMOptimizer(
params=admm_params, qubo_optimizer=qubo_optimizer, continuous_optimizer=convex_optimizer
)
# run ADMM to solve problem
result = admm.solve(qp)
print(result.prettyprint())
plt.plot(result.state.residuals)
plt.xlabel("Iterations")
plt.ylabel("Residuals")
plt.show()
# define QUBO optimizer
qubo_optimizer = qaoa
# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex # uncomment to use CPLEX instead
# initialize ADMM with quantum QUBO optimizer and classical convex optimizer
admm_q = ADMMOptimizer(
params=admm_params, qubo_optimizer=qubo_optimizer, continuous_optimizer=convex_optimizer
)
# run ADMM to solve problem
result_q = admm_q.solve(qp)
print(result.prettyprint())
plt.clf()
plt.plot(result_q.state.residuals)
plt.xlabel("Iterations")
plt.ylabel("Residuals")
plt.show()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
# useful additional packages
import matplotlib.pyplot as plt
import numpy as np
import networkx as nx
from qiskit_aer import Aer
from qiskit.tools.visualization import plot_histogram
from qiskit.circuit.library import TwoLocal
from qiskit_optimization.applications import Maxcut, Tsp
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import SPSA
from qiskit.utils import algorithm_globals
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
# Generating a graph of 4 nodes
n = 4 # Number of nodes in graph
G = nx.Graph()
G.add_nodes_from(np.arange(0, n, 1))
elist = [(0, 1, 1.0), (0, 2, 1.0), (0, 3, 1.0), (1, 2, 1.0), (2, 3, 1.0)]
# tuple is (i,j,weight) where (i,j) is the edge
G.add_weighted_edges_from(elist)
colors = ["r" for node in G.nodes()]
pos = nx.spring_layout(G)
def draw_graph(G, colors, pos):
default_axes = plt.axes(frameon=True)
nx.draw_networkx(G, node_color=colors, node_size=600, alpha=0.8, ax=default_axes, pos=pos)
edge_labels = nx.get_edge_attributes(G, "weight")
nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels)
draw_graph(G, colors, pos)
# Computing the weight matrix from the random graph
w = np.zeros([n, n])
for i in range(n):
for j in range(n):
temp = G.get_edge_data(i, j, default=0)
if temp != 0:
w[i, j] = temp["weight"]
print(w)
best_cost_brute = 0
for b in range(2**n):
x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]
cost = 0
for i in range(n):
for j in range(n):
cost = cost + w[i, j] * x[i] * (1 - x[j])
if best_cost_brute < cost:
best_cost_brute = cost
xbest_brute = x
print("case = " + str(x) + " cost = " + str(cost))
colors = ["r" if xbest_brute[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
print("\nBest solution = " + str(xbest_brute) + " cost = " + str(best_cost_brute))
max_cut = Maxcut(w)
qp = max_cut.to_quadratic_program()
print(qp.prettyprint())
qubitOp, offset = qp.to_ising()
print("Offset:", offset)
print("Ising Hamiltonian:")
print(str(qubitOp))
# solving Quadratic Program using exact classical eigensolver
exact = MinimumEigenOptimizer(NumPyMinimumEigensolver())
result = exact.solve(qp)
print(result.prettyprint())
# Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector
ee = NumPyMinimumEigensolver()
result = ee.compute_minimum_eigenvalue(qubitOp)
x = max_cut.sample_most_likely(result.eigenstate)
print("energy:", result.eigenvalue.real)
print("max-cut objective:", result.eigenvalue.real + offset)
print("solution:", x)
print("solution objective:", qp.objective.evaluate(x))
colors = ["r" if x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
# construct SamplingVQE
optimizer = SPSA(maxiter=300)
ry = TwoLocal(qubitOp.num_qubits, "ry", "cz", reps=5, entanglement="linear")
vqe = SamplingVQE(sampler=Sampler(), ansatz=ry, optimizer=optimizer)
# run SamplingVQE
result = vqe.compute_minimum_eigenvalue(qubitOp)
# print results
x = max_cut.sample_most_likely(result.eigenstate)
print("energy:", result.eigenvalue.real)
print("time:", result.optimizer_time)
print("max-cut objective:", result.eigenvalue.real + offset)
print("solution:", x)
print("solution objective:", qp.objective.evaluate(x))
# plot results
colors = ["r" if x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
# create minimum eigen optimizer based on SamplingVQE
vqe_optimizer = MinimumEigenOptimizer(vqe)
# solve quadratic program
result = vqe_optimizer.solve(qp)
print(result.prettyprint())
colors = ["r" if result.x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
# Generating a graph of 3 nodes
n = 3
num_qubits = n**2
tsp = Tsp.create_random_instance(n, seed=123)
adj_matrix = nx.to_numpy_array(tsp.graph)
print("distance\n", adj_matrix)
colors = ["r" for node in tsp.graph.nodes]
pos = [tsp.graph.nodes[node]["pos"] for node in tsp.graph.nodes]
draw_graph(tsp.graph, colors, pos)
from itertools import permutations
def brute_force_tsp(w, N):
a = list(permutations(range(1, N)))
last_best_distance = 1e10
for i in a:
distance = 0
pre_j = 0
for j in i:
distance = distance + w[j, pre_j]
pre_j = j
distance = distance + w[pre_j, 0]
order = (0,) + i
if distance < last_best_distance:
best_order = order
last_best_distance = distance
print("order = " + str(order) + " Distance = " + str(distance))
return last_best_distance, best_order
best_distance, best_order = brute_force_tsp(adj_matrix, n)
print(
"Best order from brute force = "
+ str(best_order)
+ " with total distance = "
+ str(best_distance)
)
def draw_tsp_solution(G, order, colors, pos):
G2 = nx.DiGraph()
G2.add_nodes_from(G)
n = len(order)
for i in range(n):
j = (i + 1) % n
G2.add_edge(order[i], order[j], weight=G[order[i]][order[j]]["weight"])
default_axes = plt.axes(frameon=True)
nx.draw_networkx(
G2, node_color=colors, edge_color="b", node_size=600, alpha=0.8, ax=default_axes, pos=pos
)
edge_labels = nx.get_edge_attributes(G2, "weight")
nx.draw_networkx_edge_labels(G2, pos, font_color="b", edge_labels=edge_labels)
draw_tsp_solution(tsp.graph, best_order, colors, pos)
qp = tsp.to_quadratic_program()
print(qp.prettyprint())
from qiskit_optimization.converters import QuadraticProgramToQubo
qp2qubo = QuadraticProgramToQubo()
qubo = qp2qubo.convert(qp)
qubitOp, offset = qubo.to_ising()
print("Offset:", offset)
print("Ising Hamiltonian:")
print(str(qubitOp))
result = exact.solve(qubo)
print(result.prettyprint())
# Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector
ee = NumPyMinimumEigensolver()
result = ee.compute_minimum_eigenvalue(qubitOp)
print("energy:", result.eigenvalue.real)
print("tsp objective:", result.eigenvalue.real + offset)
x = tsp.sample_most_likely(result.eigenstate)
print("feasible:", qubo.is_feasible(x))
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
optimizer = SPSA(maxiter=300)
ry = TwoLocal(qubitOp.num_qubits, "ry", "cz", reps=5, entanglement="linear")
vqe = SamplingVQE(sampler=Sampler(), ansatz=ry, optimizer=optimizer)
result = vqe.compute_minimum_eigenvalue(qubitOp)
print("energy:", result.eigenvalue.real)
print("time:", result.optimizer_time)
x = tsp.sample_most_likely(result.eigenstate)
print("feasible:", qubo.is_feasible(x))
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
# create minimum eigen optimizer based on SamplingVQE
vqe_optimizer = MinimumEigenOptimizer(vqe)
# solve quadratic program
result = vqe_optimizer.solve(qp)
print(result.prettyprint())
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import matplotlib.pyplot as plt
try:
import cplex
from cplex.exceptions import CplexError
except:
print("Warning: Cplex not found.")
import math
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE
from qiskit.algorithms.optimizers import SPSA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Sampler
# Initialize the problem by defining the parameters
n = 3 # number of nodes + depot (n+1)
K = 2 # number of vehicles
# Get the data
class Initializer:
def __init__(self, n):
self.n = n
def generate_instance(self):
n = self.n
# np.random.seed(33)
np.random.seed(1543)
xc = (np.random.rand(n) - 0.5) * 10
yc = (np.random.rand(n) - 0.5) * 10
instance = np.zeros([n, n])
for ii in range(0, n):
for jj in range(ii + 1, n):
instance[ii, jj] = (xc[ii] - xc[jj]) ** 2 + (yc[ii] - yc[jj]) ** 2
instance[jj, ii] = instance[ii, jj]
return xc, yc, instance
# Initialize the problem by randomly generating the instance
initializer = Initializer(n)
xc, yc, instance = initializer.generate_instance()
class ClassicalOptimizer:
def __init__(self, instance, n, K):
self.instance = instance
self.n = n # number of nodes
self.K = K # number of vehicles
def compute_allowed_combinations(self):
f = math.factorial
return f(self.n) / f(self.K) / f(self.n - self.K)
def cplex_solution(self):
# refactoring
instance = self.instance
n = self.n
K = self.K
my_obj = list(instance.reshape(1, n**2)[0]) + [0.0 for x in range(0, n - 1)]
my_ub = [1 for x in range(0, n**2 + n - 1)]
my_lb = [0 for x in range(0, n**2)] + [0.1 for x in range(0, n - 1)]
my_ctype = "".join(["I" for x in range(0, n**2)]) + "".join(
["C" for x in range(0, n - 1)]
)
my_rhs = (
2 * ([K] + [1 for x in range(0, n - 1)])
+ [1 - 0.1 for x in range(0, (n - 1) ** 2 - (n - 1))]
+ [0 for x in range(0, n)]
)
my_sense = (
"".join(["E" for x in range(0, 2 * n)])
+ "".join(["L" for x in range(0, (n - 1) ** 2 - (n - 1))])
+ "".join(["E" for x in range(0, n)])
)
try:
my_prob = cplex.Cplex()
self.populatebyrow(my_prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs)
my_prob.solve()
except CplexError as exc:
print(exc)
return
x = my_prob.solution.get_values()
x = np.array(x)
cost = my_prob.solution.get_objective_value()
return x, cost
def populatebyrow(self, prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs):
n = self.n
prob.objective.set_sense(prob.objective.sense.minimize)
prob.variables.add(obj=my_obj, lb=my_lb, ub=my_ub, types=my_ctype)
prob.set_log_stream(None)
prob.set_error_stream(None)
prob.set_warning_stream(None)
prob.set_results_stream(None)
rows = []
for ii in range(0, n):
col = [x for x in range(0 + n * ii, n + n * ii)]
coef = [1 for x in range(0, n)]
rows.append([col, coef])
for ii in range(0, n):
col = [x for x in range(0 + ii, n**2, n)]
coef = [1 for x in range(0, n)]
rows.append([col, coef])
# Sub-tour elimination constraints:
for ii in range(0, n):
for jj in range(0, n):
if (ii != jj) and (ii * jj > 0):
col = [ii + (jj * n), n**2 + ii - 1, n**2 + jj - 1]
coef = [1, 1, -1]
rows.append([col, coef])
for ii in range(0, n):
col = [(ii) * (n + 1)]
coef = [1]
rows.append([col, coef])
prob.linear_constraints.add(lin_expr=rows, senses=my_sense, rhs=my_rhs)
# Instantiate the classical optimizer class
classical_optimizer = ClassicalOptimizer(instance, n, K)
# Print number of feasible solutions
print("Number of feasible solutions = " + str(classical_optimizer.compute_allowed_combinations()))
# Solve the problem in a classical fashion via CPLEX
x = None
z = None
try:
x, classical_cost = classical_optimizer.cplex_solution()
# Put the solution in the z variable
z = [x[ii] for ii in range(n**2) if ii // n != ii % n]
# Print the solution
print(z)
except:
print("CPLEX may be missing.")
# Visualize the solution
def visualize_solution(xc, yc, x, C, n, K, title_str):
plt.figure()
plt.scatter(xc, yc, s=200)
for i in range(len(xc)):
plt.annotate(i, (xc[i] + 0.15, yc[i]), size=16, color="r")
plt.plot(xc[0], yc[0], "r*", ms=20)
plt.grid()
for ii in range(0, n**2):
if x[ii] > 0:
ix = ii // n
iy = ii % n
plt.arrow(
xc[ix],
yc[ix],
xc[iy] - xc[ix],
yc[iy] - yc[ix],
length_includes_head=True,
head_width=0.25,
)
plt.title(title_str + " cost = " + str(int(C * 100) / 100.0))
plt.show()
if x is not None:
visualize_solution(xc, yc, x, classical_cost, n, K, "Classical")
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.algorithms import MinimumEigenOptimizer
class QuantumOptimizer:
def __init__(self, instance, n, K):
self.instance = instance
self.n = n
self.K = K
def binary_representation(self, x_sol=0):
instance = self.instance
n = self.n
K = self.K
A = np.max(instance) * 100 # A parameter of cost function
# Determine the weights w
instance_vec = instance.reshape(n**2)
w_list = [instance_vec[x] for x in range(n**2) if instance_vec[x] > 0]
w = np.zeros(n * (n - 1))
for ii in range(len(w_list)):
w[ii] = w_list[ii]
# Some variables I will use
Id_n = np.eye(n)
Im_n_1 = np.ones([n - 1, n - 1])
Iv_n_1 = np.ones(n)
Iv_n_1[0] = 0
Iv_n = np.ones(n - 1)
neg_Iv_n_1 = np.ones(n) - Iv_n_1
v = np.zeros([n, n * (n - 1)])
for ii in range(n):
count = ii - 1
for jj in range(n * (n - 1)):
if jj // (n - 1) == ii:
count = ii
if jj // (n - 1) != ii and jj % (n - 1) == count:
v[ii][jj] = 1.0
vn = np.sum(v[1:], axis=0)
# Q defines the interactions between variables
Q = A * (np.kron(Id_n, Im_n_1) + np.dot(v.T, v))
# g defines the contribution from the individual variables
g = (
w
- 2 * A * (np.kron(Iv_n_1, Iv_n) + vn.T)
- 2 * A * K * (np.kron(neg_Iv_n_1, Iv_n) + v[0].T)
)
# c is the constant offset
c = 2 * A * (n - 1) + 2 * A * (K**2)
try:
max(x_sol)
# Evaluates the cost distance from a binary representation of a path
fun = (
lambda x: np.dot(np.around(x), np.dot(Q, np.around(x)))
+ np.dot(g, np.around(x))
+ c
)
cost = fun(x_sol)
except:
cost = 0
return Q, g, c, cost
def construct_problem(self, Q, g, c) -> QuadraticProgram:
qp = QuadraticProgram()
for i in range(n * (n - 1)):
qp.binary_var(str(i))
qp.objective.quadratic = Q
qp.objective.linear = g
qp.objective.constant = c
return qp
def solve_problem(self, qp):
algorithm_globals.random_seed = 10598
vqe = SamplingVQE(sampler=Sampler(), optimizer=SPSA(), ansatz=RealAmplitudes())
optimizer = MinimumEigenOptimizer(min_eigen_solver=vqe)
result = optimizer.solve(qp)
# compute cost of the obtained result
_, _, _, level = self.binary_representation(x_sol=result.x)
return result.x, level
# Instantiate the quantum optimizer class with parameters:
quantum_optimizer = QuantumOptimizer(instance, n, K)
# Check if the binary representation is correct
try:
if z is not None:
Q, g, c, binary_cost = quantum_optimizer.binary_representation(x_sol=z)
print("Binary cost:", binary_cost, "classical cost:", classical_cost)
if np.abs(binary_cost - classical_cost) < 0.01:
print("Binary formulation is correct")
else:
print("Error in the binary formulation")
else:
print("Could not verify the correctness, due to CPLEX solution being unavailable.")
Q, g, c, binary_cost = quantum_optimizer.binary_representation()
print("Binary cost:", binary_cost)
except NameError as e:
print("Warning: Please run the cells above first.")
print(e)
qp = quantum_optimizer.construct_problem(Q, g, c)
quantum_solution, quantum_cost = quantum_optimizer.solve_problem(qp)
print(quantum_solution, quantum_cost)
# Put the solution in a way that is compatible with the classical variables
x_quantum = np.zeros(n**2)
kk = 0
for ii in range(n**2):
if ii // n != ii % n:
x_quantum[ii] = quantum_solution[kk]
kk += 1
# visualize the solution
visualize_solution(xc, yc, x_quantum, quantum_cost, n, K, "Quantum")
# and visualize the classical for comparison
if x is not None:
visualize_solution(xc, yc, x, classical_cost, n, K, "Classical")
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.circuit.library import RealAmplitudes
from qiskit.algorithms.optimizers import COBYLA
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver, SamplingVQE
from qiskit.primitives import Sampler
from qiskit_optimization.converters import LinearEqualityToPenalty
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_optimization.translators import from_docplex_mp
from qiskit.utils import algorithm_globals
import numpy as np
import matplotlib.pyplot as plt
from docplex.mp.model import Model
algorithm_globals.random_seed = 123456
# prepare problem instance
n = 6 # number of assets
q = 0.5 # risk factor
budget = n // 2 # budget
penalty = 2 * n # scaling of penalty term
# instance from [1]
mu = np.array([0.7313, 0.9893, 0.2725, 0.8750, 0.7667, 0.3622])
sigma = np.array(
[
[0.7312, -0.6233, 0.4689, -0.5452, -0.0082, -0.3809],
[-0.6233, 2.4732, -0.7538, 2.4659, -0.0733, 0.8945],
[0.4689, -0.7538, 1.1543, -1.4095, 0.0007, -0.4301],
[-0.5452, 2.4659, -1.4095, 3.5067, 0.2012, 1.0922],
[-0.0082, -0.0733, 0.0007, 0.2012, 0.6231, 0.1509],
[-0.3809, 0.8945, -0.4301, 1.0922, 0.1509, 0.8992],
]
)
# or create random instance
# mu, sigma = portfolio.random_model(n, seed=123) # expected returns and covariance matrix
# create docplex model
mdl = Model("portfolio_optimization")
x = mdl.binary_var_list(range(n), name="x")
objective = mdl.sum([mu[i] * x[i] for i in range(n)])
objective -= q * mdl.sum([sigma[i, j] * x[i] * x[j] for i in range(n) for j in range(n)])
mdl.maximize(objective)
mdl.add_constraint(mdl.sum(x[i] for i in range(n)) == budget)
# case to
qp = from_docplex_mp(mdl)
# solve classically as reference
opt_result = MinimumEigenOptimizer(NumPyMinimumEigensolver()).solve(qp)
print(opt_result.prettyprint())
# we convert the problem to an unconstrained problem for further analysis,
# otherwise this would not be necessary as the MinimumEigenSolver would do this
# translation automatically
linear2penalty = LinearEqualityToPenalty(penalty=penalty)
qp = linear2penalty.convert(qp)
_, offset = qp.to_ising()
# set classical optimizer
maxiter = 100
optimizer = COBYLA(maxiter=maxiter)
# set variational ansatz
ansatz = RealAmplitudes(n, reps=1)
m = ansatz.num_parameters
# set sampler
sampler = Sampler()
# run variational optimization for different values of alpha
alphas = [1.0, 0.50, 0.25] # confidence levels to be evaluated
# dictionaries to store optimization progress and results
objectives = {alpha: [] for alpha in alphas} # set of tested objective functions w.r.t. alpha
results = {} # results of minimum eigensolver w.r.t alpha
# callback to store intermediate results
def callback(i, params, obj, stddev, alpha):
# we translate the objective from the internal Ising representation
# to the original optimization problem
objectives[alpha].append(np.real_if_close(-(obj + offset)))
# loop over all given alpha values
for alpha in alphas:
# initialize SamplingVQE using CVaR
vqe = SamplingVQE(
sampler=sampler,
ansatz=ansatz,
optimizer=optimizer,
aggregation=alpha,
callback=lambda i, params, obj, stddev: callback(i, params, obj, stddev, alpha),
)
# initialize optimization algorithm based on CVaR-SamplingVQE
opt_alg = MinimumEigenOptimizer(vqe)
# solve problem
results[alpha] = opt_alg.solve(qp)
# print results
print("alpha = {}:".format(alpha))
print(results[alpha].prettyprint())
print()
# plot resulting history of objective values
plt.figure(figsize=(10, 5))
plt.plot([0, maxiter], [opt_result.fval, opt_result.fval], "r--", linewidth=2, label="optimum")
for alpha in alphas:
plt.plot(objectives[alpha], label="alpha = %.2f" % alpha, linewidth=2)
plt.legend(loc="lower right", fontsize=14)
plt.xlim(0, maxiter)
plt.xticks(fontsize=14)
plt.xlabel("iterations", fontsize=14)
plt.yticks(fontsize=14)
plt.ylabel("objective value", fontsize=14)
plt.show()
# evaluate and sort all objective values
objective_values = np.zeros(2**n)
for i in range(2**n):
x_bin = ("{0:0%sb}" % n).format(i)
x = [0 if x_ == "0" else 1 for x_ in reversed(x_bin)]
objective_values[i] = qp.objective.evaluate(x)
ind = np.argsort(objective_values)
# evaluate final optimal probability for each alpha
for alpha in alphas:
probabilities = np.fromiter(
results[alpha].min_eigen_solver_result.eigenstate.binary_probabilities().values(),
dtype=float,
)
print("optimal probability (alpha = %.2f): %.4f" % (alpha, probabilities[ind][-1:]))
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.applications.vertex_cover import VertexCover
import networkx as nx
seed = 123
algorithm_globals.random_seed = seed
graph = nx.random_regular_graph(d=3, n=6, seed=seed)
pos = nx.spring_layout(graph, seed=seed)
prob = VertexCover(graph)
prob.draw(pos=pos)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# Numpy Eigensolver
meo = MinimumEigenOptimizer(min_eigen_solver=NumPyMinimumEigensolver())
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
prob.draw(result, pos=pos)
# QAOA
meo = MinimumEigenOptimizer(min_eigen_solver=QAOA(reps=1, sampler=Sampler(), optimizer=COBYLA()))
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
print("\ntime:", result.min_eigen_solver_result.optimizer_time)
prob.draw(result, pos=pos)
from qiskit_optimization.applications import Knapsack
prob = Knapsack(values=[3, 4, 5, 6, 7], weights=[2, 3, 4, 5, 6], max_weight=10)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# Numpy Eigensolver
meo = MinimumEigenOptimizer(min_eigen_solver=NumPyMinimumEigensolver())
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
# QAOA
meo = MinimumEigenOptimizer(min_eigen_solver=QAOA(reps=1, sampler=Sampler(), optimizer=COBYLA()))
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
print("\ntime:", result.min_eigen_solver_result.optimizer_time)
from qiskit_optimization.converters import QuadraticProgramToQubo
# the same knapsack problem instance as in the previous section
prob = Knapsack(values=[3, 4, 5, 6, 7], weights=[2, 3, 4, 5, 6], max_weight=10)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# intermediate QUBO form of the optimization problem
conv = QuadraticProgramToQubo()
qubo = conv.convert(qp)
print(qubo.prettyprint())
# qubit Hamiltonian and offset
op, offset = qubo.to_ising()
print(f"num qubits: {op.num_qubits}, offset: {offset}\n")
print(op)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import copy
# Problem modelling imports
from docplex.mp.model import Model
# Qiskit imports
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit.utils.algorithm_globals import algorithm_globals
from qiskit_optimization.algorithms import MinimumEigenOptimizer, CplexOptimizer
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.problems.variable import VarType
from qiskit_optimization.converters.quadratic_program_to_qubo import QuadraticProgramToQubo
from qiskit_optimization.translators import from_docplex_mp
def create_problem(mu: np.array, sigma: np.array, total: int = 3) -> QuadraticProgram:
"""Solve the quadratic program using docplex."""
mdl = Model()
x = [mdl.binary_var("x%s" % i) for i in range(len(sigma))]
objective = mdl.sum([mu[i] * x[i] for i in range(len(mu))])
objective -= 2 * mdl.sum(
[sigma[i, j] * x[i] * x[j] for i in range(len(mu)) for j in range(len(mu))]
)
mdl.maximize(objective)
cost = mdl.sum(x)
mdl.add_constraint(cost == total)
qp = from_docplex_mp(mdl)
return qp
def relax_problem(problem) -> QuadraticProgram:
"""Change all variables to continuous."""
relaxed_problem = copy.deepcopy(problem)
for variable in relaxed_problem.variables:
variable.vartype = VarType.CONTINUOUS
return relaxed_problem
mu = np.array([3.418, 2.0913, 6.2415, 4.4436, 10.892, 3.4051])
sigma = np.array(
[
[1.07978412, 0.00768914, 0.11227606, -0.06842969, -0.01016793, -0.00839765],
[0.00768914, 0.10922887, -0.03043424, -0.0020045, 0.00670929, 0.0147937],
[0.11227606, -0.03043424, 0.985353, 0.02307313, -0.05249785, 0.00904119],
[-0.06842969, -0.0020045, 0.02307313, 0.6043817, 0.03740115, -0.00945322],
[-0.01016793, 0.00670929, -0.05249785, 0.03740115, 0.79839634, 0.07616951],
[-0.00839765, 0.0147937, 0.00904119, -0.00945322, 0.07616951, 1.08464544],
]
)
qubo = create_problem(mu, sigma)
print(qubo.prettyprint())
result = CplexOptimizer().solve(qubo)
print(result.prettyprint())
qp = relax_problem(QuadraticProgramToQubo().convert(qubo))
print(qp.prettyprint())
sol = CplexOptimizer().solve(qp)
print(sol.prettyprint())
c_stars = sol.samples[0].x
print(c_stars)
algorithm_globals.random_seed = 12345
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 1.0])
exact_mes = NumPyMinimumEigensolver()
qaoa = MinimumEigenOptimizer(qaoa_mes)
qaoa_result = qaoa.solve(qubo)
print(qaoa_result.prettyprint())
from qiskit import QuantumCircuit
thetas = [2 * np.arcsin(np.sqrt(c_star)) for c_star in c_stars]
init_qc = QuantumCircuit(len(sigma))
for idx, theta in enumerate(thetas):
init_qc.ry(theta, idx)
init_qc.draw(output="mpl")
from qiskit.circuit import Parameter
beta = Parameter("β")
ws_mixer = QuantumCircuit(len(sigma))
for idx, theta in enumerate(thetas):
ws_mixer.ry(-theta, idx)
ws_mixer.rz(-2 * beta, idx)
ws_mixer.ry(theta, idx)
ws_mixer.draw(output="mpl")
ws_qaoa_mes = QAOA(
sampler=Sampler(),
optimizer=COBYLA(),
initial_state=init_qc,
mixer=ws_mixer,
initial_point=[0.0, 1.0],
)
ws_qaoa = MinimumEigenOptimizer(ws_qaoa_mes)
ws_qaoa_result = ws_qaoa.solve(qubo)
print(ws_qaoa_result.prettyprint())
def format_qaoa_samples(samples, max_len: int = 10):
qaoa_res = []
for s in samples:
if sum(s.x) == 3:
qaoa_res.append(("".join([str(int(_)) for _ in s.x]), s.fval, s.probability))
res = sorted(qaoa_res, key=lambda x: -x[1])[0:max_len]
return [(_[0] + f": value: {_[1]:.3f}, probability: {1e2*_[2]:.1f}%") for _ in res]
format_qaoa_samples(qaoa_result.samples)
format_qaoa_samples(ws_qaoa_result.samples)
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 1.0])
ws_qaoa = WarmStartQAOAOptimizer(
pre_solver=CplexOptimizer(), relax_for_pre_solver=True, qaoa=qaoa_mes, epsilon=0.0
)
ws_result = ws_qaoa.solve(qubo)
print(ws_result.prettyprint())
format_qaoa_samples(ws_result.samples)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization.problems import QuadraticProgram
# define a problem
qp = QuadraticProgram()
qp.binary_var("x")
qp.integer_var(name="y", lowerbound=-1, upperbound=4)
qp.maximize(quadratic={("x", "y"): 1})
qp.linear_constraint({"x": 1, "y": -1}, "<=", 0)
print(qp.prettyprint())
from qiskit_optimization.algorithms import CplexOptimizer, GurobiOptimizer
cplex_result = CplexOptimizer().solve(qp)
gurobi_result = GurobiOptimizer().solve(qp)
print("cplex")
print(cplex_result.prettyprint())
print()
print("gurobi")
print(gurobi_result.prettyprint())
result = CplexOptimizer(disp=True, cplex_parameters={"threads": 1, "timelimit": 0.1}).solve(qp)
print(result.prettyprint())
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_aer import Aer
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
meo = MinimumEigenOptimizer(QAOA(sampler=Sampler(), optimizer=COBYLA(maxiter=100)))
result = meo.solve(qp)
print(result.prettyprint())
print("\ndisplay the best 5 solution samples")
for sample in result.samples[:5]:
print(sample)
# docplex model
from docplex.mp.model import Model
docplex_model = Model("docplex")
x = docplex_model.binary_var("x")
y = docplex_model.integer_var(-1, 4, "y")
docplex_model.maximize(x * y)
docplex_model.add_constraint(x <= y)
docplex_model.prettyprint()
# gurobi model
import gurobipy as gp
gurobipy_model = gp.Model("gurobi")
x = gurobipy_model.addVar(vtype=gp.GRB.BINARY, name="x")
y = gurobipy_model.addVar(vtype=gp.GRB.INTEGER, lb=-1, ub=4, name="y")
gurobipy_model.setObjective(x * y, gp.GRB.MAXIMIZE)
gurobipy_model.addConstr(x - y <= 0)
gurobipy_model.update()
gurobipy_model.display()
from qiskit_optimization.translators import from_docplex_mp, from_gurobipy
qp = from_docplex_mp(docplex_model)
print("QuadraticProgram obtained from docpblex")
print(qp.prettyprint())
print("-------------")
print("QuadraticProgram obtained from gurobipy")
qp2 = from_gurobipy(gurobipy_model)
print(qp2.prettyprint())
from qiskit_optimization.translators import to_gurobipy, to_docplex_mp
gmod = to_gurobipy(from_docplex_mp(docplex_model))
print("convert docplex to gurobipy via QuadraticProgram")
gmod.display()
dmod = to_docplex_mp(from_gurobipy(gurobipy_model))
print("\nconvert gurobipy to docplex via QuadraticProgram")
print(dmod.export_as_lp_string())
ind_mod = Model("docplex")
x = ind_mod.binary_var("x")
y = ind_mod.integer_var(-1, 2, "y")
z = ind_mod.integer_var(-1, 2, "z")
ind_mod.maximize(3 * x + y - z)
ind_mod.add_indicator(x, y >= z, 1)
print(ind_mod.export_as_lp_string())
qp = from_docplex_mp(ind_mod)
result = meo.solve(qp) # apply QAOA to QuadraticProgram
print("QAOA")
print(result.prettyprint())
print("-----\nCPLEX")
print(ind_mod.solve()) # apply CPLEX directly to the Docplex model
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit import IBMQ
IBMQ.load_account()
provider = IBMQ.get_provider(hub="ibm-q", group="open", project="main")
program_id = "qaoa"
qaoa_program = provider.runtime.program(program_id)
print(f"Program name: {qaoa_program.name}, Program id: {qaoa_program.program_id}")
print(qaoa_program.parameters())
import numpy as np
from qiskit.tools import job_monitor
from qiskit.opflow import PauliSumOp, Z, I
from qiskit.algorithms.optimizers import SPSA
# Define the cost operator to run.
op = (
(Z ^ Z ^ I ^ I ^ I)
- (I ^ I ^ Z ^ Z ^ I)
+ (I ^ I ^ Z ^ I ^ Z)
- (Z ^ I ^ Z ^ I ^ I)
- (I ^ Z ^ Z ^ I ^ I)
+ (I ^ Z ^ I ^ Z ^ I)
+ (I ^ I ^ I ^ Z ^ Z)
)
# SPSA helps deal with noisy environments.
optimizer = SPSA(maxiter=100)
# We will run a depth two QAOA.
reps = 2
# The initial point for the optimization, chosen at random.
initial_point = np.random.random(2 * reps)
# The backend that will run the programm.
options = {"backend_name": "ibmq_qasm_simulator"}
# The inputs of the program as described above.
runtime_inputs = {
"operator": op,
"reps": reps,
"optimizer": optimizer,
"initial_point": initial_point,
"shots": 2**13,
# Set to True when running on real backends to reduce circuit
# depth by leveraging swap strategies. If False the
# given optimization_level (default is 1) will be used.
"use_swap_strategies": False,
# Set to True when optimizing sparse problems.
"use_initial_mapping": False,
# Set to true when using echoed-cross-resonance hardware.
"use_pulse_efficient": False,
}
job = provider.runtime.run(
program_id=program_id,
options=options,
inputs=runtime_inputs,
)
job_monitor(job)
print(f"Job id: {job.job_id()}")
print(f"Job status: {job.status()}")
result = job.result()
from collections import defaultdict
def op_adj_mat(op: PauliSumOp) -> np.array:
"""Extract the adjacency matrix from the op."""
adj_mat = np.zeros((op.num_qubits, op.num_qubits))
for pauli, coeff in op.primitive.to_list():
idx = tuple([i for i, c in enumerate(pauli[::-1]) if c == "Z"]) # index of Z
adj_mat[idx[0], idx[1]], adj_mat[idx[1], idx[0]] = np.real(coeff), np.real(coeff)
return adj_mat
def get_cost(bit_str: str, adj_mat: np.array) -> float:
"""Return the cut value of the bit string."""
n, x = len(bit_str), [int(bit) for bit in bit_str[::-1]]
cost = 0
for i in range(n):
for j in range(n):
cost += adj_mat[i, j] * x[i] * (1 - x[j])
return cost
def get_cut_distribution(result) -> dict:
"""Extract the cut distribution from the result.
Returns:
A dict of cut value: probability.
"""
adj_mat = op_adj_mat(PauliSumOp.from_list(result["inputs"]["operator"]))
state_results = []
for bit_str, amp in result["eigenstate"].items():
state_results.append((bit_str, get_cost(bit_str, adj_mat), amp**2 * 100))
vals = defaultdict(int)
for res in state_results:
vals[res[1]] += res[2]
return dict(vals)
import matplotlib.pyplot as plt
cut_vals = get_cut_distribution(result)
fig, axs = plt.subplots(1, 2, figsize=(14, 5))
axs[0].plot(result["optimizer_history"]["energy"])
axs[1].bar(list(cut_vals.keys()), list(cut_vals.values()))
axs[0].set_xlabel("Energy evaluation number")
axs[0].set_ylabel("Energy")
axs[1].set_xlabel("Cut value")
axs[1].set_ylabel("Probability")
from qiskit_optimization.runtime import QAOAClient
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_optimization import QuadraticProgram
qubo = QuadraticProgram()
qubo.binary_var("x")
qubo.binary_var("y")
qubo.binary_var("z")
qubo.minimize(linear=[1, -2, 3], quadratic={("x", "y"): 1, ("x", "z"): -1, ("y", "z"): 2})
print(qubo.prettyprint())
qaoa_mes = QAOAClient(
provider=provider, backend=provider.get_backend("ibmq_qasm_simulator"), reps=2, alpha=0.75
)
qaoa = MinimumEigenOptimizer(qaoa_mes)
result = qaoa.solve(qubo)
print(result.prettyprint())
from qiskit.transpiler import PassManager
from qiskit.circuit.library.standard_gates.equivalence_library import (
StandardEquivalenceLibrary as std_eqlib,
)
from qiskit.transpiler.passes import (
Collect2qBlocks,
ConsolidateBlocks,
UnrollCustomDefinitions,
BasisTranslator,
Optimize1qGatesDecomposition,
)
from qiskit.transpiler.passes.calibration.builders import RZXCalibrationBuilderNoEcho
from qiskit.transpiler.passes.optimization.echo_rzx_weyl_decomposition import (
EchoRZXWeylDecomposition,
)
from qiskit.test.mock import FakeBelem
backend = FakeBelem()
inst_map = backend.defaults().instruction_schedule_map
channel_map = backend.configuration().qubit_channel_mapping
rzx_basis = ["rzx", "rz", "x", "sx"]
pulse_efficient = PassManager(
[
# Consolidate consecutive two-qubit operations.
Collect2qBlocks(),
ConsolidateBlocks(basis_gates=["rz", "sx", "x", "rxx"]),
# Rewrite circuit in terms of Weyl-decomposed echoed RZX gates.
EchoRZXWeylDecomposition(backend.defaults().instruction_schedule_map),
# Attach scaled CR pulse schedules to the RZX gates.
RZXCalibrationBuilderNoEcho(
instruction_schedule_map=inst_map, qubit_channel_mapping=channel_map
),
# Simplify single-qubit gates.
UnrollCustomDefinitions(std_eqlib, rzx_basis),
BasisTranslator(std_eqlib, rzx_basis),
Optimize1qGatesDecomposition(rzx_basis),
]
)
from qiskit import QuantumCircuit
circ = QuantumCircuit(3)
circ.h([0, 1, 2])
circ.rzx(0.5, 0, 1)
circ.swap(0, 1)
circ.cx(2, 1)
circ.rz(0.4, 1)
circ.cx(2, 1)
circ.rx(1.23, 2)
circ.cx(2, 1)
circ.draw("mpl")
pulse_efficient.run(circ).draw("mpl", fold=False)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
problem = QuadraticProgram("sample")
problem.binary_var("x")
problem.binary_var("y")
problem.maximize(linear={"x": 1, "y": -2})
print(problem.prettyprint())
from qiskit.algorithms import NumPyMinimumEigensolver
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = NumPyMinimumEigensolver()
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = NumPyMinimumEigensolver()
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import MinimumEigenOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
mes = QAOA(optimizer=COBYLA(), quantum_instance=qins)
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
shots = 1000
mes = QAOA(sampler=Sampler(), optimizer=COBYLA())
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms import VQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import MinimumEigenOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
mes = VQE(ansatz=RealAmplitudes(), optimizer=COBYLA(), quantum_instance=qins)
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = SamplingVQE(sampler=Sampler(), ansatz=RealAmplitudes(), optimizer=COBYLA())
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Estimator
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = VQE(estimator=Estimator(), ansatz=RealAmplitudes(), optimizer=COBYLA())
try:
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
except TypeError as ex:
print(ex)
from qiskit import BasicAer
from qiskit.algorithms import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer, SlsqpOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
qaoa = QAOA(optimizer=COBYLA(), quantum_instance=qins)
optimizer = WarmStartQAOAOptimizer(
pre_solver=SlsqpOptimizer(), relax_for_pre_solver=True, qaoa=qaoa, epsilon=0.25
)
result = optimizer.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer, SlsqpOptimizer
qaoa = QAOA(sampler=Sampler(), optimizer=COBYLA())
optimizer = WarmStartQAOAOptimizer(
pre_solver=SlsqpOptimizer(), relax_for_pre_solver=True, qaoa=qaoa, epsilon=0.25
)
result = optimizer.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import GroverOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
optimizer = GroverOptimizer(num_value_qubits=3, num_iterations=3, quantum_instance=qins)
result = optimizer.solve(problem)
print(result)
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer
optimizer = GroverOptimizer(num_value_qubits=3, num_iterations=3, sampler=Sampler())
result = optimizer.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
try:
optimizer = GroverOptimizer(
num_value_qubits=3, num_iterations=3, quantum_instance=qins, sampler=Sampler()
)
# raises an error because both quantum_instance and sampler are set.
except ValueError as ex:
print(ex)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.translators import from_docplex_mp
# Make a Docplex model
from docplex.mp.model import Model
mdl = Model("docplex model")
x = mdl.binary_var("x")
y = mdl.integer_var(lb=-1, ub=5, name="y")
mdl.minimize(x + 2 * y)
mdl.add_constraint(x - y == 3)
mdl.add_constraint((x + y) * (x - y) <= 1)
print(mdl.export_as_lp_string())
# load from a Docplex model
mod = from_docplex_mp(mdl)
print(type(mod))
print()
print(mod.prettyprint())
# make an empty problem
mod = QuadraticProgram("my problem")
print(mod.prettyprint())
# Add variables
mod.binary_var(name="x")
mod.integer_var(name="y", lowerbound=-1, upperbound=5)
mod.continuous_var(name="z", lowerbound=-1, upperbound=5)
print(mod.prettyprint())
# Add objective function using dictionaries
mod.minimize(constant=3, linear={"x": 1}, quadratic={("x", "y"): 2, ("z", "z"): -1})
print(mod.prettyprint())
# Add objective function using lists/arrays
mod.minimize(constant=3, linear=[1, 0, 0], quadratic=[[0, 1, 0], [1, 0, 0], [0, 0, -1]])
print(mod.prettyprint())
print("constant:\t\t\t", mod.objective.constant)
print("linear dict:\t\t\t", mod.objective.linear.to_dict())
print("linear array:\t\t\t", mod.objective.linear.to_array())
print("linear array as sparse matrix:\n", mod.objective.linear.coefficients, "\n")
print("quadratic dict w/ index:\t", mod.objective.quadratic.to_dict())
print("quadratic dict w/ name:\t\t", mod.objective.quadratic.to_dict(use_name=True))
print(
"symmetric quadratic dict w/ name:\t",
mod.objective.quadratic.to_dict(use_name=True, symmetric=True),
)
print("quadratic matrix:\n", mod.objective.quadratic.to_array(), "\n")
print("symmetric quadratic matrix:\n", mod.objective.quadratic.to_array(symmetric=True), "\n")
print("quadratic matrix as sparse matrix:\n", mod.objective.quadratic.coefficients)
# Add linear constraints
mod.linear_constraint(linear={"x": 1, "y": 2}, sense="==", rhs=3, name="lin_eq")
mod.linear_constraint(linear={"x": 1, "y": 2}, sense="<=", rhs=3, name="lin_leq")
mod.linear_constraint(linear={"x": 1, "y": 2}, sense=">=", rhs=3, name="lin_geq")
print(mod.prettyprint())
# Add quadratic constraints
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense="==",
rhs=1,
name="quad_eq",
)
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense="<=",
rhs=1,
name="quad_leq",
)
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense=">=",
rhs=1,
name="quad_geq",
)
print(mod.prettyprint())
lin_geq = mod.get_linear_constraint("lin_geq")
print("lin_geq:", lin_geq.linear.to_dict(use_name=True), lin_geq.sense, lin_geq.rhs)
quad_geq = mod.get_quadratic_constraint("quad_geq")
print(
"quad_geq:",
quad_geq.linear.to_dict(use_name=True),
quad_geq.quadratic.to_dict(use_name=True),
quad_geq.sense,
lin_geq.rhs,
)
# Remove constraints
mod.remove_linear_constraint("lin_eq")
mod.remove_quadratic_constraint("quad_leq")
print(mod.prettyprint())
sub = mod.substitute_variables(constants={"x": 0}, variables={"y": ("z", -1)})
print(sub.prettyprint())
sub = mod.substitute_variables(constants={"x": -1})
print(sub.status)
from qiskit_optimization import QiskitOptimizationError
try:
sub = mod.substitute_variables(constants={"x": -1}, variables={"y": ("x", 1)})
except QiskitOptimizationError as e:
print("Error: {}".format(e))
mod = QuadraticProgram()
mod.binary_var(name="e")
mod.binary_var(name="f")
mod.continuous_var(name="g")
mod.minimize(linear=[1, 2, 3])
print(mod.export_as_lp_string())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
qp = QuadraticProgram()
qp.binary_var("x")
qp.binary_var("y")
qp.integer_var(lowerbound=0, upperbound=7, name="z")
qp.maximize(linear={"x": 2, "y": 1, "z": 1})
qp.linear_constraint(linear={"x": 1, "y": 1, "z": 1}, sense="LE", rhs=5.5, name="xyz_leq")
qp.linear_constraint(linear={"x": 1, "y": 1, "z": 1}, sense="GE", rhs=2.5, name="xyz_geq")
print(qp.prettyprint())
from qiskit_optimization.converters import InequalityToEquality
ineq2eq = InequalityToEquality()
qp_eq = ineq2eq.convert(qp)
print(qp_eq.prettyprint())
print(qp_eq.prettyprint())
from qiskit_optimization.converters import IntegerToBinary
int2bin = IntegerToBinary()
qp_eq_bin = int2bin.convert(qp_eq)
print(qp_eq_bin.prettyprint())
print(qp_eq_bin.prettyprint())
from qiskit_optimization.converters import LinearEqualityToPenalty
lineq2penalty = LinearEqualityToPenalty()
qubo = lineq2penalty.convert(qp_eq_bin)
print(qubo.prettyprint())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import (
MinimumEigenOptimizer,
RecursiveMinimumEigenOptimizer,
SolutionSample,
OptimizationResultStatus,
)
from qiskit_optimization import QuadraticProgram
from qiskit.visualization import plot_histogram
from typing import List, Tuple
import numpy as np
# create a QUBO
qubo = QuadraticProgram()
qubo.binary_var("x")
qubo.binary_var("y")
qubo.binary_var("z")
qubo.minimize(linear=[1, -2, 3], quadratic={("x", "y"): 1, ("x", "z"): -1, ("y", "z"): 2})
print(qubo.prettyprint())
op, offset = qubo.to_ising()
print("offset: {}".format(offset))
print("operator:")
print(op)
qp = QuadraticProgram()
qp.from_ising(op, offset, linear=True)
print(qp.prettyprint())
algorithm_globals.random_seed = 10598
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 0.0])
exact_mes = NumPyMinimumEigensolver()
qaoa = MinimumEigenOptimizer(qaoa_mes) # using QAOA
exact = MinimumEigenOptimizer(exact_mes) # using the exact classical numpy minimum eigen solver
exact_result = exact.solve(qubo)
print(exact_result.prettyprint())
qaoa_result = qaoa.solve(qubo)
print(qaoa_result.prettyprint())
print("variable order:", [var.name for var in qaoa_result.variables])
for s in qaoa_result.samples:
print(s)
def get_filtered_samples(
samples: List[SolutionSample],
threshold: float = 0,
allowed_status: Tuple[OptimizationResultStatus] = (OptimizationResultStatus.SUCCESS,),
):
res = []
for s in samples:
if s.status in allowed_status and s.probability > threshold:
res.append(s)
return res
filtered_samples = get_filtered_samples(
qaoa_result.samples, threshold=0.005, allowed_status=(OptimizationResultStatus.SUCCESS,)
)
for s in filtered_samples:
print(s)
fvals = [s.fval for s in qaoa_result.samples]
probabilities = [s.probability for s in qaoa_result.samples]
np.mean(fvals)
np.std(fvals)
samples_for_plot = {
" ".join(f"{qaoa_result.variables[i].name}={int(v)}" for i, v in enumerate(s.x)): s.probability
for s in filtered_samples
}
samples_for_plot
plot_histogram(samples_for_plot)
rqaoa = RecursiveMinimumEigenOptimizer(qaoa, min_num_vars=1, min_num_vars_optimizer=exact)
rqaoa_result = rqaoa.solve(qubo)
print(rqaoa_result.prettyprint())
filtered_samples = get_filtered_samples(
rqaoa_result.samples, threshold=0.005, allowed_status=(OptimizationResultStatus.SUCCESS,)
)
samples_for_plot = {
" ".join(f"{rqaoa_result.variables[i].name}={int(v)}" for i, v in enumerate(s.x)): s.probability
for s in filtered_samples
}
samples_for_plot
plot_histogram(samples_for_plot)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer, MinimumEigenOptimizer
from qiskit_optimization.translators import from_docplex_mp
from docplex.mp.model import Model
model = Model()
x0 = model.binary_var(name="x0")
x1 = model.binary_var(name="x1")
x2 = model.binary_var(name="x2")
model.minimize(-x0 + 2 * x1 - 3 * x2 - 2 * x0 * x2 - 1 * x1 * x2)
qp = from_docplex_mp(model)
print(qp.prettyprint())
grover_optimizer = GroverOptimizer(6, num_iterations=10, sampler=Sampler())
results = grover_optimizer.solve(qp)
print(results.prettyprint())
exact_solver = MinimumEigenOptimizer(NumPyMinimumEigensolver())
exact_result = exact_solver.solve(qp)
print(exact_result.prettyprint())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import matplotlib.pyplot as plt
from docplex.mp.model import Model
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import CobylaOptimizer, MinimumEigenOptimizer
from qiskit_optimization.algorithms.admm_optimizer import ADMMParameters, ADMMOptimizer
from qiskit_optimization.translators import from_docplex_mp
# If CPLEX is installed, you can uncomment this line to import the CplexOptimizer.
# CPLEX can be used in this tutorial to solve the convex continuous problem,
# but also as a reference to solve the QUBO, or even the full problem.
#
# from qiskit.optimization.algorithms import CplexOptimizer
# define COBYLA optimizer to handle convex continuous problems.
cobyla = CobylaOptimizer()
# define QAOA via the minimum eigen optimizer
qaoa = MinimumEigenOptimizer(QAOA(sampler=Sampler(), optimizer=COBYLA()))
# exact QUBO solver as classical benchmark
exact = MinimumEigenOptimizer(NumPyMinimumEigensolver()) # to solve QUBOs
# in case CPLEX is installed it can also be used for the convex problems, the QUBO,
# or as a benchmark for the full problem.
#
# cplex = CplexOptimizer()
# construct model using docplex
mdl = Model("ex6")
v = mdl.binary_var(name="v")
w = mdl.binary_var(name="w")
t = mdl.binary_var(name="t")
u = mdl.continuous_var(name="u")
mdl.minimize(v + w + t + 5 * (u - 2) ** 2)
mdl.add_constraint(v + 2 * w + t + u <= 3, "cons1")
mdl.add_constraint(v + w + t >= 1, "cons2")
mdl.add_constraint(v + w == 1, "cons3")
# load quadratic program from docplex model
qp = from_docplex_mp(mdl)
print(qp.prettyprint())
admm_params = ADMMParameters(
rho_initial=1001, beta=1000, factor_c=900, maxiter=100, three_block=True, tol=1.0e-6
)
# define QUBO optimizer
qubo_optimizer = exact
# qubo_optimizer = cplex # uncomment to use CPLEX instead
# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex # uncomment to use CPLEX instead
# initialize ADMM with classical QUBO and convex optimizer
admm = ADMMOptimizer(
params=admm_params, qubo_optimizer=qubo_optimizer, continuous_optimizer=convex_optimizer
)
# run ADMM to solve problem
result = admm.solve(qp)
print(result.prettyprint())
plt.plot(result.state.residuals)
plt.xlabel("Iterations")
plt.ylabel("Residuals")
plt.show()
# define QUBO optimizer
qubo_optimizer = qaoa
# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex # uncomment to use CPLEX instead
# initialize ADMM with quantum QUBO optimizer and classical convex optimizer
admm_q = ADMMOptimizer(
params=admm_params, qubo_optimizer=qubo_optimizer, continuous_optimizer=convex_optimizer
)
# run ADMM to solve problem
result_q = admm_q.solve(qp)
print(result.prettyprint())
plt.clf()
plt.plot(result_q.state.residuals)
plt.xlabel("Iterations")
plt.ylabel("Residuals")
plt.show()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
# useful additional packages
import matplotlib.pyplot as plt
import numpy as np
import networkx as nx
from qiskit_aer import Aer
from qiskit.tools.visualization import plot_histogram
from qiskit.circuit.library import TwoLocal
from qiskit_optimization.applications import Maxcut, Tsp
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import SPSA
from qiskit.utils import algorithm_globals
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
# Generating a graph of 4 nodes
n = 4 # Number of nodes in graph
G = nx.Graph()
G.add_nodes_from(np.arange(0, n, 1))
elist = [(0, 1, 1.0), (0, 2, 1.0), (0, 3, 1.0), (1, 2, 1.0), (2, 3, 1.0)]
# tuple is (i,j,weight) where (i,j) is the edge
G.add_weighted_edges_from(elist)
colors = ["r" for node in G.nodes()]
pos = nx.spring_layout(G)
def draw_graph(G, colors, pos):
default_axes = plt.axes(frameon=True)
nx.draw_networkx(G, node_color=colors, node_size=600, alpha=0.8, ax=default_axes, pos=pos)
edge_labels = nx.get_edge_attributes(G, "weight")
nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels)
draw_graph(G, colors, pos)
# Computing the weight matrix from the random graph
w = np.zeros([n, n])
for i in range(n):
for j in range(n):
temp = G.get_edge_data(i, j, default=0)
if temp != 0:
w[i, j] = temp["weight"]
print(w)
best_cost_brute = 0
for b in range(2**n):
x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]
cost = 0
for i in range(n):
for j in range(n):
cost = cost + w[i, j] * x[i] * (1 - x[j])
if best_cost_brute < cost:
best_cost_brute = cost
xbest_brute = x
print("case = " + str(x) + " cost = " + str(cost))
colors = ["r" if xbest_brute[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
print("\nBest solution = " + str(xbest_brute) + " cost = " + str(best_cost_brute))
max_cut = Maxcut(w)
qp = max_cut.to_quadratic_program()
print(qp.prettyprint())
qubitOp, offset = qp.to_ising()
print("Offset:", offset)
print("Ising Hamiltonian:")
print(str(qubitOp))
# solving Quadratic Program using exact classical eigensolver
exact = MinimumEigenOptimizer(NumPyMinimumEigensolver())
result = exact.solve(qp)
print(result.prettyprint())
# Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector
ee = NumPyMinimumEigensolver()
result = ee.compute_minimum_eigenvalue(qubitOp)
x = max_cut.sample_most_likely(result.eigenstate)
print("energy:", result.eigenvalue.real)
print("max-cut objective:", result.eigenvalue.real + offset)
print("solution:", x)
print("solution objective:", qp.objective.evaluate(x))
colors = ["r" if x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
# construct SamplingVQE
optimizer = SPSA(maxiter=300)
ry = TwoLocal(qubitOp.num_qubits, "ry", "cz", reps=5, entanglement="linear")
vqe = SamplingVQE(sampler=Sampler(), ansatz=ry, optimizer=optimizer)
# run SamplingVQE
result = vqe.compute_minimum_eigenvalue(qubitOp)
# print results
x = max_cut.sample_most_likely(result.eigenstate)
print("energy:", result.eigenvalue.real)
print("time:", result.optimizer_time)
print("max-cut objective:", result.eigenvalue.real + offset)
print("solution:", x)
print("solution objective:", qp.objective.evaluate(x))
# plot results
colors = ["r" if x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
# create minimum eigen optimizer based on SamplingVQE
vqe_optimizer = MinimumEigenOptimizer(vqe)
# solve quadratic program
result = vqe_optimizer.solve(qp)
print(result.prettyprint())
colors = ["r" if result.x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
# Generating a graph of 3 nodes
n = 3
num_qubits = n**2
tsp = Tsp.create_random_instance(n, seed=123)
adj_matrix = nx.to_numpy_array(tsp.graph)
print("distance\n", adj_matrix)
colors = ["r" for node in tsp.graph.nodes]
pos = [tsp.graph.nodes[node]["pos"] for node in tsp.graph.nodes]
draw_graph(tsp.graph, colors, pos)
from itertools import permutations
def brute_force_tsp(w, N):
a = list(permutations(range(1, N)))
last_best_distance = 1e10
for i in a:
distance = 0
pre_j = 0
for j in i:
distance = distance + w[j, pre_j]
pre_j = j
distance = distance + w[pre_j, 0]
order = (0,) + i
if distance < last_best_distance:
best_order = order
last_best_distance = distance
print("order = " + str(order) + " Distance = " + str(distance))
return last_best_distance, best_order
best_distance, best_order = brute_force_tsp(adj_matrix, n)
print(
"Best order from brute force = "
+ str(best_order)
+ " with total distance = "
+ str(best_distance)
)
def draw_tsp_solution(G, order, colors, pos):
G2 = nx.DiGraph()
G2.add_nodes_from(G)
n = len(order)
for i in range(n):
j = (i + 1) % n
G2.add_edge(order[i], order[j], weight=G[order[i]][order[j]]["weight"])
default_axes = plt.axes(frameon=True)
nx.draw_networkx(
G2, node_color=colors, edge_color="b", node_size=600, alpha=0.8, ax=default_axes, pos=pos
)
edge_labels = nx.get_edge_attributes(G2, "weight")
nx.draw_networkx_edge_labels(G2, pos, font_color="b", edge_labels=edge_labels)
draw_tsp_solution(tsp.graph, best_order, colors, pos)
qp = tsp.to_quadratic_program()
print(qp.prettyprint())
from qiskit_optimization.converters import QuadraticProgramToQubo
qp2qubo = QuadraticProgramToQubo()
qubo = qp2qubo.convert(qp)
qubitOp, offset = qubo.to_ising()
print("Offset:", offset)
print("Ising Hamiltonian:")
print(str(qubitOp))
result = exact.solve(qubo)
print(result.prettyprint())
# Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector
ee = NumPyMinimumEigensolver()
result = ee.compute_minimum_eigenvalue(qubitOp)
print("energy:", result.eigenvalue.real)
print("tsp objective:", result.eigenvalue.real + offset)
x = tsp.sample_most_likely(result.eigenstate)
print("feasible:", qubo.is_feasible(x))
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
optimizer = SPSA(maxiter=300)
ry = TwoLocal(qubitOp.num_qubits, "ry", "cz", reps=5, entanglement="linear")
vqe = SamplingVQE(sampler=Sampler(), ansatz=ry, optimizer=optimizer)
result = vqe.compute_minimum_eigenvalue(qubitOp)
print("energy:", result.eigenvalue.real)
print("time:", result.optimizer_time)
x = tsp.sample_most_likely(result.eigenstate)
print("feasible:", qubo.is_feasible(x))
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
# create minimum eigen optimizer based on SamplingVQE
vqe_optimizer = MinimumEigenOptimizer(vqe)
# solve quadratic program
result = vqe_optimizer.solve(qp)
print(result.prettyprint())
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import matplotlib.pyplot as plt
try:
import cplex
from cplex.exceptions import CplexError
except:
print("Warning: Cplex not found.")
import math
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE
from qiskit.algorithms.optimizers import SPSA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Sampler
# Initialize the problem by defining the parameters
n = 3 # number of nodes + depot (n+1)
K = 2 # number of vehicles
# Get the data
class Initializer:
def __init__(self, n):
self.n = n
def generate_instance(self):
n = self.n
# np.random.seed(33)
np.random.seed(1543)
xc = (np.random.rand(n) - 0.5) * 10
yc = (np.random.rand(n) - 0.5) * 10
instance = np.zeros([n, n])
for ii in range(0, n):
for jj in range(ii + 1, n):
instance[ii, jj] = (xc[ii] - xc[jj]) ** 2 + (yc[ii] - yc[jj]) ** 2
instance[jj, ii] = instance[ii, jj]
return xc, yc, instance
# Initialize the problem by randomly generating the instance
initializer = Initializer(n)
xc, yc, instance = initializer.generate_instance()
class ClassicalOptimizer:
def __init__(self, instance, n, K):
self.instance = instance
self.n = n # number of nodes
self.K = K # number of vehicles
def compute_allowed_combinations(self):
f = math.factorial
return f(self.n) / f(self.K) / f(self.n - self.K)
def cplex_solution(self):
# refactoring
instance = self.instance
n = self.n
K = self.K
my_obj = list(instance.reshape(1, n**2)[0]) + [0.0 for x in range(0, n - 1)]
my_ub = [1 for x in range(0, n**2 + n - 1)]
my_lb = [0 for x in range(0, n**2)] + [0.1 for x in range(0, n - 1)]
my_ctype = "".join(["I" for x in range(0, n**2)]) + "".join(
["C" for x in range(0, n - 1)]
)
my_rhs = (
2 * ([K] + [1 for x in range(0, n - 1)])
+ [1 - 0.1 for x in range(0, (n - 1) ** 2 - (n - 1))]
+ [0 for x in range(0, n)]
)
my_sense = (
"".join(["E" for x in range(0, 2 * n)])
+ "".join(["L" for x in range(0, (n - 1) ** 2 - (n - 1))])
+ "".join(["E" for x in range(0, n)])
)
try:
my_prob = cplex.Cplex()
self.populatebyrow(my_prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs)
my_prob.solve()
except CplexError as exc:
print(exc)
return
x = my_prob.solution.get_values()
x = np.array(x)
cost = my_prob.solution.get_objective_value()
return x, cost
def populatebyrow(self, prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs):
n = self.n
prob.objective.set_sense(prob.objective.sense.minimize)
prob.variables.add(obj=my_obj, lb=my_lb, ub=my_ub, types=my_ctype)
prob.set_log_stream(None)
prob.set_error_stream(None)
prob.set_warning_stream(None)
prob.set_results_stream(None)
rows = []
for ii in range(0, n):
col = [x for x in range(0 + n * ii, n + n * ii)]
coef = [1 for x in range(0, n)]
rows.append([col, coef])
for ii in range(0, n):
col = [x for x in range(0 + ii, n**2, n)]
coef = [1 for x in range(0, n)]
rows.append([col, coef])
# Sub-tour elimination constraints:
for ii in range(0, n):
for jj in range(0, n):
if (ii != jj) and (ii * jj > 0):
col = [ii + (jj * n), n**2 + ii - 1, n**2 + jj - 1]
coef = [1, 1, -1]
rows.append([col, coef])
for ii in range(0, n):
col = [(ii) * (n + 1)]
coef = [1]
rows.append([col, coef])
prob.linear_constraints.add(lin_expr=rows, senses=my_sense, rhs=my_rhs)
# Instantiate the classical optimizer class
classical_optimizer = ClassicalOptimizer(instance, n, K)
# Print number of feasible solutions
print("Number of feasible solutions = " + str(classical_optimizer.compute_allowed_combinations()))
# Solve the problem in a classical fashion via CPLEX
x = None
z = None
try:
x, classical_cost = classical_optimizer.cplex_solution()
# Put the solution in the z variable
z = [x[ii] for ii in range(n**2) if ii // n != ii % n]
# Print the solution
print(z)
except:
print("CPLEX may be missing.")
# Visualize the solution
def visualize_solution(xc, yc, x, C, n, K, title_str):
plt.figure()
plt.scatter(xc, yc, s=200)
for i in range(len(xc)):
plt.annotate(i, (xc[i] + 0.15, yc[i]), size=16, color="r")
plt.plot(xc[0], yc[0], "r*", ms=20)
plt.grid()
for ii in range(0, n**2):
if x[ii] > 0:
ix = ii // n
iy = ii % n
plt.arrow(
xc[ix],
yc[ix],
xc[iy] - xc[ix],
yc[iy] - yc[ix],
length_includes_head=True,
head_width=0.25,
)
plt.title(title_str + " cost = " + str(int(C * 100) / 100.0))
plt.show()
if x is not None:
visualize_solution(xc, yc, x, classical_cost, n, K, "Classical")
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.algorithms import MinimumEigenOptimizer
class QuantumOptimizer:
def __init__(self, instance, n, K):
self.instance = instance
self.n = n
self.K = K
def binary_representation(self, x_sol=0):
instance = self.instance
n = self.n
K = self.K
A = np.max(instance) * 100 # A parameter of cost function
# Determine the weights w
instance_vec = instance.reshape(n**2)
w_list = [instance_vec[x] for x in range(n**2) if instance_vec[x] > 0]
w = np.zeros(n * (n - 1))
for ii in range(len(w_list)):
w[ii] = w_list[ii]
# Some variables I will use
Id_n = np.eye(n)
Im_n_1 = np.ones([n - 1, n - 1])
Iv_n_1 = np.ones(n)
Iv_n_1[0] = 0
Iv_n = np.ones(n - 1)
neg_Iv_n_1 = np.ones(n) - Iv_n_1
v = np.zeros([n, n * (n - 1)])
for ii in range(n):
count = ii - 1
for jj in range(n * (n - 1)):
if jj // (n - 1) == ii:
count = ii
if jj // (n - 1) != ii and jj % (n - 1) == count:
v[ii][jj] = 1.0
vn = np.sum(v[1:], axis=0)
# Q defines the interactions between variables
Q = A * (np.kron(Id_n, Im_n_1) + np.dot(v.T, v))
# g defines the contribution from the individual variables
g = (
w
- 2 * A * (np.kron(Iv_n_1, Iv_n) + vn.T)
- 2 * A * K * (np.kron(neg_Iv_n_1, Iv_n) + v[0].T)
)
# c is the constant offset
c = 2 * A * (n - 1) + 2 * A * (K**2)
try:
max(x_sol)
# Evaluates the cost distance from a binary representation of a path
fun = (
lambda x: np.dot(np.around(x), np.dot(Q, np.around(x)))
+ np.dot(g, np.around(x))
+ c
)
cost = fun(x_sol)
except:
cost = 0
return Q, g, c, cost
def construct_problem(self, Q, g, c) -> QuadraticProgram:
qp = QuadraticProgram()
for i in range(n * (n - 1)):
qp.binary_var(str(i))
qp.objective.quadratic = Q
qp.objective.linear = g
qp.objective.constant = c
return qp
def solve_problem(self, qp):
algorithm_globals.random_seed = 10598
vqe = SamplingVQE(sampler=Sampler(), optimizer=SPSA(), ansatz=RealAmplitudes())
optimizer = MinimumEigenOptimizer(min_eigen_solver=vqe)
result = optimizer.solve(qp)
# compute cost of the obtained result
_, _, _, level = self.binary_representation(x_sol=result.x)
return result.x, level
# Instantiate the quantum optimizer class with parameters:
quantum_optimizer = QuantumOptimizer(instance, n, K)
# Check if the binary representation is correct
try:
if z is not None:
Q, g, c, binary_cost = quantum_optimizer.binary_representation(x_sol=z)
print("Binary cost:", binary_cost, "classical cost:", classical_cost)
if np.abs(binary_cost - classical_cost) < 0.01:
print("Binary formulation is correct")
else:
print("Error in the binary formulation")
else:
print("Could not verify the correctness, due to CPLEX solution being unavailable.")
Q, g, c, binary_cost = quantum_optimizer.binary_representation()
print("Binary cost:", binary_cost)
except NameError as e:
print("Warning: Please run the cells above first.")
print(e)
qp = quantum_optimizer.construct_problem(Q, g, c)
quantum_solution, quantum_cost = quantum_optimizer.solve_problem(qp)
print(quantum_solution, quantum_cost)
# Put the solution in a way that is compatible with the classical variables
x_quantum = np.zeros(n**2)
kk = 0
for ii in range(n**2):
if ii // n != ii % n:
x_quantum[ii] = quantum_solution[kk]
kk += 1
# visualize the solution
visualize_solution(xc, yc, x_quantum, quantum_cost, n, K, "Quantum")
# and visualize the classical for comparison
if x is not None:
visualize_solution(xc, yc, x, classical_cost, n, K, "Classical")
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.circuit.library import RealAmplitudes
from qiskit.algorithms.optimizers import COBYLA
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver, SamplingVQE
from qiskit.primitives import Sampler
from qiskit_optimization.converters import LinearEqualityToPenalty
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_optimization.translators import from_docplex_mp
from qiskit.utils import algorithm_globals
import numpy as np
import matplotlib.pyplot as plt
from docplex.mp.model import Model
algorithm_globals.random_seed = 123456
# prepare problem instance
n = 6 # number of assets
q = 0.5 # risk factor
budget = n // 2 # budget
penalty = 2 * n # scaling of penalty term
# instance from [1]
mu = np.array([0.7313, 0.9893, 0.2725, 0.8750, 0.7667, 0.3622])
sigma = np.array(
[
[0.7312, -0.6233, 0.4689, -0.5452, -0.0082, -0.3809],
[-0.6233, 2.4732, -0.7538, 2.4659, -0.0733, 0.8945],
[0.4689, -0.7538, 1.1543, -1.4095, 0.0007, -0.4301],
[-0.5452, 2.4659, -1.4095, 3.5067, 0.2012, 1.0922],
[-0.0082, -0.0733, 0.0007, 0.2012, 0.6231, 0.1509],
[-0.3809, 0.8945, -0.4301, 1.0922, 0.1509, 0.8992],
]
)
# or create random instance
# mu, sigma = portfolio.random_model(n, seed=123) # expected returns and covariance matrix
# create docplex model
mdl = Model("portfolio_optimization")
x = mdl.binary_var_list(range(n), name="x")
objective = mdl.sum([mu[i] * x[i] for i in range(n)])
objective -= q * mdl.sum([sigma[i, j] * x[i] * x[j] for i in range(n) for j in range(n)])
mdl.maximize(objective)
mdl.add_constraint(mdl.sum(x[i] for i in range(n)) == budget)
# case to
qp = from_docplex_mp(mdl)
# solve classically as reference
opt_result = MinimumEigenOptimizer(NumPyMinimumEigensolver()).solve(qp)
print(opt_result.prettyprint())
# we convert the problem to an unconstrained problem for further analysis,
# otherwise this would not be necessary as the MinimumEigenSolver would do this
# translation automatically
linear2penalty = LinearEqualityToPenalty(penalty=penalty)
qp = linear2penalty.convert(qp)
_, offset = qp.to_ising()
# set classical optimizer
maxiter = 100
optimizer = COBYLA(maxiter=maxiter)
# set variational ansatz
ansatz = RealAmplitudes(n, reps=1)
m = ansatz.num_parameters
# set sampler
sampler = Sampler()
# run variational optimization for different values of alpha
alphas = [1.0, 0.50, 0.25] # confidence levels to be evaluated
# dictionaries to store optimization progress and results
objectives = {alpha: [] for alpha in alphas} # set of tested objective functions w.r.t. alpha
results = {} # results of minimum eigensolver w.r.t alpha
# callback to store intermediate results
def callback(i, params, obj, stddev, alpha):
# we translate the objective from the internal Ising representation
# to the original optimization problem
objectives[alpha].append(np.real_if_close(-(obj + offset)))
# loop over all given alpha values
for alpha in alphas:
# initialize SamplingVQE using CVaR
vqe = SamplingVQE(
sampler=sampler,
ansatz=ansatz,
optimizer=optimizer,
aggregation=alpha,
callback=lambda i, params, obj, stddev: callback(i, params, obj, stddev, alpha),
)
# initialize optimization algorithm based on CVaR-SamplingVQE
opt_alg = MinimumEigenOptimizer(vqe)
# solve problem
results[alpha] = opt_alg.solve(qp)
# print results
print("alpha = {}:".format(alpha))
print(results[alpha].prettyprint())
print()
# plot resulting history of objective values
plt.figure(figsize=(10, 5))
plt.plot([0, maxiter], [opt_result.fval, opt_result.fval], "r--", linewidth=2, label="optimum")
for alpha in alphas:
plt.plot(objectives[alpha], label="alpha = %.2f" % alpha, linewidth=2)
plt.legend(loc="lower right", fontsize=14)
plt.xlim(0, maxiter)
plt.xticks(fontsize=14)
plt.xlabel("iterations", fontsize=14)
plt.yticks(fontsize=14)
plt.ylabel("objective value", fontsize=14)
plt.show()
# evaluate and sort all objective values
objective_values = np.zeros(2**n)
for i in range(2**n):
x_bin = ("{0:0%sb}" % n).format(i)
x = [0 if x_ == "0" else 1 for x_ in reversed(x_bin)]
objective_values[i] = qp.objective.evaluate(x)
ind = np.argsort(objective_values)
# evaluate final optimal probability for each alpha
for alpha in alphas:
probabilities = np.fromiter(
results[alpha].min_eigen_solver_result.eigenstate.binary_probabilities().values(),
dtype=float,
)
print("optimal probability (alpha = %.2f): %.4f" % (alpha, probabilities[ind][-1:]))
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.applications.vertex_cover import VertexCover
import networkx as nx
seed = 123
algorithm_globals.random_seed = seed
graph = nx.random_regular_graph(d=3, n=6, seed=seed)
pos = nx.spring_layout(graph, seed=seed)
prob = VertexCover(graph)
prob.draw(pos=pos)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# Numpy Eigensolver
meo = MinimumEigenOptimizer(min_eigen_solver=NumPyMinimumEigensolver())
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
prob.draw(result, pos=pos)
# QAOA
meo = MinimumEigenOptimizer(min_eigen_solver=QAOA(reps=1, sampler=Sampler(), optimizer=COBYLA()))
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
print("\ntime:", result.min_eigen_solver_result.optimizer_time)
prob.draw(result, pos=pos)
from qiskit_optimization.applications import Knapsack
prob = Knapsack(values=[3, 4, 5, 6, 7], weights=[2, 3, 4, 5, 6], max_weight=10)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# Numpy Eigensolver
meo = MinimumEigenOptimizer(min_eigen_solver=NumPyMinimumEigensolver())
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
# QAOA
meo = MinimumEigenOptimizer(min_eigen_solver=QAOA(reps=1, sampler=Sampler(), optimizer=COBYLA()))
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
print("\ntime:", result.min_eigen_solver_result.optimizer_time)
from qiskit_optimization.converters import QuadraticProgramToQubo
# the same knapsack problem instance as in the previous section
prob = Knapsack(values=[3, 4, 5, 6, 7], weights=[2, 3, 4, 5, 6], max_weight=10)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# intermediate QUBO form of the optimization problem
conv = QuadraticProgramToQubo()
qubo = conv.convert(qp)
print(qubo.prettyprint())
# qubit Hamiltonian and offset
op, offset = qubo.to_ising()
print(f"num qubits: {op.num_qubits}, offset: {offset}\n")
print(op)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import copy
# Problem modelling imports
from docplex.mp.model import Model
# Qiskit imports
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit.utils.algorithm_globals import algorithm_globals
from qiskit_optimization.algorithms import MinimumEigenOptimizer, CplexOptimizer
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.problems.variable import VarType
from qiskit_optimization.converters.quadratic_program_to_qubo import QuadraticProgramToQubo
from qiskit_optimization.translators import from_docplex_mp
def create_problem(mu: np.array, sigma: np.array, total: int = 3) -> QuadraticProgram:
"""Solve the quadratic program using docplex."""
mdl = Model()
x = [mdl.binary_var("x%s" % i) for i in range(len(sigma))]
objective = mdl.sum([mu[i] * x[i] for i in range(len(mu))])
objective -= 2 * mdl.sum(
[sigma[i, j] * x[i] * x[j] for i in range(len(mu)) for j in range(len(mu))]
)
mdl.maximize(objective)
cost = mdl.sum(x)
mdl.add_constraint(cost == total)
qp = from_docplex_mp(mdl)
return qp
def relax_problem(problem) -> QuadraticProgram:
"""Change all variables to continuous."""
relaxed_problem = copy.deepcopy(problem)
for variable in relaxed_problem.variables:
variable.vartype = VarType.CONTINUOUS
return relaxed_problem
mu = np.array([3.418, 2.0913, 6.2415, 4.4436, 10.892, 3.4051])
sigma = np.array(
[
[1.07978412, 0.00768914, 0.11227606, -0.06842969, -0.01016793, -0.00839765],
[0.00768914, 0.10922887, -0.03043424, -0.0020045, 0.00670929, 0.0147937],
[0.11227606, -0.03043424, 0.985353, 0.02307313, -0.05249785, 0.00904119],
[-0.06842969, -0.0020045, 0.02307313, 0.6043817, 0.03740115, -0.00945322],
[-0.01016793, 0.00670929, -0.05249785, 0.03740115, 0.79839634, 0.07616951],
[-0.00839765, 0.0147937, 0.00904119, -0.00945322, 0.07616951, 1.08464544],
]
)
qubo = create_problem(mu, sigma)
print(qubo.prettyprint())
result = CplexOptimizer().solve(qubo)
print(result.prettyprint())
qp = relax_problem(QuadraticProgramToQubo().convert(qubo))
print(qp.prettyprint())
sol = CplexOptimizer().solve(qp)
print(sol.prettyprint())
c_stars = sol.samples[0].x
print(c_stars)
algorithm_globals.random_seed = 12345
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 1.0])
exact_mes = NumPyMinimumEigensolver()
qaoa = MinimumEigenOptimizer(qaoa_mes)
qaoa_result = qaoa.solve(qubo)
print(qaoa_result.prettyprint())
from qiskit import QuantumCircuit
thetas = [2 * np.arcsin(np.sqrt(c_star)) for c_star in c_stars]
init_qc = QuantumCircuit(len(sigma))
for idx, theta in enumerate(thetas):
init_qc.ry(theta, idx)
init_qc.draw(output="mpl")
from qiskit.circuit import Parameter
beta = Parameter("β")
ws_mixer = QuantumCircuit(len(sigma))
for idx, theta in enumerate(thetas):
ws_mixer.ry(-theta, idx)
ws_mixer.rz(-2 * beta, idx)
ws_mixer.ry(theta, idx)
ws_mixer.draw(output="mpl")
ws_qaoa_mes = QAOA(
sampler=Sampler(),
optimizer=COBYLA(),
initial_state=init_qc,
mixer=ws_mixer,
initial_point=[0.0, 1.0],
)
ws_qaoa = MinimumEigenOptimizer(ws_qaoa_mes)
ws_qaoa_result = ws_qaoa.solve(qubo)
print(ws_qaoa_result.prettyprint())
def format_qaoa_samples(samples, max_len: int = 10):
qaoa_res = []
for s in samples:
if sum(s.x) == 3:
qaoa_res.append(("".join([str(int(_)) for _ in s.x]), s.fval, s.probability))
res = sorted(qaoa_res, key=lambda x: -x[1])[0:max_len]
return [(_[0] + f": value: {_[1]:.3f}, probability: {1e2*_[2]:.1f}%") for _ in res]
format_qaoa_samples(qaoa_result.samples)
format_qaoa_samples(ws_qaoa_result.samples)
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 1.0])
ws_qaoa = WarmStartQAOAOptimizer(
pre_solver=CplexOptimizer(), relax_for_pre_solver=True, qaoa=qaoa_mes, epsilon=0.0
)
ws_result = ws_qaoa.solve(qubo)
print(ws_result.prettyprint())
format_qaoa_samples(ws_result.samples)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization.problems import QuadraticProgram
# define a problem
qp = QuadraticProgram()
qp.binary_var("x")
qp.integer_var(name="y", lowerbound=-1, upperbound=4)
qp.maximize(quadratic={("x", "y"): 1})
qp.linear_constraint({"x": 1, "y": -1}, "<=", 0)
print(qp.prettyprint())
from qiskit_optimization.algorithms import CplexOptimizer, GurobiOptimizer
cplex_result = CplexOptimizer().solve(qp)
gurobi_result = GurobiOptimizer().solve(qp)
print("cplex")
print(cplex_result.prettyprint())
print()
print("gurobi")
print(gurobi_result.prettyprint())
result = CplexOptimizer(disp=True, cplex_parameters={"threads": 1, "timelimit": 0.1}).solve(qp)
print(result.prettyprint())
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_aer import Aer
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
meo = MinimumEigenOptimizer(QAOA(sampler=Sampler(), optimizer=COBYLA(maxiter=100)))
result = meo.solve(qp)
print(result.prettyprint())
print("\ndisplay the best 5 solution samples")
for sample in result.samples[:5]:
print(sample)
# docplex model
from docplex.mp.model import Model
docplex_model = Model("docplex")
x = docplex_model.binary_var("x")
y = docplex_model.integer_var(-1, 4, "y")
docplex_model.maximize(x * y)
docplex_model.add_constraint(x <= y)
docplex_model.prettyprint()
# gurobi model
import gurobipy as gp
gurobipy_model = gp.Model("gurobi")
x = gurobipy_model.addVar(vtype=gp.GRB.BINARY, name="x")
y = gurobipy_model.addVar(vtype=gp.GRB.INTEGER, lb=-1, ub=4, name="y")
gurobipy_model.setObjective(x * y, gp.GRB.MAXIMIZE)
gurobipy_model.addConstr(x - y <= 0)
gurobipy_model.update()
gurobipy_model.display()
from qiskit_optimization.translators import from_docplex_mp, from_gurobipy
qp = from_docplex_mp(docplex_model)
print("QuadraticProgram obtained from docpblex")
print(qp.prettyprint())
print("-------------")
print("QuadraticProgram obtained from gurobipy")
qp2 = from_gurobipy(gurobipy_model)
print(qp2.prettyprint())
from qiskit_optimization.translators import to_gurobipy, to_docplex_mp
gmod = to_gurobipy(from_docplex_mp(docplex_model))
print("convert docplex to gurobipy via QuadraticProgram")
gmod.display()
dmod = to_docplex_mp(from_gurobipy(gurobipy_model))
print("\nconvert gurobipy to docplex via QuadraticProgram")
print(dmod.export_as_lp_string())
ind_mod = Model("docplex")
x = ind_mod.binary_var("x")
y = ind_mod.integer_var(-1, 2, "y")
z = ind_mod.integer_var(-1, 2, "z")
ind_mod.maximize(3 * x + y - z)
ind_mod.add_indicator(x, y >= z, 1)
print(ind_mod.export_as_lp_string())
qp = from_docplex_mp(ind_mod)
result = meo.solve(qp) # apply QAOA to QuadraticProgram
print("QAOA")
print(result.prettyprint())
print("-----\nCPLEX")
print(ind_mod.solve()) # apply CPLEX directly to the Docplex model
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit import IBMQ
IBMQ.load_account()
provider = IBMQ.get_provider(hub="ibm-q", group="open", project="main")
program_id = "qaoa"
qaoa_program = provider.runtime.program(program_id)
print(f"Program name: {qaoa_program.name}, Program id: {qaoa_program.program_id}")
print(qaoa_program.parameters())
import numpy as np
from qiskit.tools import job_monitor
from qiskit.opflow import PauliSumOp, Z, I
from qiskit.algorithms.optimizers import SPSA
# Define the cost operator to run.
op = (
(Z ^ Z ^ I ^ I ^ I)
- (I ^ I ^ Z ^ Z ^ I)
+ (I ^ I ^ Z ^ I ^ Z)
- (Z ^ I ^ Z ^ I ^ I)
- (I ^ Z ^ Z ^ I ^ I)
+ (I ^ Z ^ I ^ Z ^ I)
+ (I ^ I ^ I ^ Z ^ Z)
)
# SPSA helps deal with noisy environments.
optimizer = SPSA(maxiter=100)
# We will run a depth two QAOA.
reps = 2
# The initial point for the optimization, chosen at random.
initial_point = np.random.random(2 * reps)
# The backend that will run the programm.
options = {"backend_name": "ibmq_qasm_simulator"}
# The inputs of the program as described above.
runtime_inputs = {
"operator": op,
"reps": reps,
"optimizer": optimizer,
"initial_point": initial_point,
"shots": 2**13,
# Set to True when running on real backends to reduce circuit
# depth by leveraging swap strategies. If False the
# given optimization_level (default is 1) will be used.
"use_swap_strategies": False,
# Set to True when optimizing sparse problems.
"use_initial_mapping": False,
# Set to true when using echoed-cross-resonance hardware.
"use_pulse_efficient": False,
}
job = provider.runtime.run(
program_id=program_id,
options=options,
inputs=runtime_inputs,
)
job_monitor(job)
print(f"Job id: {job.job_id()}")
print(f"Job status: {job.status()}")
result = job.result()
from collections import defaultdict
def op_adj_mat(op: PauliSumOp) -> np.array:
"""Extract the adjacency matrix from the op."""
adj_mat = np.zeros((op.num_qubits, op.num_qubits))
for pauli, coeff in op.primitive.to_list():
idx = tuple([i for i, c in enumerate(pauli[::-1]) if c == "Z"]) # index of Z
adj_mat[idx[0], idx[1]], adj_mat[idx[1], idx[0]] = np.real(coeff), np.real(coeff)
return adj_mat
def get_cost(bit_str: str, adj_mat: np.array) -> float:
"""Return the cut value of the bit string."""
n, x = len(bit_str), [int(bit) for bit in bit_str[::-1]]
cost = 0
for i in range(n):
for j in range(n):
cost += adj_mat[i, j] * x[i] * (1 - x[j])
return cost
def get_cut_distribution(result) -> dict:
"""Extract the cut distribution from the result.
Returns:
A dict of cut value: probability.
"""
adj_mat = op_adj_mat(PauliSumOp.from_list(result["inputs"]["operator"]))
state_results = []
for bit_str, amp in result["eigenstate"].items():
state_results.append((bit_str, get_cost(bit_str, adj_mat), amp**2 * 100))
vals = defaultdict(int)
for res in state_results:
vals[res[1]] += res[2]
return dict(vals)
import matplotlib.pyplot as plt
cut_vals = get_cut_distribution(result)
fig, axs = plt.subplots(1, 2, figsize=(14, 5))
axs[0].plot(result["optimizer_history"]["energy"])
axs[1].bar(list(cut_vals.keys()), list(cut_vals.values()))
axs[0].set_xlabel("Energy evaluation number")
axs[0].set_ylabel("Energy")
axs[1].set_xlabel("Cut value")
axs[1].set_ylabel("Probability")
from qiskit_optimization.runtime import QAOAClient
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_optimization import QuadraticProgram
qubo = QuadraticProgram()
qubo.binary_var("x")
qubo.binary_var("y")
qubo.binary_var("z")
qubo.minimize(linear=[1, -2, 3], quadratic={("x", "y"): 1, ("x", "z"): -1, ("y", "z"): 2})
print(qubo.prettyprint())
qaoa_mes = QAOAClient(
provider=provider, backend=provider.get_backend("ibmq_qasm_simulator"), reps=2, alpha=0.75
)
qaoa = MinimumEigenOptimizer(qaoa_mes)
result = qaoa.solve(qubo)
print(result.prettyprint())
from qiskit.transpiler import PassManager
from qiskit.circuit.library.standard_gates.equivalence_library import (
StandardEquivalenceLibrary as std_eqlib,
)
from qiskit.transpiler.passes import (
Collect2qBlocks,
ConsolidateBlocks,
UnrollCustomDefinitions,
BasisTranslator,
Optimize1qGatesDecomposition,
)
from qiskit.transpiler.passes.calibration.builders import RZXCalibrationBuilderNoEcho
from qiskit.transpiler.passes.optimization.echo_rzx_weyl_decomposition import (
EchoRZXWeylDecomposition,
)
from qiskit.test.mock import FakeBelem
backend = FakeBelem()
inst_map = backend.defaults().instruction_schedule_map
channel_map = backend.configuration().qubit_channel_mapping
rzx_basis = ["rzx", "rz", "x", "sx"]
pulse_efficient = PassManager(
[
# Consolidate consecutive two-qubit operations.
Collect2qBlocks(),
ConsolidateBlocks(basis_gates=["rz", "sx", "x", "rxx"]),
# Rewrite circuit in terms of Weyl-decomposed echoed RZX gates.
EchoRZXWeylDecomposition(backend.defaults().instruction_schedule_map),
# Attach scaled CR pulse schedules to the RZX gates.
RZXCalibrationBuilderNoEcho(
instruction_schedule_map=inst_map, qubit_channel_mapping=channel_map
),
# Simplify single-qubit gates.
UnrollCustomDefinitions(std_eqlib, rzx_basis),
BasisTranslator(std_eqlib, rzx_basis),
Optimize1qGatesDecomposition(rzx_basis),
]
)
from qiskit import QuantumCircuit
circ = QuantumCircuit(3)
circ.h([0, 1, 2])
circ.rzx(0.5, 0, 1)
circ.swap(0, 1)
circ.cx(2, 1)
circ.rz(0.4, 1)
circ.cx(2, 1)
circ.rx(1.23, 2)
circ.cx(2, 1)
circ.draw("mpl")
pulse_efficient.run(circ).draw("mpl", fold=False)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
problem = QuadraticProgram("sample")
problem.binary_var("x")
problem.binary_var("y")
problem.maximize(linear={"x": 1, "y": -2})
print(problem.prettyprint())
from qiskit.algorithms import NumPyMinimumEigensolver
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = NumPyMinimumEigensolver()
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = NumPyMinimumEigensolver()
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import MinimumEigenOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
mes = QAOA(optimizer=COBYLA(), quantum_instance=qins)
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
shots = 1000
mes = QAOA(sampler=Sampler(), optimizer=COBYLA())
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms import VQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import MinimumEigenOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
mes = VQE(ansatz=RealAmplitudes(), optimizer=COBYLA(), quantum_instance=qins)
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = SamplingVQE(sampler=Sampler(), ansatz=RealAmplitudes(), optimizer=COBYLA())
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
result = meo.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import VQE
from qiskit.algorithms.optimizers import COBYLA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Estimator
from qiskit_optimization.algorithms import MinimumEigenOptimizer
mes = VQE(estimator=Estimator(), ansatz=RealAmplitudes(), optimizer=COBYLA())
try:
meo = MinimumEigenOptimizer(min_eigen_solver=mes)
except TypeError as ex:
print(ex)
from qiskit import BasicAer
from qiskit.algorithms import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer, SlsqpOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
qaoa = QAOA(optimizer=COBYLA(), quantum_instance=qins)
optimizer = WarmStartQAOAOptimizer(
pre_solver=SlsqpOptimizer(), relax_for_pre_solver=True, qaoa=qaoa, epsilon=0.25
)
result = optimizer.solve(problem)
print(result)
from qiskit.algorithms.minimum_eigensolvers import QAOA
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer, SlsqpOptimizer
qaoa = QAOA(sampler=Sampler(), optimizer=COBYLA())
optimizer = WarmStartQAOAOptimizer(
pre_solver=SlsqpOptimizer(), relax_for_pre_solver=True, qaoa=qaoa, epsilon=0.25
)
result = optimizer.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit_optimization.algorithms import GroverOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
optimizer = GroverOptimizer(num_value_qubits=3, num_iterations=3, quantum_instance=qins)
result = optimizer.solve(problem)
print(result)
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer
optimizer = GroverOptimizer(num_value_qubits=3, num_iterations=3, sampler=Sampler())
result = optimizer.solve(problem)
print(result)
from qiskit import BasicAer
from qiskit.algorithms.optimizers import COBYLA
from qiskit.utils import QuantumInstance
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer
backend = BasicAer.get_backend("qasm_simulator")
shots = 1000
qins = QuantumInstance(backend=backend, shots=shots)
try:
optimizer = GroverOptimizer(
num_value_qubits=3, num_iterations=3, quantum_instance=qins, sampler=Sampler()
)
# raises an error because both quantum_instance and sampler are set.
except ValueError as ex:
print(ex)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.translators import from_docplex_mp
# Make a Docplex model
from docplex.mp.model import Model
mdl = Model("docplex model")
x = mdl.binary_var("x")
y = mdl.integer_var(lb=-1, ub=5, name="y")
mdl.minimize(x + 2 * y)
mdl.add_constraint(x - y == 3)
mdl.add_constraint((x + y) * (x - y) <= 1)
print(mdl.export_as_lp_string())
# load from a Docplex model
mod = from_docplex_mp(mdl)
print(type(mod))
print()
print(mod.prettyprint())
# make an empty problem
mod = QuadraticProgram("my problem")
print(mod.prettyprint())
# Add variables
mod.binary_var(name="x")
mod.integer_var(name="y", lowerbound=-1, upperbound=5)
mod.continuous_var(name="z", lowerbound=-1, upperbound=5)
print(mod.prettyprint())
# Add objective function using dictionaries
mod.minimize(constant=3, linear={"x": 1}, quadratic={("x", "y"): 2, ("z", "z"): -1})
print(mod.prettyprint())
# Add objective function using lists/arrays
mod.minimize(constant=3, linear=[1, 0, 0], quadratic=[[0, 1, 0], [1, 0, 0], [0, 0, -1]])
print(mod.prettyprint())
print("constant:\t\t\t", mod.objective.constant)
print("linear dict:\t\t\t", mod.objective.linear.to_dict())
print("linear array:\t\t\t", mod.objective.linear.to_array())
print("linear array as sparse matrix:\n", mod.objective.linear.coefficients, "\n")
print("quadratic dict w/ index:\t", mod.objective.quadratic.to_dict())
print("quadratic dict w/ name:\t\t", mod.objective.quadratic.to_dict(use_name=True))
print(
"symmetric quadratic dict w/ name:\t",
mod.objective.quadratic.to_dict(use_name=True, symmetric=True),
)
print("quadratic matrix:\n", mod.objective.quadratic.to_array(), "\n")
print("symmetric quadratic matrix:\n", mod.objective.quadratic.to_array(symmetric=True), "\n")
print("quadratic matrix as sparse matrix:\n", mod.objective.quadratic.coefficients)
# Add linear constraints
mod.linear_constraint(linear={"x": 1, "y": 2}, sense="==", rhs=3, name="lin_eq")
mod.linear_constraint(linear={"x": 1, "y": 2}, sense="<=", rhs=3, name="lin_leq")
mod.linear_constraint(linear={"x": 1, "y": 2}, sense=">=", rhs=3, name="lin_geq")
print(mod.prettyprint())
# Add quadratic constraints
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense="==",
rhs=1,
name="quad_eq",
)
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense="<=",
rhs=1,
name="quad_leq",
)
mod.quadratic_constraint(
linear={"x": 1, "y": 1},
quadratic={("x", "x"): 1, ("y", "z"): -1},
sense=">=",
rhs=1,
name="quad_geq",
)
print(mod.prettyprint())
lin_geq = mod.get_linear_constraint("lin_geq")
print("lin_geq:", lin_geq.linear.to_dict(use_name=True), lin_geq.sense, lin_geq.rhs)
quad_geq = mod.get_quadratic_constraint("quad_geq")
print(
"quad_geq:",
quad_geq.linear.to_dict(use_name=True),
quad_geq.quadratic.to_dict(use_name=True),
quad_geq.sense,
lin_geq.rhs,
)
# Remove constraints
mod.remove_linear_constraint("lin_eq")
mod.remove_quadratic_constraint("quad_leq")
print(mod.prettyprint())
sub = mod.substitute_variables(constants={"x": 0}, variables={"y": ("z", -1)})
print(sub.prettyprint())
sub = mod.substitute_variables(constants={"x": -1})
print(sub.status)
from qiskit_optimization import QiskitOptimizationError
try:
sub = mod.substitute_variables(constants={"x": -1}, variables={"y": ("x", 1)})
except QiskitOptimizationError as e:
print("Error: {}".format(e))
mod = QuadraticProgram()
mod.binary_var(name="e")
mod.binary_var(name="f")
mod.continuous_var(name="g")
mod.minimize(linear=[1, 2, 3])
print(mod.export_as_lp_string())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization import QuadraticProgram
qp = QuadraticProgram()
qp.binary_var("x")
qp.binary_var("y")
qp.integer_var(lowerbound=0, upperbound=7, name="z")
qp.maximize(linear={"x": 2, "y": 1, "z": 1})
qp.linear_constraint(linear={"x": 1, "y": 1, "z": 1}, sense="LE", rhs=5.5, name="xyz_leq")
qp.linear_constraint(linear={"x": 1, "y": 1, "z": 1}, sense="GE", rhs=2.5, name="xyz_geq")
print(qp.prettyprint())
from qiskit_optimization.converters import InequalityToEquality
ineq2eq = InequalityToEquality()
qp_eq = ineq2eq.convert(qp)
print(qp_eq.prettyprint())
print(qp_eq.prettyprint())
from qiskit_optimization.converters import IntegerToBinary
int2bin = IntegerToBinary()
qp_eq_bin = int2bin.convert(qp_eq)
print(qp_eq_bin.prettyprint())
print(qp_eq_bin.prettyprint())
from qiskit_optimization.converters import LinearEqualityToPenalty
lineq2penalty = LinearEqualityToPenalty()
qubo = lineq2penalty.convert(qp_eq_bin)
print(qubo.prettyprint())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import (
MinimumEigenOptimizer,
RecursiveMinimumEigenOptimizer,
SolutionSample,
OptimizationResultStatus,
)
from qiskit_optimization import QuadraticProgram
from qiskit.visualization import plot_histogram
from typing import List, Tuple
import numpy as np
# create a QUBO
qubo = QuadraticProgram()
qubo.binary_var("x")
qubo.binary_var("y")
qubo.binary_var("z")
qubo.minimize(linear=[1, -2, 3], quadratic={("x", "y"): 1, ("x", "z"): -1, ("y", "z"): 2})
print(qubo.prettyprint())
op, offset = qubo.to_ising()
print("offset: {}".format(offset))
print("operator:")
print(op)
qp = QuadraticProgram()
qp.from_ising(op, offset, linear=True)
print(qp.prettyprint())
algorithm_globals.random_seed = 10598
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 0.0])
exact_mes = NumPyMinimumEigensolver()
qaoa = MinimumEigenOptimizer(qaoa_mes) # using QAOA
exact = MinimumEigenOptimizer(exact_mes) # using the exact classical numpy minimum eigen solver
exact_result = exact.solve(qubo)
print(exact_result.prettyprint())
qaoa_result = qaoa.solve(qubo)
print(qaoa_result.prettyprint())
print("variable order:", [var.name for var in qaoa_result.variables])
for s in qaoa_result.samples:
print(s)
def get_filtered_samples(
samples: List[SolutionSample],
threshold: float = 0,
allowed_status: Tuple[OptimizationResultStatus] = (OptimizationResultStatus.SUCCESS,),
):
res = []
for s in samples:
if s.status in allowed_status and s.probability > threshold:
res.append(s)
return res
filtered_samples = get_filtered_samples(
qaoa_result.samples, threshold=0.005, allowed_status=(OptimizationResultStatus.SUCCESS,)
)
for s in filtered_samples:
print(s)
fvals = [s.fval for s in qaoa_result.samples]
probabilities = [s.probability for s in qaoa_result.samples]
np.mean(fvals)
np.std(fvals)
samples_for_plot = {
" ".join(f"{qaoa_result.variables[i].name}={int(v)}" for i, v in enumerate(s.x)): s.probability
for s in filtered_samples
}
samples_for_plot
plot_histogram(samples_for_plot)
rqaoa = RecursiveMinimumEigenOptimizer(qaoa, min_num_vars=1, min_num_vars_optimizer=exact)
rqaoa_result = rqaoa.solve(qubo)
print(rqaoa_result.prettyprint())
filtered_samples = get_filtered_samples(
rqaoa_result.samples, threshold=0.005, allowed_status=(OptimizationResultStatus.SUCCESS,)
)
samples_for_plot = {
" ".join(f"{rqaoa_result.variables[i].name}={int(v)}" for i, v in enumerate(s.x)): s.probability
for s in filtered_samples
}
samples_for_plot
plot_histogram(samples_for_plot)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import GroverOptimizer, MinimumEigenOptimizer
from qiskit_optimization.translators import from_docplex_mp
from docplex.mp.model import Model
model = Model()
x0 = model.binary_var(name="x0")
x1 = model.binary_var(name="x1")
x2 = model.binary_var(name="x2")
model.minimize(-x0 + 2 * x1 - 3 * x2 - 2 * x0 * x2 - 1 * x1 * x2)
qp = from_docplex_mp(model)
print(qp.prettyprint())
grover_optimizer = GroverOptimizer(6, num_iterations=10, sampler=Sampler())
results = grover_optimizer.solve(qp)
print(results.prettyprint())
exact_solver = MinimumEigenOptimizer(NumPyMinimumEigensolver())
exact_result = exact_solver.solve(qp)
print(exact_result.prettyprint())
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import matplotlib.pyplot as plt
from docplex.mp.model import Model
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import CobylaOptimizer, MinimumEigenOptimizer
from qiskit_optimization.algorithms.admm_optimizer import ADMMParameters, ADMMOptimizer
from qiskit_optimization.translators import from_docplex_mp
# If CPLEX is installed, you can uncomment this line to import the CplexOptimizer.
# CPLEX can be used in this tutorial to solve the convex continuous problem,
# but also as a reference to solve the QUBO, or even the full problem.
#
# from qiskit.optimization.algorithms import CplexOptimizer
# define COBYLA optimizer to handle convex continuous problems.
cobyla = CobylaOptimizer()
# define QAOA via the minimum eigen optimizer
qaoa = MinimumEigenOptimizer(QAOA(sampler=Sampler(), optimizer=COBYLA()))
# exact QUBO solver as classical benchmark
exact = MinimumEigenOptimizer(NumPyMinimumEigensolver()) # to solve QUBOs
# in case CPLEX is installed it can also be used for the convex problems, the QUBO,
# or as a benchmark for the full problem.
#
# cplex = CplexOptimizer()
# construct model using docplex
mdl = Model("ex6")
v = mdl.binary_var(name="v")
w = mdl.binary_var(name="w")
t = mdl.binary_var(name="t")
u = mdl.continuous_var(name="u")
mdl.minimize(v + w + t + 5 * (u - 2) ** 2)
mdl.add_constraint(v + 2 * w + t + u <= 3, "cons1")
mdl.add_constraint(v + w + t >= 1, "cons2")
mdl.add_constraint(v + w == 1, "cons3")
# load quadratic program from docplex model
qp = from_docplex_mp(mdl)
print(qp.prettyprint())
admm_params = ADMMParameters(
rho_initial=1001, beta=1000, factor_c=900, maxiter=100, three_block=True, tol=1.0e-6
)
# define QUBO optimizer
qubo_optimizer = exact
# qubo_optimizer = cplex # uncomment to use CPLEX instead
# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex # uncomment to use CPLEX instead
# initialize ADMM with classical QUBO and convex optimizer
admm = ADMMOptimizer(
params=admm_params, qubo_optimizer=qubo_optimizer, continuous_optimizer=convex_optimizer
)
# run ADMM to solve problem
result = admm.solve(qp)
print(result.prettyprint())
plt.plot(result.state.residuals)
plt.xlabel("Iterations")
plt.ylabel("Residuals")
plt.show()
# define QUBO optimizer
qubo_optimizer = qaoa
# define classical optimizer
convex_optimizer = cobyla
# convex_optimizer = cplex # uncomment to use CPLEX instead
# initialize ADMM with quantum QUBO optimizer and classical convex optimizer
admm_q = ADMMOptimizer(
params=admm_params, qubo_optimizer=qubo_optimizer, continuous_optimizer=convex_optimizer
)
# run ADMM to solve problem
result_q = admm_q.solve(qp)
print(result.prettyprint())
plt.clf()
plt.plot(result_q.state.residuals)
plt.xlabel("Iterations")
plt.ylabel("Residuals")
plt.show()
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
# useful additional packages
import matplotlib.pyplot as plt
import numpy as np
import networkx as nx
from qiskit_aer import Aer
from qiskit.tools.visualization import plot_histogram
from qiskit.circuit.library import TwoLocal
from qiskit_optimization.applications import Maxcut, Tsp
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import SPSA
from qiskit.utils import algorithm_globals
from qiskit.primitives import Sampler
from qiskit_optimization.algorithms import MinimumEigenOptimizer
# Generating a graph of 4 nodes
n = 4 # Number of nodes in graph
G = nx.Graph()
G.add_nodes_from(np.arange(0, n, 1))
elist = [(0, 1, 1.0), (0, 2, 1.0), (0, 3, 1.0), (1, 2, 1.0), (2, 3, 1.0)]
# tuple is (i,j,weight) where (i,j) is the edge
G.add_weighted_edges_from(elist)
colors = ["r" for node in G.nodes()]
pos = nx.spring_layout(G)
def draw_graph(G, colors, pos):
default_axes = plt.axes(frameon=True)
nx.draw_networkx(G, node_color=colors, node_size=600, alpha=0.8, ax=default_axes, pos=pos)
edge_labels = nx.get_edge_attributes(G, "weight")
nx.draw_networkx_edge_labels(G, pos=pos, edge_labels=edge_labels)
draw_graph(G, colors, pos)
# Computing the weight matrix from the random graph
w = np.zeros([n, n])
for i in range(n):
for j in range(n):
temp = G.get_edge_data(i, j, default=0)
if temp != 0:
w[i, j] = temp["weight"]
print(w)
best_cost_brute = 0
for b in range(2**n):
x = [int(t) for t in reversed(list(bin(b)[2:].zfill(n)))]
cost = 0
for i in range(n):
for j in range(n):
cost = cost + w[i, j] * x[i] * (1 - x[j])
if best_cost_brute < cost:
best_cost_brute = cost
xbest_brute = x
print("case = " + str(x) + " cost = " + str(cost))
colors = ["r" if xbest_brute[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
print("\nBest solution = " + str(xbest_brute) + " cost = " + str(best_cost_brute))
max_cut = Maxcut(w)
qp = max_cut.to_quadratic_program()
print(qp.prettyprint())
qubitOp, offset = qp.to_ising()
print("Offset:", offset)
print("Ising Hamiltonian:")
print(str(qubitOp))
# solving Quadratic Program using exact classical eigensolver
exact = MinimumEigenOptimizer(NumPyMinimumEigensolver())
result = exact.solve(qp)
print(result.prettyprint())
# Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector
ee = NumPyMinimumEigensolver()
result = ee.compute_minimum_eigenvalue(qubitOp)
x = max_cut.sample_most_likely(result.eigenstate)
print("energy:", result.eigenvalue.real)
print("max-cut objective:", result.eigenvalue.real + offset)
print("solution:", x)
print("solution objective:", qp.objective.evaluate(x))
colors = ["r" if x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
# construct SamplingVQE
optimizer = SPSA(maxiter=300)
ry = TwoLocal(qubitOp.num_qubits, "ry", "cz", reps=5, entanglement="linear")
vqe = SamplingVQE(sampler=Sampler(), ansatz=ry, optimizer=optimizer)
# run SamplingVQE
result = vqe.compute_minimum_eigenvalue(qubitOp)
# print results
x = max_cut.sample_most_likely(result.eigenstate)
print("energy:", result.eigenvalue.real)
print("time:", result.optimizer_time)
print("max-cut objective:", result.eigenvalue.real + offset)
print("solution:", x)
print("solution objective:", qp.objective.evaluate(x))
# plot results
colors = ["r" if x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
# create minimum eigen optimizer based on SamplingVQE
vqe_optimizer = MinimumEigenOptimizer(vqe)
# solve quadratic program
result = vqe_optimizer.solve(qp)
print(result.prettyprint())
colors = ["r" if result.x[i] == 0 else "c" for i in range(n)]
draw_graph(G, colors, pos)
# Generating a graph of 3 nodes
n = 3
num_qubits = n**2
tsp = Tsp.create_random_instance(n, seed=123)
adj_matrix = nx.to_numpy_array(tsp.graph)
print("distance\n", adj_matrix)
colors = ["r" for node in tsp.graph.nodes]
pos = [tsp.graph.nodes[node]["pos"] for node in tsp.graph.nodes]
draw_graph(tsp.graph, colors, pos)
from itertools import permutations
def brute_force_tsp(w, N):
a = list(permutations(range(1, N)))
last_best_distance = 1e10
for i in a:
distance = 0
pre_j = 0
for j in i:
distance = distance + w[j, pre_j]
pre_j = j
distance = distance + w[pre_j, 0]
order = (0,) + i
if distance < last_best_distance:
best_order = order
last_best_distance = distance
print("order = " + str(order) + " Distance = " + str(distance))
return last_best_distance, best_order
best_distance, best_order = brute_force_tsp(adj_matrix, n)
print(
"Best order from brute force = "
+ str(best_order)
+ " with total distance = "
+ str(best_distance)
)
def draw_tsp_solution(G, order, colors, pos):
G2 = nx.DiGraph()
G2.add_nodes_from(G)
n = len(order)
for i in range(n):
j = (i + 1) % n
G2.add_edge(order[i], order[j], weight=G[order[i]][order[j]]["weight"])
default_axes = plt.axes(frameon=True)
nx.draw_networkx(
G2, node_color=colors, edge_color="b", node_size=600, alpha=0.8, ax=default_axes, pos=pos
)
edge_labels = nx.get_edge_attributes(G2, "weight")
nx.draw_networkx_edge_labels(G2, pos, font_color="b", edge_labels=edge_labels)
draw_tsp_solution(tsp.graph, best_order, colors, pos)
qp = tsp.to_quadratic_program()
print(qp.prettyprint())
from qiskit_optimization.converters import QuadraticProgramToQubo
qp2qubo = QuadraticProgramToQubo()
qubo = qp2qubo.convert(qp)
qubitOp, offset = qubo.to_ising()
print("Offset:", offset)
print("Ising Hamiltonian:")
print(str(qubitOp))
result = exact.solve(qubo)
print(result.prettyprint())
# Making the Hamiltonian in its full form and getting the lowest eigenvalue and eigenvector
ee = NumPyMinimumEigensolver()
result = ee.compute_minimum_eigenvalue(qubitOp)
print("energy:", result.eigenvalue.real)
print("tsp objective:", result.eigenvalue.real + offset)
x = tsp.sample_most_likely(result.eigenstate)
print("feasible:", qubo.is_feasible(x))
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
optimizer = SPSA(maxiter=300)
ry = TwoLocal(qubitOp.num_qubits, "ry", "cz", reps=5, entanglement="linear")
vqe = SamplingVQE(sampler=Sampler(), ansatz=ry, optimizer=optimizer)
result = vqe.compute_minimum_eigenvalue(qubitOp)
print("energy:", result.eigenvalue.real)
print("time:", result.optimizer_time)
x = tsp.sample_most_likely(result.eigenstate)
print("feasible:", qubo.is_feasible(x))
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
algorithm_globals.random_seed = 123
seed = 10598
# create minimum eigen optimizer based on SamplingVQE
vqe_optimizer = MinimumEigenOptimizer(vqe)
# solve quadratic program
result = vqe_optimizer.solve(qp)
print(result.prettyprint())
z = tsp.interpret(x)
print("solution:", z)
print("solution objective:", tsp.tsp_value(z, adj_matrix))
draw_tsp_solution(tsp.graph, z, colors, pos)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import matplotlib.pyplot as plt
try:
import cplex
from cplex.exceptions import CplexError
except:
print("Warning: Cplex not found.")
import math
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import SamplingVQE
from qiskit.algorithms.optimizers import SPSA
from qiskit.circuit.library import RealAmplitudes
from qiskit.primitives import Sampler
# Initialize the problem by defining the parameters
n = 3 # number of nodes + depot (n+1)
K = 2 # number of vehicles
# Get the data
class Initializer:
def __init__(self, n):
self.n = n
def generate_instance(self):
n = self.n
# np.random.seed(33)
np.random.seed(1543)
xc = (np.random.rand(n) - 0.5) * 10
yc = (np.random.rand(n) - 0.5) * 10
instance = np.zeros([n, n])
for ii in range(0, n):
for jj in range(ii + 1, n):
instance[ii, jj] = (xc[ii] - xc[jj]) ** 2 + (yc[ii] - yc[jj]) ** 2
instance[jj, ii] = instance[ii, jj]
return xc, yc, instance
# Initialize the problem by randomly generating the instance
initializer = Initializer(n)
xc, yc, instance = initializer.generate_instance()
class ClassicalOptimizer:
def __init__(self, instance, n, K):
self.instance = instance
self.n = n # number of nodes
self.K = K # number of vehicles
def compute_allowed_combinations(self):
f = math.factorial
return f(self.n) / f(self.K) / f(self.n - self.K)
def cplex_solution(self):
# refactoring
instance = self.instance
n = self.n
K = self.K
my_obj = list(instance.reshape(1, n**2)[0]) + [0.0 for x in range(0, n - 1)]
my_ub = [1 for x in range(0, n**2 + n - 1)]
my_lb = [0 for x in range(0, n**2)] + [0.1 for x in range(0, n - 1)]
my_ctype = "".join(["I" for x in range(0, n**2)]) + "".join(
["C" for x in range(0, n - 1)]
)
my_rhs = (
2 * ([K] + [1 for x in range(0, n - 1)])
+ [1 - 0.1 for x in range(0, (n - 1) ** 2 - (n - 1))]
+ [0 for x in range(0, n)]
)
my_sense = (
"".join(["E" for x in range(0, 2 * n)])
+ "".join(["L" for x in range(0, (n - 1) ** 2 - (n - 1))])
+ "".join(["E" for x in range(0, n)])
)
try:
my_prob = cplex.Cplex()
self.populatebyrow(my_prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs)
my_prob.solve()
except CplexError as exc:
print(exc)
return
x = my_prob.solution.get_values()
x = np.array(x)
cost = my_prob.solution.get_objective_value()
return x, cost
def populatebyrow(self, prob, my_obj, my_ub, my_lb, my_ctype, my_sense, my_rhs):
n = self.n
prob.objective.set_sense(prob.objective.sense.minimize)
prob.variables.add(obj=my_obj, lb=my_lb, ub=my_ub, types=my_ctype)
prob.set_log_stream(None)
prob.set_error_stream(None)
prob.set_warning_stream(None)
prob.set_results_stream(None)
rows = []
for ii in range(0, n):
col = [x for x in range(0 + n * ii, n + n * ii)]
coef = [1 for x in range(0, n)]
rows.append([col, coef])
for ii in range(0, n):
col = [x for x in range(0 + ii, n**2, n)]
coef = [1 for x in range(0, n)]
rows.append([col, coef])
# Sub-tour elimination constraints:
for ii in range(0, n):
for jj in range(0, n):
if (ii != jj) and (ii * jj > 0):
col = [ii + (jj * n), n**2 + ii - 1, n**2 + jj - 1]
coef = [1, 1, -1]
rows.append([col, coef])
for ii in range(0, n):
col = [(ii) * (n + 1)]
coef = [1]
rows.append([col, coef])
prob.linear_constraints.add(lin_expr=rows, senses=my_sense, rhs=my_rhs)
# Instantiate the classical optimizer class
classical_optimizer = ClassicalOptimizer(instance, n, K)
# Print number of feasible solutions
print("Number of feasible solutions = " + str(classical_optimizer.compute_allowed_combinations()))
# Solve the problem in a classical fashion via CPLEX
x = None
z = None
try:
x, classical_cost = classical_optimizer.cplex_solution()
# Put the solution in the z variable
z = [x[ii] for ii in range(n**2) if ii // n != ii % n]
# Print the solution
print(z)
except:
print("CPLEX may be missing.")
# Visualize the solution
def visualize_solution(xc, yc, x, C, n, K, title_str):
plt.figure()
plt.scatter(xc, yc, s=200)
for i in range(len(xc)):
plt.annotate(i, (xc[i] + 0.15, yc[i]), size=16, color="r")
plt.plot(xc[0], yc[0], "r*", ms=20)
plt.grid()
for ii in range(0, n**2):
if x[ii] > 0:
ix = ii // n
iy = ii % n
plt.arrow(
xc[ix],
yc[ix],
xc[iy] - xc[ix],
yc[iy] - yc[ix],
length_includes_head=True,
head_width=0.25,
)
plt.title(title_str + " cost = " + str(int(C * 100) / 100.0))
plt.show()
if x is not None:
visualize_solution(xc, yc, x, classical_cost, n, K, "Classical")
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.algorithms import MinimumEigenOptimizer
class QuantumOptimizer:
def __init__(self, instance, n, K):
self.instance = instance
self.n = n
self.K = K
def binary_representation(self, x_sol=0):
instance = self.instance
n = self.n
K = self.K
A = np.max(instance) * 100 # A parameter of cost function
# Determine the weights w
instance_vec = instance.reshape(n**2)
w_list = [instance_vec[x] for x in range(n**2) if instance_vec[x] > 0]
w = np.zeros(n * (n - 1))
for ii in range(len(w_list)):
w[ii] = w_list[ii]
# Some variables I will use
Id_n = np.eye(n)
Im_n_1 = np.ones([n - 1, n - 1])
Iv_n_1 = np.ones(n)
Iv_n_1[0] = 0
Iv_n = np.ones(n - 1)
neg_Iv_n_1 = np.ones(n) - Iv_n_1
v = np.zeros([n, n * (n - 1)])
for ii in range(n):
count = ii - 1
for jj in range(n * (n - 1)):
if jj // (n - 1) == ii:
count = ii
if jj // (n - 1) != ii and jj % (n - 1) == count:
v[ii][jj] = 1.0
vn = np.sum(v[1:], axis=0)
# Q defines the interactions between variables
Q = A * (np.kron(Id_n, Im_n_1) + np.dot(v.T, v))
# g defines the contribution from the individual variables
g = (
w
- 2 * A * (np.kron(Iv_n_1, Iv_n) + vn.T)
- 2 * A * K * (np.kron(neg_Iv_n_1, Iv_n) + v[0].T)
)
# c is the constant offset
c = 2 * A * (n - 1) + 2 * A * (K**2)
try:
max(x_sol)
# Evaluates the cost distance from a binary representation of a path
fun = (
lambda x: np.dot(np.around(x), np.dot(Q, np.around(x)))
+ np.dot(g, np.around(x))
+ c
)
cost = fun(x_sol)
except:
cost = 0
return Q, g, c, cost
def construct_problem(self, Q, g, c) -> QuadraticProgram:
qp = QuadraticProgram()
for i in range(n * (n - 1)):
qp.binary_var(str(i))
qp.objective.quadratic = Q
qp.objective.linear = g
qp.objective.constant = c
return qp
def solve_problem(self, qp):
algorithm_globals.random_seed = 10598
vqe = SamplingVQE(sampler=Sampler(), optimizer=SPSA(), ansatz=RealAmplitudes())
optimizer = MinimumEigenOptimizer(min_eigen_solver=vqe)
result = optimizer.solve(qp)
# compute cost of the obtained result
_, _, _, level = self.binary_representation(x_sol=result.x)
return result.x, level
# Instantiate the quantum optimizer class with parameters:
quantum_optimizer = QuantumOptimizer(instance, n, K)
# Check if the binary representation is correct
try:
if z is not None:
Q, g, c, binary_cost = quantum_optimizer.binary_representation(x_sol=z)
print("Binary cost:", binary_cost, "classical cost:", classical_cost)
if np.abs(binary_cost - classical_cost) < 0.01:
print("Binary formulation is correct")
else:
print("Error in the binary formulation")
else:
print("Could not verify the correctness, due to CPLEX solution being unavailable.")
Q, g, c, binary_cost = quantum_optimizer.binary_representation()
print("Binary cost:", binary_cost)
except NameError as e:
print("Warning: Please run the cells above first.")
print(e)
qp = quantum_optimizer.construct_problem(Q, g, c)
quantum_solution, quantum_cost = quantum_optimizer.solve_problem(qp)
print(quantum_solution, quantum_cost)
# Put the solution in a way that is compatible with the classical variables
x_quantum = np.zeros(n**2)
kk = 0
for ii in range(n**2):
if ii // n != ii % n:
x_quantum[ii] = quantum_solution[kk]
kk += 1
# visualize the solution
visualize_solution(xc, yc, x_quantum, quantum_cost, n, K, "Quantum")
# and visualize the classical for comparison
if x is not None:
visualize_solution(xc, yc, x, classical_cost, n, K, "Classical")
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit.circuit.library import RealAmplitudes
from qiskit.algorithms.optimizers import COBYLA
from qiskit.algorithms.minimum_eigensolvers import NumPyMinimumEigensolver, SamplingVQE
from qiskit.primitives import Sampler
from qiskit_optimization.converters import LinearEqualityToPenalty
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit_optimization.translators import from_docplex_mp
from qiskit.utils import algorithm_globals
import numpy as np
import matplotlib.pyplot as plt
from docplex.mp.model import Model
algorithm_globals.random_seed = 123456
# prepare problem instance
n = 6 # number of assets
q = 0.5 # risk factor
budget = n // 2 # budget
penalty = 2 * n # scaling of penalty term
# instance from [1]
mu = np.array([0.7313, 0.9893, 0.2725, 0.8750, 0.7667, 0.3622])
sigma = np.array(
[
[0.7312, -0.6233, 0.4689, -0.5452, -0.0082, -0.3809],
[-0.6233, 2.4732, -0.7538, 2.4659, -0.0733, 0.8945],
[0.4689, -0.7538, 1.1543, -1.4095, 0.0007, -0.4301],
[-0.5452, 2.4659, -1.4095, 3.5067, 0.2012, 1.0922],
[-0.0082, -0.0733, 0.0007, 0.2012, 0.6231, 0.1509],
[-0.3809, 0.8945, -0.4301, 1.0922, 0.1509, 0.8992],
]
)
# or create random instance
# mu, sigma = portfolio.random_model(n, seed=123) # expected returns and covariance matrix
# create docplex model
mdl = Model("portfolio_optimization")
x = mdl.binary_var_list(range(n), name="x")
objective = mdl.sum([mu[i] * x[i] for i in range(n)])
objective -= q * mdl.sum([sigma[i, j] * x[i] * x[j] for i in range(n) for j in range(n)])
mdl.maximize(objective)
mdl.add_constraint(mdl.sum(x[i] for i in range(n)) == budget)
# case to
qp = from_docplex_mp(mdl)
# solve classically as reference
opt_result = MinimumEigenOptimizer(NumPyMinimumEigensolver()).solve(qp)
print(opt_result.prettyprint())
# we convert the problem to an unconstrained problem for further analysis,
# otherwise this would not be necessary as the MinimumEigenSolver would do this
# translation automatically
linear2penalty = LinearEqualityToPenalty(penalty=penalty)
qp = linear2penalty.convert(qp)
_, offset = qp.to_ising()
# set classical optimizer
maxiter = 100
optimizer = COBYLA(maxiter=maxiter)
# set variational ansatz
ansatz = RealAmplitudes(n, reps=1)
m = ansatz.num_parameters
# set sampler
sampler = Sampler()
# run variational optimization for different values of alpha
alphas = [1.0, 0.50, 0.25] # confidence levels to be evaluated
# dictionaries to store optimization progress and results
objectives = {alpha: [] for alpha in alphas} # set of tested objective functions w.r.t. alpha
results = {} # results of minimum eigensolver w.r.t alpha
# callback to store intermediate results
def callback(i, params, obj, stddev, alpha):
# we translate the objective from the internal Ising representation
# to the original optimization problem
objectives[alpha].append(np.real_if_close(-(obj + offset)))
# loop over all given alpha values
for alpha in alphas:
# initialize SamplingVQE using CVaR
vqe = SamplingVQE(
sampler=sampler,
ansatz=ansatz,
optimizer=optimizer,
aggregation=alpha,
callback=lambda i, params, obj, stddev: callback(i, params, obj, stddev, alpha),
)
# initialize optimization algorithm based on CVaR-SamplingVQE
opt_alg = MinimumEigenOptimizer(vqe)
# solve problem
results[alpha] = opt_alg.solve(qp)
# print results
print("alpha = {}:".format(alpha))
print(results[alpha].prettyprint())
print()
# plot resulting history of objective values
plt.figure(figsize=(10, 5))
plt.plot([0, maxiter], [opt_result.fval, opt_result.fval], "r--", linewidth=2, label="optimum")
for alpha in alphas:
plt.plot(objectives[alpha], label="alpha = %.2f" % alpha, linewidth=2)
plt.legend(loc="lower right", fontsize=14)
plt.xlim(0, maxiter)
plt.xticks(fontsize=14)
plt.xlabel("iterations", fontsize=14)
plt.yticks(fontsize=14)
plt.ylabel("objective value", fontsize=14)
plt.show()
# evaluate and sort all objective values
objective_values = np.zeros(2**n)
for i in range(2**n):
x_bin = ("{0:0%sb}" % n).format(i)
x = [0 if x_ == "0" else 1 for x_ in reversed(x_bin)]
objective_values[i] = qp.objective.evaluate(x)
ind = np.argsort(objective_values)
# evaluate final optimal probability for each alpha
for alpha in alphas:
probabilities = np.fromiter(
results[alpha].min_eigen_solver_result.eigenstate.binary_probabilities().values(),
dtype=float,
)
print("optimal probability (alpha = %.2f): %.4f" % (alpha, probabilities[ind][-1:]))
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
from qiskit_optimization.algorithms import MinimumEigenOptimizer
from qiskit.utils import algorithm_globals
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit_optimization.applications.vertex_cover import VertexCover
import networkx as nx
seed = 123
algorithm_globals.random_seed = seed
graph = nx.random_regular_graph(d=3, n=6, seed=seed)
pos = nx.spring_layout(graph, seed=seed)
prob = VertexCover(graph)
prob.draw(pos=pos)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# Numpy Eigensolver
meo = MinimumEigenOptimizer(min_eigen_solver=NumPyMinimumEigensolver())
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
prob.draw(result, pos=pos)
# QAOA
meo = MinimumEigenOptimizer(min_eigen_solver=QAOA(reps=1, sampler=Sampler(), optimizer=COBYLA()))
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
print("\ntime:", result.min_eigen_solver_result.optimizer_time)
prob.draw(result, pos=pos)
from qiskit_optimization.applications import Knapsack
prob = Knapsack(values=[3, 4, 5, 6, 7], weights=[2, 3, 4, 5, 6], max_weight=10)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# Numpy Eigensolver
meo = MinimumEigenOptimizer(min_eigen_solver=NumPyMinimumEigensolver())
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
# QAOA
meo = MinimumEigenOptimizer(min_eigen_solver=QAOA(reps=1, sampler=Sampler(), optimizer=COBYLA()))
result = meo.solve(qp)
print(result.prettyprint())
print("\nsolution:", prob.interpret(result))
print("\ntime:", result.min_eigen_solver_result.optimizer_time)
from qiskit_optimization.converters import QuadraticProgramToQubo
# the same knapsack problem instance as in the previous section
prob = Knapsack(values=[3, 4, 5, 6, 7], weights=[2, 3, 4, 5, 6], max_weight=10)
qp = prob.to_quadratic_program()
print(qp.prettyprint())
# intermediate QUBO form of the optimization problem
conv = QuadraticProgramToQubo()
qubo = conv.convert(qp)
print(qubo.prettyprint())
# qubit Hamiltonian and offset
op, offset = qubo.to_ising()
print(f"num qubits: {op.num_qubits}, offset: {offset}\n")
print(op)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
https://github.com/qiskit-community/qiskit-translations-staging
|
qiskit-community
|
import numpy as np
import copy
# Problem modelling imports
from docplex.mp.model import Model
# Qiskit imports
from qiskit.algorithms.minimum_eigensolvers import QAOA, NumPyMinimumEigensolver
from qiskit.algorithms.optimizers import COBYLA
from qiskit.primitives import Sampler
from qiskit.utils.algorithm_globals import algorithm_globals
from qiskit_optimization.algorithms import MinimumEigenOptimizer, CplexOptimizer
from qiskit_optimization import QuadraticProgram
from qiskit_optimization.problems.variable import VarType
from qiskit_optimization.converters.quadratic_program_to_qubo import QuadraticProgramToQubo
from qiskit_optimization.translators import from_docplex_mp
def create_problem(mu: np.array, sigma: np.array, total: int = 3) -> QuadraticProgram:
"""Solve the quadratic program using docplex."""
mdl = Model()
x = [mdl.binary_var("x%s" % i) for i in range(len(sigma))]
objective = mdl.sum([mu[i] * x[i] for i in range(len(mu))])
objective -= 2 * mdl.sum(
[sigma[i, j] * x[i] * x[j] for i in range(len(mu)) for j in range(len(mu))]
)
mdl.maximize(objective)
cost = mdl.sum(x)
mdl.add_constraint(cost == total)
qp = from_docplex_mp(mdl)
return qp
def relax_problem(problem) -> QuadraticProgram:
"""Change all variables to continuous."""
relaxed_problem = copy.deepcopy(problem)
for variable in relaxed_problem.variables:
variable.vartype = VarType.CONTINUOUS
return relaxed_problem
mu = np.array([3.418, 2.0913, 6.2415, 4.4436, 10.892, 3.4051])
sigma = np.array(
[
[1.07978412, 0.00768914, 0.11227606, -0.06842969, -0.01016793, -0.00839765],
[0.00768914, 0.10922887, -0.03043424, -0.0020045, 0.00670929, 0.0147937],
[0.11227606, -0.03043424, 0.985353, 0.02307313, -0.05249785, 0.00904119],
[-0.06842969, -0.0020045, 0.02307313, 0.6043817, 0.03740115, -0.00945322],
[-0.01016793, 0.00670929, -0.05249785, 0.03740115, 0.79839634, 0.07616951],
[-0.00839765, 0.0147937, 0.00904119, -0.00945322, 0.07616951, 1.08464544],
]
)
qubo = create_problem(mu, sigma)
print(qubo.prettyprint())
result = CplexOptimizer().solve(qubo)
print(result.prettyprint())
qp = relax_problem(QuadraticProgramToQubo().convert(qubo))
print(qp.prettyprint())
sol = CplexOptimizer().solve(qp)
print(sol.prettyprint())
c_stars = sol.samples[0].x
print(c_stars)
algorithm_globals.random_seed = 12345
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 1.0])
exact_mes = NumPyMinimumEigensolver()
qaoa = MinimumEigenOptimizer(qaoa_mes)
qaoa_result = qaoa.solve(qubo)
print(qaoa_result.prettyprint())
from qiskit import QuantumCircuit
thetas = [2 * np.arcsin(np.sqrt(c_star)) for c_star in c_stars]
init_qc = QuantumCircuit(len(sigma))
for idx, theta in enumerate(thetas):
init_qc.ry(theta, idx)
init_qc.draw(output="mpl")
from qiskit.circuit import Parameter
beta = Parameter("β")
ws_mixer = QuantumCircuit(len(sigma))
for idx, theta in enumerate(thetas):
ws_mixer.ry(-theta, idx)
ws_mixer.rz(-2 * beta, idx)
ws_mixer.ry(theta, idx)
ws_mixer.draw(output="mpl")
ws_qaoa_mes = QAOA(
sampler=Sampler(),
optimizer=COBYLA(),
initial_state=init_qc,
mixer=ws_mixer,
initial_point=[0.0, 1.0],
)
ws_qaoa = MinimumEigenOptimizer(ws_qaoa_mes)
ws_qaoa_result = ws_qaoa.solve(qubo)
print(ws_qaoa_result.prettyprint())
def format_qaoa_samples(samples, max_len: int = 10):
qaoa_res = []
for s in samples:
if sum(s.x) == 3:
qaoa_res.append(("".join([str(int(_)) for _ in s.x]), s.fval, s.probability))
res = sorted(qaoa_res, key=lambda x: -x[1])[0:max_len]
return [(_[0] + f": value: {_[1]:.3f}, probability: {1e2*_[2]:.1f}%") for _ in res]
format_qaoa_samples(qaoa_result.samples)
format_qaoa_samples(ws_qaoa_result.samples)
from qiskit_optimization.algorithms import WarmStartQAOAOptimizer
qaoa_mes = QAOA(sampler=Sampler(), optimizer=COBYLA(), initial_point=[0.0, 1.0])
ws_qaoa = WarmStartQAOAOptimizer(
pre_solver=CplexOptimizer(), relax_for_pre_solver=True, qaoa=qaoa_mes, epsilon=0.0
)
ws_result = ws_qaoa.solve(qubo)
print(ws_result.prettyprint())
format_qaoa_samples(ws_result.samples)
import qiskit.tools.jupyter
%qiskit_version_table
%qiskit_copyright
|
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