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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_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_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
|
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