def setUp(self):
self.n_qubits = 5
self.constant = 1.7
self.chemical_potential = 2.
# Obtain random Hermitian and antisymmetric matrices
self.hermitian_mat = random_hermitian_matrix(self.n_qubits)
self.antisymmetric_mat = random_antisymmetric_matrix(self.n_qubits)
self.combined_hermitian = (
self.hermitian_mat -
self.chemical_potential * numpy.eye(self.n_qubits))
# Initialize a particle-number-conserving Hamiltonian
self.quad_ham_pc = QuadraticHamiltonian(
self.constant, self.hermitian_mat)
# Initialize a non-particle-number-conserving Hamiltonian
self.quad_ham_npc = QuadraticHamiltonian(
self.constant, self.hermitian_mat, self.antisymmetric_mat,
self.chemical_potential)
# Initialize the sparse operators and get their ground energies
self.quad_ham_pc_sparse = get_sparse_operator(self.quad_ham_pc)
self.quad_ham_npc_sparse = get_sparse_operator(self.quad_ham_npc)
self.pc_ground_energy, self.pc_ground_state = get_ground_state(
self.quad_ham_pc_sparse)
self.npc_ground_energy, self.npc_ground_state = get_ground_state(
self.quad_ham_npc_sparse)
def test_hf_state_energy_close_to_ground_energy_at_high_density(self):
grid_length = 8
dimension = 1
spinless = True
n_particles = grid_length**dimension // 2
# High density -> small length_scale.
length_scale = 0.25
grid = Grid(dimension, grid_length, length_scale)
hamiltonian = jellium_model(grid, spinless)
hamiltonian_sparse = get_sparse_operator(hamiltonian)
hf_state = hartree_fock_state_jellium(grid,
n_particles,
spinless,
plane_wave=True)
restricted_hamiltonian = jw_number_restrict_operator(
hamiltonian_sparse, n_particles)
E_g = get_ground_state(restricted_hamiltonian)[0]
E_HF_plane_wave = expectation(hamiltonian_sparse, hf_state)
self.assertAlmostEqual(E_g, E_HF_plane_wave, places=5)
def test_ground_state_particle_nonconserving(self):
"""Test getting the ground state preparation circuit for a Hamiltonian
that does not conserve particle number."""
for n_qubits in self.n_qubits_range:
# Initialize a particle-number-conserving Hamiltonian
quadratic_hamiltonian = random_quadratic_hamiltonian(
n_qubits, False, True)
# Compute the true ground state
sparse_operator = get_sparse_operator(quadratic_hamiltonian)
ground_energy, _ = get_ground_state(sparse_operator)
# Obtain the circuit
circuit_description, start_orbitals = (
gaussian_state_preparation_circuit(quadratic_hamiltonian))
# Initialize the starting state
state = jw_configuration_state(start_orbitals, n_qubits)
# Apply the circuit
particle_hole_transformation = (
jw_sparse_particle_hole_transformation_last_mode(n_qubits))
for parallel_ops in circuit_description:
for op in parallel_ops:
if op == 'pht':
state = particle_hole_transformation.dot(state)
else:
i, j, theta, phi = op
state = jw_sparse_givens_rotation(
i, j, theta, phi, n_qubits).dot(state)
# Check that the state obtained using the circuit is a ground state
difference = sparse_operator * state - ground_energy * state
discrepancy = numpy.amax(numpy.abs(difference))
self.assertAlmostEqual(discrepancy, 0)
def test_orbital_energies(self):
"""Test getting the orbital energies."""
# Test the particle-number-conserving case
orbital_energies, constant = self.quad_ham_pc.orbital_energies()
# Test the ground energy
energy = numpy.sum(
orbital_energies[orbital_energies < -EQ_TOLERANCE]) + constant
quad_ham_pc_sparse = get_sparse_operator(self.quad_ham_pc)
ground_energy, ground_state = get_ground_state(quad_ham_pc_sparse)
self.assertAlmostEqual(energy, ground_energy)
# Test the non-particle-number-conserving case
orbital_energies, constant = self.quad_ham_npc.orbital_energies()
# Test the ground energy
energy = constant
quad_ham_npc_sparse = get_sparse_operator(self.quad_ham_npc)
ground_energy, ground_state = get_ground_state(quad_ham_npc_sparse)
self.assertAlmostEqual(energy, ground_energy)
def test_apply_constraints(self):
# Get norm of original operator.
original_norm = 0.
for term, coefficient in self.fermion_hamiltonian.terms.items():
if term != ():
original_norm += abs(coefficient)
# Get modified operator.
modified_operator = apply_constraints(self.fermion_hamiltonian,
self.n_fermions)
modified_operator.compress()
# Get norm of modified operator.
modified_norm = 0.
for term, coefficient in modified_operator.terms.items():
if term != ():
modified_norm += abs(coefficient)
self.assertTrue(modified_norm < original_norm)
# Map both to sparse matrix under Jordan-Wigner.
sparse_original = get_sparse_operator(self.fermion_hamiltonian)
sparse_modified = get_sparse_operator(modified_operator)
# Check spectra.
sparse_original = jw_number_restrict_operator(sparse_original,
self.n_fermions)
sparse_modified = jw_number_restrict_operator(sparse_modified,
self.n_fermions)
original_spectrum = sparse_eigenspectrum(sparse_original)
modified_spectrum = sparse_eigenspectrum(sparse_modified)
spectral_deviation = numpy.amax(
numpy.absolute(original_spectrum - modified_spectrum))
self.assertAlmostEqual(spectral_deviation, 0.)
# Check expectation value.
energy, wavefunction = get_ground_state(sparse_original)
modified_energy = expectation(sparse_modified, wavefunction)
self.assertAlmostEqual(modified_energy, energy)
# Test consistency with cvxopt.
scipy_operator = apply_constraints(self.fermion_hamiltonian,
self.n_fermions,
use_scipy=False)
# Get norm.
scipy_norm = 0.
for term, coefficient in scipy_operator.terms.items():
if term != ():
scipy_norm += abs(coefficient)
self.assertAlmostEqual(scipy_norm, modified_norm)
def test_constraint_matrix(self):
# Randomly project operator with constraints.
numpy.random.seed(8)
constraints = constraint_matrix(self.n_orbitals, self.n_fermions)
n_constraints, n_terms = constraints.shape
self.assertEqual(1 + self.n_orbitals**2 + self.n_orbitals**4, n_terms)
random_weights = numpy.random.randn(n_constraints)
vectorized_operator = operator_to_vector(self.fermion_hamiltonian)
modification_vector = constraints.transpose() * random_weights
new_operator_vector = vectorized_operator + modification_vector
modified_operator = vector_to_operator(new_operator_vector,
self.n_orbitals)
# Map both to sparse matrix under Jordan-Wigner.
sparse_original = get_sparse_operator(self.fermion_hamiltonian)
sparse_modified = get_sparse_operator(modified_operator)
# Check expectation value.
energy, wavefunction = get_ground_state(sparse_original)
modified_energy = expectation(sparse_modified, wavefunction)
self.assertAlmostEqual(modified_energy, energy)
def energy_levels(separation):
g = [('H', (0., 0., 0.)), ('H', (0., 0., separation))]
d = str(separation)
m = MolecularData(g,
basis,
multiplicity,
description=d,
data_directory=data_directory)
run_psi4(m, run_fci=True, delete_output=True)
_, s = get_ground_state(
get_sparse_operator(
normal_ordered(
get_fermion_operator(
m.get_molecular_hamiltonian(
active_indices=range(active_spatial_orbitals))))))
h = normal_ordered(
get_fermion_operator(
m.get_molecular_hamiltonian(
active_indices=range(active_spatial_orbitals +
virtual_spatial_orbitals))))
o = vqse_operators(s)
return generalized_eigenvalues(h_matrix(h, o, s), s_matrix(o, s))
# Get the Hamiltonian in an active space.
molecular_hamiltonian = molecule.get_molecular_hamiltonian(
occupied_indices=range(active_space_start),
active_indices=range(active_space_start, active_space_stop))
# Map operator to fermions and qubits.
fermion_hamiltonian = get_fermion_operator(molecular_hamiltonian)
qubit_hamiltonian = jordan_wigner(fermion_hamiltonian)
qubit_hamiltonian.compress()
print('The Jordan-Wigner Hamiltonian in canonical basis follows:\n{}'.format(
qubit_hamiltonian))
# Get sparse operator and ground state energy.
sparse_hamiltonian = get_sparse_operator(qubit_hamiltonian)
energy, state = get_ground_state(sparse_hamiltonian)
print('Ground state energy before rotation is {} Hartree.\n'.format(energy))
# Randomly rotate.
n_orbitals = molecular_hamiltonian.n_qubits // 2
n_variables = int(n_orbitals * (n_orbitals - 1) / 2)
random_angles = numpy.pi * (1. - 2. * numpy.random.rand(n_variables))
kappa = numpy.zeros((n_orbitals, n_orbitals))
index = 0
for p in range(n_orbitals):
for q in range(p + 1, n_orbitals):
kappa[p, q] = random_angles[index]
kappa[q, p] = -numpy.conjugate(random_angles[index])
index += 1
# Build the unitary rotation matrix.
from openfermion.hamiltonians import fermi_hubbard
from openfermion.transforms import get_sparse_operator, jordan_wigner
from openfermion.utils import get_ground_state
# Set model.
x_dimension = 2
y_dimension = 2
tunneling = 2.
coulomb = 1.
magnetic_field = 0.5
chemical_potential = 0.25
periodic = 1
spinless = 1
# Get fermion operator.
hubbard_model = fermi_hubbard(
x_dimension, y_dimension, tunneling, coulomb, chemical_potential,
magnetic_field, periodic, spinless)
print (hubbard_model)
# Get qubit operator under Jordan-Wigner.
jw_hamiltonian = jordan_wigner(hubbard_model)
jw_hamiltonian.compress()
print (jw_hamiltonian)
# Get scipy.sparse.csc representation.
sparse_operator = get_sparse_operator(hubbard_model)
print (sparse_operator)
print ('\nEnergy of the model is {} in units of T and J.'.format(
get_ground_state(sparse_operator)[0]))
