def setUp(self):
self.x_dimension = 2
self.y_dimension = 3
# Create a Hamiltonian with nearest-neighbor hopping terms
self.ferm_op = fermi_hubbard(self.x_dimension, self.y_dimension, 1., 0.,
0., 0., False, True)
# Get the ground energy and ground state
self.ferm_op_sparse = get_sparse_operator(self.ferm_op)
self.ferm_op_ground_energy, self.ferm_op_ground_state = (
get_ground_state(self.ferm_op_sparse))
# Transform the FermionOperator to a QubitOperator
self.transformed_op = verstraete_cirac_2d_square(
self.ferm_op,
self.x_dimension,
self.y_dimension,
add_auxiliary_hamiltonian=True,
snake=False)
# Get the ground energy and state of the transformed operator
self.transformed_sparse = get_sparse_operator(self.transformed_op)
self.transformed_ground_energy, self.transformed_ground_state = (
get_ground_state(self.transformed_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_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)
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 test_all(self):
# Test reverse Jordan-Wigner.
fermion_hamiltonian = reverse_jordan_wigner(self.qubit_hamiltonian)
fermion_hamiltonian = normal_ordered(fermion_hamiltonian)
self.assertTrue(self.fermion_hamiltonian == fermion_hamiltonian)
# Test mapping to interaction operator.
fermion_hamiltonian = get_fermion_operator(self.molecular_hamiltonian)
fermion_hamiltonian = normal_ordered(fermion_hamiltonian)
self.assertTrue(self.fermion_hamiltonian == fermion_hamiltonian)
# Test RDM energy.
fci_rdm_energy = self.nuclear_repulsion
fci_rdm_energy += numpy.sum(self.fci_rdm.one_body_tensor *
self.one_body)
fci_rdm_energy += numpy.sum(self.fci_rdm.two_body_tensor *
self.two_body)
self.assertAlmostEqual(fci_rdm_energy, self.molecule.fci_energy)
# Confirm expectation on qubit Hamiltonian using reverse JW matches.
qubit_rdm = self.fci_rdm.get_qubit_expectations(self.qubit_hamiltonian)
qubit_energy = 0.0
for term, coefficient in qubit_rdm.terms.items():
qubit_energy += coefficient * self.qubit_hamiltonian.terms[term]
self.assertAlmostEqual(qubit_energy, self.molecule.fci_energy)
# Confirm fermionic RDMs can be built from measured qubit RDMs.
new_fermi_rdm = get_interaction_rdm(qubit_rdm)
new_fermi_rdm.expectation(self.molecular_hamiltonian)
self.assertAlmostEqual(fci_rdm_energy, self.molecule.fci_energy)
# Test sparse matrices.
energy, wavefunction = get_ground_state(self.hamiltonian_matrix)
self.assertAlmostEqual(energy, self.molecule.fci_energy)
expected_energy = expectation(self.hamiltonian_matrix, wavefunction)
self.assertAlmostEqual(expected_energy, energy)
# Make sure you can reproduce Hartree-Fock energy.
hf_state = jw_hartree_fock_state(self.molecule.n_electrons,
count_qubits(self.qubit_hamiltonian))
hf_density = get_density_matrix([hf_state], [1.])
expected_hf_density_energy = expectation(self.hamiltonian_matrix,
hf_density)
expected_hf_energy = expectation(self.hamiltonian_matrix, hf_state)
self.assertAlmostEqual(expected_hf_energy, self.molecule.hf_energy)
self.assertAlmostEqual(expected_hf_density_energy,
self.molecule.hf_energy)
# Check that frozen core result matches frozen core FCI from psi4.
# Recore frozen core result from external calculation.
self.frozen_core_fci_energy = -7.8807607374168
no_core_fci_energy = numpy.linalg.eigh(
self.hamiltonian_matrix_no_core.toarray())[0][0]
self.assertAlmostEqual(no_core_fci_energy, self.frozen_core_fci_energy)
# Check that the freeze_orbitals function has the same effect as the
# as the occupied_indices option of get_molecular_hamiltonian.
frozen_hamiltonian = freeze_orbitals(
get_fermion_operator(self.molecular_hamiltonian), [0, 1])
self.assertTrue(frozen_hamiltonian == get_fermion_operator(
self.molecular_hamiltonian_no_core))
