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_number_restricted_spectra_match_molecule(self):
hamiltonian_fop = get_fermion_operator(self.molecular_hamiltonian)
sparse_ham_number_preserving = get_number_preserving_sparse_operator(
hamiltonian_fop,
self.molecule.n_qubits,
self.molecule.n_electrons,
spin_preserving=False)
sparse_ham = get_sparse_operator(hamiltonian_fop,
self.molecule.n_qubits)
sparse_ham_restricted_number_preserving = jw_number_restrict_operator(
sparse_ham,
n_electrons=self.molecule.n_electrons,
n_qubits=self.molecule.n_qubits)
spectrum_from_new_sparse_method = sparse_eigenspectrum(
sparse_ham_number_preserving)
spectrum_from_old_sparse_method = sparse_eigenspectrum(
sparse_ham_restricted_number_preserving)
spectral_deviation = numpy.amax(
numpy.absolute(spectrum_from_new_sparse_method -
spectrum_from_old_sparse_method))
self.assertAlmostEqual(spectral_deviation, 0.)
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_number_restricted_spectra_match_hubbard(self):
hamiltonian_fop = self.hubbard_hamiltonian
sparse_ham_number_preserving = get_number_preserving_sparse_operator(
hamiltonian_fop,
8,
4,
spin_preserving=False)
sparse_ham = get_sparse_operator(hamiltonian_fop,
8)
sparse_ham_restricted_number_preserving = jw_number_restrict_operator(
sparse_ham,
n_electrons=4,
n_qubits=8)
spectrum_from_new_sparse_method = sparse_eigenspectrum(
sparse_ham_number_preserving)
spectrum_from_old_sparse_method = sparse_eigenspectrum(
sparse_ham_restricted_number_preserving)
spectral_deviation = numpy.amax(numpy.absolute(
spectrum_from_new_sparse_method - spectrum_from_old_sparse_method))
self.assertAlmostEqual(spectral_deviation, 0.)
