def test_error_operator(self):
FO = FermionOperator
terms = []
for i in range(4):
terms.append(FO(((i, 1), ((i + 1) % 4, 0)), -0.0123370055014))
terms.append(FO(((i, 1), ((i - 1) % 4, 0)), -0.0123370055014))
if i in [0, 2]:
terms.append(
normal_ordered(
FO(((i + 1, 1), (i, 1), (i + 1, 0), (i, 0)),
3.18309886184)))
if i < 2:
terms.append(
normal_ordered(
FO(((i, 1), ((i + 2) % 4, 1), (i, 0),
((i + 2) % 4, 0)), 22.2816920329)))
self.assertAlmostEqual(
low_depth_second_order_trotter_error_operator(terms).terms[((3, 1),
(2, 1),
(1, 1),
(2, 0),
(1, 0),
(0,
0))],
0.75)
def test_quad_single_term(self):
op = QuadOperator('p4 p3 p2 p1') + QuadOperator('p3 p2')
self.assertTrue(op == normal_ordered(op))
op = QuadOperator('q0 p0') - QuadOperator('p0 q0')
expected = QuadOperator('', 2.j)
self.assertTrue(expected == normal_ordered(op, hbar=2.))
def test_convert_forward_back(self):
n_qubits = 6
random_operator = get_fermion_operator(
random_interaction_operator(n_qubits))
chemist_operator = chemist_ordered(random_operator)
normalized_chemist = normal_ordered(chemist_operator)
difference = normalized_chemist - normal_ordered(random_operator)
self.assertAlmostEqual(0., difference.induced_norm())
def test_quad_triple(self):
op_132 = QuadOperator(((1, 'p'), (3, 'q'), (2, 'q')))
op_123 = QuadOperator(((1, 'p'), (2, 'q'), (3, 'q')))
op_321 = QuadOperator(((3, 'q'), (2, 'q'), (1, 'p')))
self.assertTrue(op_132 == normal_ordered(op_123))
self.assertTrue(op_132 == normal_ordered(op_132))
self.assertTrue(op_132 == normal_ordered(op_321))
def test_fermion_triple(self):
op_132 = FermionOperator(((1, 1), (3, 0), (2, 0)))
op_123 = FermionOperator(((1, 1), (2, 0), (3, 0)))
op_321 = FermionOperator(((3, 0), (2, 0), (1, 1)))
self.assertTrue(op_132 == normal_ordered(-op_123))
self.assertTrue(op_132 == normal_ordered(op_132))
self.assertTrue(op_132 == normal_ordered(op_321))
def test_inverse_fourier_transform_2d(self):
grid = Grid(dimensions=2, scale=1.5, length=3)
spinless = True
geometry = [('H', (0, 0)), ('H', (0.5, 0.8))]
h_plane_wave = plane_wave_hamiltonian(grid, geometry, spinless, True)
h_dual_basis = plane_wave_hamiltonian(grid, geometry, spinless, False)
h_dual_basis_t = inverse_fourier_transform(h_dual_basis, grid, spinless)
self.assertEqual(normal_ordered(h_dual_basis_t),
normal_ordered(h_plane_wave))
def test_inverse_fourier_transform_1d(self):
grid = Grid(dimensions=1, scale=1.5, length=4)
spinless_set = [True, False]
geometry = [('H', (0,)), ('H', (0.5,))]
for spinless in spinless_set:
h_plane_wave = plane_wave_hamiltonian(grid, geometry, spinless,
True)
h_dual_basis = plane_wave_hamiltonian(grid, geometry, spinless,
False)
h_dual_basis_t = inverse_fourier_transform(h_dual_basis, grid,
spinless)
self.assertEqual(normal_ordered(h_dual_basis_t),
normal_ordered(h_plane_wave))
def test_erpa_eom_ham_lih():
filename = os.path.join(DATA_DIRECTORY, "H1-Li1_sto-3g_singlet_1.45.hdf5")
molecule = MolecularData(filename=filename)
reduced_ham = make_reduced_hamiltonian(
molecule.get_molecular_hamiltonian(), molecule.n_electrons)
rha_fermion = get_fermion_operator(reduced_ham)
permuted_hijkl = np.einsum('ijlk', reduced_ham.two_body_tensor)
opdm = np.diag([1] * molecule.n_electrons + [0] *
(molecule.n_qubits - molecule.n_electrons))
tpdm = 2 * wedge(opdm, opdm, (1, 1), (1, 1))
rdms = InteractionRDM(opdm, tpdm)
dim = 3 # so we don't do the full basis. This would make the test long
full_basis = {} # erpa basis. A, B basis in RPA language
cnt = 0
# start from 1 to make test shorter
for p, q in product(range(1, dim), repeat=2):
if p < q:
full_basis[(p, q)] = cnt
full_basis[(q, p)] = cnt + dim * (dim - 1) // 2
cnt += 1
for rkey in full_basis.keys():
p, q = rkey
for ckey in full_basis.keys():
r, s = ckey
for sigma, tau in product([0, 1], repeat=2):
test = erpa_eom_hamiltonian(permuted_hijkl, tpdm,
2 * q + sigma, 2 * p + sigma,
2 * r + tau, 2 * s + tau).real
qp_op = FermionOperator(
((2 * q + sigma, 1), (2 * p + sigma, 0)))
rs_op = FermionOperator(((2 * r + tau, 1), (2 * s + tau, 0)))
erpa_op = normal_ordered(
commutator(qp_op, commutator(rha_fermion, rs_op)))
true = rdms.expectation(get_interaction_operator(erpa_op))
assert np.isclose(true, test)
def test_interaction_operator(self):
for n_orbitals, real, _ in itertools.product((1, 2, 5), (True, False),
range(5)):
operator = random_interaction_operator(n_orbitals, real=real)
normal_ordered_operator = normal_ordered(operator)
expected_qubit_operator = jordan_wigner(operator)
actual_qubit_operator = jordan_wigner(normal_ordered_operator)
assert expected_qubit_operator == actual_qubit_operator
two_body_tensor = normal_ordered_operator.two_body_tensor
n_orbitals = len(two_body_tensor)
ones = numpy.ones((n_orbitals,) * 2)
triu = numpy.triu(ones, 1)
shape = (n_orbitals**2, 1)
mask = (triu.reshape(shape) * ones.reshape(shape[::-1]) +
ones.reshape(shape) * triu.reshape(shape[::-1])).reshape(
(n_orbitals,) * 4)
assert numpy.allclose(mask * two_body_tensor,
numpy.zeros((n_orbitals,) * 4))
for term in normal_ordered_operator:
order = len(term) // 2
left_term, right_term = term[:order], term[order:]
assert all(i[1] == 1 for i in left_term)
assert all(i[1] == 0 for i in right_term)
assert left_term == tuple(sorted(left_term, reverse=True))
assert right_term == tuple(sorted(right_term, reverse=True))
def setUp(self):
geometry = [('H', (0., 0., 0.)), ('H', (0., 0., 0.7414))]
basis = 'sto-3g'
multiplicity = 1
filename = os.path.join(THIS_DIRECTORY, 'data',
'H2_sto-3g_singlet_0.7414')
self.molecule = MolecularData(geometry,
basis,
multiplicity,
filename=filename)
self.molecule.load()
# Get molecular Hamiltonian.
self.molecular_hamiltonian = self.molecule.get_molecular_hamiltonian()
# Get FCI RDM.
self.fci_rdm = self.molecule.get_molecular_rdm(use_fci=1)
# Get explicit coefficients.
self.nuclear_repulsion = self.molecular_hamiltonian.constant
self.one_body = self.molecular_hamiltonian.one_body_tensor
self.two_body = self.molecular_hamiltonian.two_body_tensor
# Get fermion Hamiltonian.
self.fermion_hamiltonian = normal_ordered(
get_fermion_operator(self.molecular_hamiltonian))
# Get qubit Hamiltonian.
self.qubit_hamiltonian = jordan_wigner(self.fermion_hamiltonian)
# Get the sparse matrix.
self.hamiltonian_matrix = get_sparse_operator(
self.molecular_hamiltonian)
def double_commutator(op1,
op2,
op3,
indices2=None,
indices3=None,
is_hopping_operator2=None,
is_hopping_operator3=None):
"""Return the double commutator [op1, [op2, op3]].
Args:
op1, op2, op3 (FermionOperators or BosonOperators): operators for
the commutator. All three operators must be of the same type.
indices2, indices3 (set): The indices op2 and op3 act on.
is_hopping_operator2 (bool): Whether op2 is a hopping operator.
is_hopping_operator3 (bool): Whether op3 is a hopping operator.
Returns:
The double commutator of the given operators.
"""
if is_hopping_operator2 and is_hopping_operator3:
indices2 = set(indices2)
indices3 = set(indices3)
# Determine which indices both op2 and op3 act on.
try:
intersection, = indices2.intersection(indices3)
except ValueError:
return FermionOperator.zero()
# Remove the intersection from the set of indices, since it will get
# cancelled out in the final result.
indices2.remove(intersection)
indices3.remove(intersection)
# Find the indices of the final output hopping operator.
index2, = indices2
index3, = indices3
coeff2 = op2.terms[list(op2.terms)[0]]
coeff3 = op3.terms[list(op3.terms)[0]]
commutator23 = (FermionOperator(
((index2, 1), (index3, 0)), coeff2 * coeff3) + FermionOperator(
((index3, 1), (index2, 0)), -coeff2 * coeff3))
else:
commutator23 = normal_ordered(commutator(op2, op3))
return normal_ordered(commutator(op1, commutator23))
def test_molecular_operator_consistency(self):
# Initialize H2 InteractionOperator.
n_qubits = 4
filename = os.path.join(THIS_DIRECTORY, 'data',
'H2_sto-3g_singlet_0.7414')
molecule = MolecularData(filename=filename)
molecule_interaction = molecule.get_molecular_hamiltonian()
molecule_operator = get_fermion_operator(molecule_interaction)
constant = molecule_interaction.constant
one_body_coefficients = molecule_interaction.one_body_tensor
two_body_coefficients = molecule_interaction.two_body_tensor
# Perform decomposition.
eigenvalues, one_body_squares, one_body_corrections, trunc_error = (
low_rank_two_body_decomposition(two_body_coefficients))
self.assertAlmostEqual(trunc_error, 0.)
# Build back operator constant and one-body components.
decomposed_operator = FermionOperator((), constant)
for p, q in itertools.product(range(n_qubits), repeat=2):
term = ((p, 1), (q, 0))
coefficient = (one_body_coefficients[p, q] +
one_body_corrections[p, q])
decomposed_operator += FermionOperator(term, coefficient)
# Build back two-body component.
for l in range(one_body_squares.shape[0]):
one_body_operator = FermionOperator()
for p, q in itertools.product(range(n_qubits), repeat=2):
term = ((p, 1), (q, 0))
coefficient = one_body_squares[l, p, q]
if abs(eigenvalues[l]) > 1e-6:
self.assertTrue(is_hermitian(one_body_squares[l]))
one_body_operator += FermionOperator(term, coefficient)
decomposed_operator += eigenvalues[l] * (one_body_operator**2)
# Test for consistency.
difference = normal_ordered(decomposed_operator - molecule_operator)
self.assertAlmostEqual(0., difference.induced_norm())
# Decompose with slightly negative operator that must use eigen
molecule = MolecularData(filename=filename)
molecule.two_body_integrals[0, 0, 0, 0] -= 1
eigenvalues, one_body_squares, one_body_corrections, trunc_error = (
low_rank_two_body_decomposition(two_body_coefficients))
self.assertAlmostEqual(trunc_error, 0.)
# Check for property errors
with self.assertRaises(TypeError):
eigenvalues, one_body_squares, _, trunc_error = (
low_rank_two_body_decomposition(two_body_coefficients + 0.01j,
truncation_threshold=1.,
final_rank=1))
def test_sum_of_ordered_terms_equals_full_hamiltonian_odd_side_len(self):
hamiltonian = normal_ordered(
fermi_hubbard(5, 5, 1.0, -0.3, periodic=False))
hamiltonian.compress()
terms = simulation_ordered_grouped_hubbard_terms_with_info(
hamiltonian)[0]
terms_total = sum(terms, FermionOperator.zero())
self.assertTrue(terms_total == hamiltonian)
def test_total_length_odd_side_length_full_hubbard(self):
hamiltonian = normal_ordered(
fermi_hubbard(5, 5, -1., -0.3, periodic=False))
hamiltonian.compress()
# Unpack result into terms, indices they act on, and whether they're
# hopping operators.
result = simulation_ordered_grouped_hubbard_terms_with_info(
hamiltonian)
terms, _, _ = result
self.assertEqual(len(terms), 105)
def get_qubit_expectations(self, qubit_operator):
"""Return expectations of QubitOperator in new QubitOperator.
Args:
qubit_operator: QubitOperator instance to be evaluated on
this InteractionRDM.
Returns:
QubitOperator: QubitOperator with coefficients
corresponding to expectation values of those operators.
Raises:
InteractionRDMError: Observable not contained in 1-RDM or 2-RDM.
"""
from openfermion.transforms.opconversions import reverse_jordan_wigner
from openfermion.utils.operator_utils import normal_ordered
qubit_operator_expectations = copy.deepcopy(qubit_operator)
for qubit_term in qubit_operator_expectations.terms:
expectation = 0.
# Map qubits back to fermions.
reversed_fermion_operators = reverse_jordan_wigner(
QubitOperator(qubit_term))
reversed_fermion_operators = normal_ordered(
reversed_fermion_operators)
# Loop through fermion terms.
for fermion_term in reversed_fermion_operators.terms:
coefficient = reversed_fermion_operators.terms[fermion_term]
# Handle molecular term.
if FermionOperator(
fermion_term).is_two_body_number_conserving():
if not fermion_term:
expectation += coefficient
else:
indices = [operator[0] for operator in fermion_term]
if len(indices) == 2:
# One-body term
indices = tuple(zip(indices, (1, 0)))
else:
# Two-body term
indices = tuple(zip(indices, (1, 1, 0, 0)))
rdm_element = self[indices]
expectation += rdm_element * coefficient
# Handle non-molecular terms.
elif len(fermion_term) > 4:
raise InteractionRDMError('Observable not contained '
'in 1-RDM or 2-RDM.')
qubit_operator_expectations.terms[qubit_term] = expectation
return qubit_operator_expectations
def test_split_operator_error_operator_VT_order_against_definition(self):
hamiltonian = (normal_ordered(fermi_hubbard(3, 3, 1., 4.0)) -
2.3 * FermionOperator.identity())
potential_terms, kinetic_terms = (
diagonal_coulomb_potential_and_kinetic_terms_as_arrays(hamiltonian)
)
potential = sum(potential_terms, FermionOperator.zero())
kinetic = sum(kinetic_terms, FermionOperator.zero())
error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='V+T'))
# V-then-T ordered double commutators: [V, [T, V]] + [T, [T, V]] / 2
inner_commutator = normal_ordered(commutator(kinetic, potential))
error_operator_definition = normal_ordered(
commutator(potential, inner_commutator))
error_operator_definition += normal_ordered(
commutator(kinetic, inner_commutator)) / 2.0
error_operator_definition /= 12.0
self.assertEqual(error_operator, error_operator_definition)
def test_fourier_transform(self):
for length in [2, 3]:
grid = Grid(dimensions=1, scale=1.5, length=length)
spinless_set = [True, False]
geometry = [('H', (0.1,)), ('H', (0.5,))]
for spinless in spinless_set:
h_plane_wave = plane_wave_hamiltonian(grid, geometry, spinless,
True)
h_dual_basis = plane_wave_hamiltonian(grid, geometry, spinless,
False)
h_plane_wave_t = fourier_transform(h_plane_wave, grid, spinless)
self.assertEqual(normal_ordered(h_plane_wave_t),
normal_ordered(h_dual_basis))
# Verify that all 3 are Hermitian
plane_wave_operator = get_sparse_operator(h_plane_wave)
dual_operator = get_sparse_operator(h_dual_basis)
plane_wave_t_operator = get_sparse_operator(h_plane_wave_t)
self.assertTrue(is_hermitian(plane_wave_operator))
self.assertTrue(is_hermitian(dual_operator))
self.assertTrue(is_hermitian(plane_wave_t_operator))
def test_sum_of_ordered_terms_equals_full_side_length_2_hopping_only(self):
hamiltonian = normal_ordered(
fermi_hubbard(2, 2, 1., 0.0, periodic=False))
hamiltonian.compress()
# Unpack result into terms, indices they act on, and whether they're
# hopping operators.
result = simulation_ordered_grouped_hubbard_terms_with_info(
hamiltonian)
terms, _, _ = result
terms_total = sum(terms, FermionOperator.zero())
self.assertTrue(terms_total == hamiltonian)
def test_operator_consistency_w_spin(self):
# Initialize a random InteractionOperator and FermionOperator.
n_orbitals = 3
n_qubits = 2 * n_orbitals
random_interaction = random_interaction_operator(n_orbitals,
expand_spin=True,
real=False,
seed=8)
random_fermion = get_fermion_operator(random_interaction)
# Convert to chemist ordered tensor.
one_body_correction, chemist_tensor = \
get_chemist_two_body_coefficients(
random_interaction.two_body_tensor, spin_basis=True)
# Convert output to FermionOperator.
output_operator = FermionOperator((), random_interaction.constant)
# Convert one-body.
one_body_coefficients = (random_interaction.one_body_tensor +
one_body_correction)
for p, q in itertools.product(range(n_qubits), repeat=2):
term = ((p, 1), (q, 0))
coefficient = one_body_coefficients[p, q]
output_operator += FermionOperator(term, coefficient)
# Convert two-body.
for p, q, r, s in itertools.product(range(n_orbitals), repeat=4):
coefficient = chemist_tensor[p, q, r, s]
# Mixed spin.
term = ((2 * p, 1), (2 * q, 0), (2 * r + 1, 1), (2 * s + 1, 0))
output_operator += FermionOperator(term, coefficient)
term = ((2 * p + 1, 1), (2 * q + 1, 0), (2 * r, 1), (2 * s, 0))
output_operator += FermionOperator(term, coefficient)
# Same spin.
term = ((2 * p, 1), (2 * q, 0), (2 * r, 1), (2 * s, 0))
output_operator += FermionOperator(term, coefficient)
term = ((2 * p + 1, 1), (2 * q + 1, 0), (2 * r + 1, 1), (2 * s + 1,
0))
output_operator += FermionOperator(term, coefficient)
# Check that difference is small.
difference = normal_ordered(random_fermion - output_operator)
self.assertAlmostEqual(0., difference.induced_norm())
def test_error_bound_using_info_even_side_length(self):
# Generate the Hamiltonian.
hamiltonian = normal_ordered(
fermi_hubbard(4, 4, 0.5, 0.2, periodic=False))
hamiltonian.compress()
# Unpack result into terms, indices they act on, and whether they're
# hopping operators.
result = simulation_ordered_grouped_hubbard_terms_with_info(
hamiltonian)
terms, indices, is_hopping = result
self.assertAlmostEqual(
low_depth_second_order_trotter_error_bound(terms, indices,
is_hopping), 13.59)
def test_is_hopping_operator_terms_with_info(self):
hamiltonian = normal_ordered(
fermi_hubbard(5, 5, 1., -1., periodic=False))
hamiltonian.compress()
# Unpack result into terms, indices they act on, and whether they're
# hopping operators.
result = simulation_ordered_grouped_hubbard_terms_with_info(
hamiltonian)
terms, _, is_hopping = result
for i in range(len(terms)):
single_term = list(terms[i].terms)[0]
is_hopping_term = not (single_term[1][1]
or single_term[0][0] == single_term[1][0])
self.assertEqual(is_hopping_term, is_hopping[i])
def test_strong_interaction_hubbard_VT_order_gives_larger_error(self):
hamiltonian = normal_ordered(fermi_hubbard(4, 4, 1., 10.0))
TV_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='T+V'))
TV_error_bound = numpy.sum(
numpy.absolute(list(TV_error_operator.terms.values())))
VT_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='V+T'))
VT_error_bound = numpy.sum(
numpy.absolute(list(VT_error_operator.terms.values())))
self.assertGreater(VT_error_bound, TV_error_bound)
def test_intermediate_interaction_hubbard_TV_order_has_larger_error(self):
hamiltonian = normal_ordered(fermi_hubbard(4, 4, 1., 4.0))
TV_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='T+V'))
TV_error_bound = numpy.sum(
numpy.absolute(list(TV_error_operator.terms.values())))
VT_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='V+T'))
VT_error_bound = numpy.sum(
numpy.absolute(list(VT_error_operator.terms.values())))
self.assertAlmostEqual(TV_error_bound, 1706.66666666666)
self.assertAlmostEqual(VT_error_bound, 1365.33333333333)
def setUp(self):
# Set up molecule.
geometry = [('Li', (0., 0., 0.)), ('H', (0., 0., 1.45))]
basis = 'sto-3g'
multiplicity = 1
filename = os.path.join(THIS_DIRECTORY, 'data',
'H1-Li1_sto-3g_singlet_1.45')
self.molecule = MolecularData(geometry,
basis,
multiplicity,
filename=filename)
self.molecule.load()
# Get molecular Hamiltonian
self.molecular_hamiltonian = self.molecule.get_molecular_hamiltonian()
self.molecular_hamiltonian_no_core = (
self.molecule.get_molecular_hamiltonian(
occupied_indices=[0],
active_indices=range(1, self.molecule.n_orbitals)))
# Get FCI RDM.
self.fci_rdm = self.molecule.get_molecular_rdm(use_fci=1)
# Get explicit coefficients.
self.nuclear_repulsion = self.molecular_hamiltonian.constant
self.one_body = self.molecular_hamiltonian.one_body_tensor
self.two_body = self.molecular_hamiltonian.two_body_tensor
# Get fermion Hamiltonian.
self.fermion_hamiltonian = normal_ordered(
get_fermion_operator(self.molecular_hamiltonian))
# Get qubit Hamiltonian.
self.qubit_hamiltonian = jordan_wigner(self.fermion_hamiltonian)
# Get explicit coefficients.
self.nuclear_repulsion = self.molecular_hamiltonian.constant
self.one_body = self.molecular_hamiltonian.one_body_tensor
self.two_body = self.molecular_hamiltonian.two_body_tensor
# Get matrix form.
self.hamiltonian_matrix = get_sparse_operator(
self.molecular_hamiltonian)
self.hamiltonian_matrix_no_core = get_sparse_operator(
self.molecular_hamiltonian_no_core)
def test_correct_indices_terms_with_info(self):
hamiltonian = normal_ordered(
fermi_hubbard(5, 5, 1., -1., periodic=False))
hamiltonian.compress()
# Unpack result into terms, indices they act on, and whether they're
# hopping operators.
result = simulation_ordered_grouped_hubbard_terms_with_info(
hamiltonian)
terms, indices, _ = result
for i in range(len(terms)):
term = list(terms[i].terms)
term_indices = set()
for single_term in term:
term_indices = term_indices.union(
[single_term[j][0] for j in range(len(single_term))])
self.assertEqual(term_indices, indices[i])
def test_hubbard_trotter_error_matches_low_depth_trotter_error(self):
hamiltonian = normal_ordered(fermi_hubbard(3, 3, 1., 2.3))
error_operator = (
fermionic_swap_trotter_error_operator_diagonal_two_body(
hamiltonian))
error_operator.compress()
# Unpack result into terms, indices they act on, and whether
# they're hopping operators.
result = simulation_ordered_grouped_low_depth_terms_with_info(
hamiltonian)
terms, indices, is_hopping = result
old_error_operator = low_depth_second_order_trotter_error_operator(
terms, indices, is_hopping, jellium_only=True)
old_error_operator -= error_operator
self.assertEqual(old_error_operator, FermionOperator.zero())
def test_1d_jellium_wigner_seitz_10_VT_order_gives_larger_error(self):
hamiltonian = normal_ordered(
jellium_model(
hypercube_grid_with_given_wigner_seitz_radius_and_filling(
1, 5, wigner_seitz_radius=10., spinless=True),
spinless=True,
plane_wave=False))
TV_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='T+V'))
TV_error_bound = numpy.sum(
numpy.absolute(list(TV_error_operator.terms.values())))
VT_error_operator = (
split_operator_trotter_error_operator_diagonal_two_body(
hamiltonian, order='V+T'))
VT_error_bound = numpy.sum(
numpy.absolute(list(VT_error_operator.terms.values())))
self.assertGreater(VT_error_bound, TV_error_bound)
def diagonal_coulomb_potential_and_kinetic_terms_as_arrays(hamiltonian):
"""Give the potential and kinetic terms of a diagonal Coulomb Hamiltonian
as arrays.
Args:
hamiltonian (FermionOperator): The diagonal Coulomb Hamiltonian to
separate the potential and kinetic terms
for. Identity is arbitrarily chosen
to be part of the potential.
Returns:
Tuple of (potential_terms, kinetic_terms). Both elements of the tuple
are numpy arrays of FermionOperators.
"""
if not isinstance(hamiltonian, FermionOperator):
try:
hamiltonian = normal_ordered(get_fermion_operator(hamiltonian))
except TypeError:
raise TypeError('hamiltonian must be either a FermionOperator '
'or DiagonalCoulombHamiltonian.')
potential = FermionOperator.zero()
kinetic = FermionOperator.zero()
for term, coeff in hamiltonian.terms.items():
acted = set(term[i][0] for i in range(len(term)))
if len(acted) == len(term) / 2:
potential += FermionOperator(term, coeff)
else:
kinetic += FermionOperator(term, coeff)
potential_terms = numpy.array([
FermionOperator(term, coeff) for term, coeff in potential.terms.items()
])
kinetic_terms = numpy.array(
[FermionOperator(term, coeff) for term, coeff in kinetic.terms.items()])
return (potential_terms, kinetic_terms)
def test_random_operator_consistency(self):
# Initialize a random InteractionOperator and FermionOperator.
n_orbitals = 3
n_qubits = 2 * n_orbitals
random_interaction = random_interaction_operator(n_orbitals,
expand_spin=True,
real=True,
seed=8)
random_fermion = get_fermion_operator(random_interaction)
# Decompose.
eigenvalues, one_body_squares, one_body_correction, error = (
low_rank_two_body_decomposition(
random_interaction.two_body_tensor))
self.assertFalse(error)
# Build back operator constant and one-body components.
decomposed_operator = FermionOperator((), random_interaction.constant)
one_body_coefficients = (random_interaction.one_body_tensor +
one_body_correction)
for p, q in itertools.product(range(n_qubits), repeat=2):
term = ((p, 1), (q, 0))
coefficient = one_body_coefficients[p, q]
decomposed_operator += FermionOperator(term, coefficient)
# Build back two-body component.
for l in range(n_orbitals**2):
one_body_operator = FermionOperator()
for p, q in itertools.product(range(n_qubits), repeat=2):
term = ((p, 1), (q, 0))
coefficient = one_body_squares[l, p, q]
one_body_operator += FermionOperator(term, coefficient)
decomposed_operator += eigenvalues[l] * (one_body_operator**2)
# Test for consistency.
difference = normal_ordered(decomposed_operator - random_fermion)
self.assertAlmostEqual(0., difference.induced_norm())
def test_1D_jellium_trotter_error_matches_low_depth_trotter_error(self):
hamiltonian = normal_ordered(
jellium_model(
hypercube_grid_with_given_wigner_seitz_radius_and_filling(
1, 5, wigner_seitz_radius=10., spinless=True),
spinless=True,
plane_wave=False))
error_operator = (
fermionic_swap_trotter_error_operator_diagonal_two_body(
hamiltonian))
error_operator.compress()
# Unpack result into terms, indices they act on, and whether
# they're hopping operators.
result = simulation_ordered_grouped_low_depth_terms_with_info(
hamiltonian)
terms, indices, is_hopping = result
old_error_operator = low_depth_second_order_trotter_error_operator(
terms, indices, is_hopping, jellium_only=True)
old_error_operator -= error_operator
self.assertEqual(old_error_operator, FermionOperator.zero())
