def __init__(self,
hamiltonian: InteractionOperator,
truncation_threshold: Optional[float]=None,
final_rank: Optional[int]=None) -> None:
self.truncation_threshold = truncation_threshold
self.final_rank = final_rank
# Get the chemist matrix.
(self.constant,
self.one_body_coefficients,
chemist_two_body_coefficients) = (
get_chemist_two_body_coefficients(hamiltonian))
# Perform the low rank decomposition of two-body operator.
self.eigenvalues, self.one_body_squares, _ = (
low_rank_two_body_decomposition(
chemist_two_body_coefficients,
truncation_threshold=self.truncation_threshold,
final_rank=self.final_rank))
# Get scaled density-density terms and basis transformation matrices.
self.scaled_density_density_matrices = [] # type: List[numpy.ndarray]
self.basis_change_matrices = [] # type: List[numpy.ndarray]
for j in range(len(self.eigenvalues)):
density_density_matrix, basis_change_matrix = (
prepare_one_body_squared_evolution(self.one_body_squares[j]))
self.scaled_density_density_matrices.append(
numpy.real(self.eigenvalues[j] * density_density_matrix))
self.basis_change_matrices.append(basis_change_matrix)
super().__init__(hamiltonian)
def test_operator_consistency(self):
# Initialize a random InteractionOperator and FermionOperator.
n_qubits = 4
random_interaction = random_interaction_operator(n_qubits,
real=False,
seed=34281)
random_fermion = get_fermion_operator(random_interaction)
# Convert to chemist ordered tensor.
io_constant, io_one_body_coefficients, io_chemist_tensor = \
get_chemist_two_body_coefficients(random_interaction)
fo_constant, fo_one_body_coefficients, fo_chemist_tensor = \
get_chemist_two_body_coefficients(random_fermion)
# Ensure consistency between FermionOperator and InteractionOperator.
self.assertAlmostEqual(io_constant, fo_constant)
one_body_difference = numpy.sum(
numpy.absolute(io_one_body_coefficients -
fo_one_body_coefficients))
self.assertAlmostEqual(0., one_body_difference)
two_body_difference = numpy.sum(
numpy.absolute(io_chemist_tensor - fo_chemist_tensor))
self.assertAlmostEqual(0., two_body_difference)
# Convert output to FermionOperator.
output_operator = FermionOperator()
output_operator += FermionOperator((), fo_constant)
# Convert one-body.
for p, q in itertools.product(range(n_qubits), repeat=2):
term = ((p, 1), (q, 0))
coefficient = fo_one_body_coefficients[p, q]
output_operator += FermionOperator(term, coefficient)
# Convert two-body.
for p, q, r, s in itertools.product(range(n_qubits), repeat=4):
term = ((p, 1), (q, 0), (r, 1), (s, 0))
coefficient = fo_chemist_tensor[p, q, r, s]
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_one_body_square_decomposition(self):
# Initialize a random two-body FermionOperator.
n_qubits = 4
random_operator = get_fermion_operator(
random_interaction_operator(n_qubits, seed=17004))
# Convert to chemist tensor.
constant, one_body_coefficients, chemist_tensor = (
get_chemist_two_body_coefficients(random_operator))
# Perform decomposition.
eigenvalues, one_body_squares, trunc_error = (
low_rank_two_body_decomposition(chemist_tensor))
# Build back two-body component.
for l in range(n_qubits**2):
# Get the squared one-body operator.
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)
one_body_squared = one_body_operator**2
# Get the squared one-body operator via one-body decomposition.
density_density_matrix, basis_transformation_matrix = (
prepare_one_body_squared_evolution(one_body_squares[l]))
two_body_operator = FermionOperator()
for p, q in itertools.product(range(n_qubits), repeat=2):
term = ((p, 1), (p, 0), (q, 1), (q, 0))
coefficient = density_density_matrix[p, q]
two_body_operator += FermionOperator(term, coefficient)
# Confirm that the rotations diagonalize the one-body squares.
hopefully_diagonal = basis_transformation_matrix.dot(
numpy.dot(
one_body_squares[l],
numpy.transpose(
numpy.conjugate(basis_transformation_matrix))))
diagonal = numpy.diag(hopefully_diagonal)
difference = hopefully_diagonal - numpy.diag(diagonal)
self.assertAlmostEqual(0., numpy.amax(numpy.absolute(difference)))
density_density_alternative = numpy.outer(diagonal, diagonal)
difference = density_density_alternative - density_density_matrix
self.assertAlmostEqual(0., numpy.amax(numpy.absolute(difference)))
# Test spectra.
one_body_squared_spectrum = eigenspectrum(one_body_squared)
two_body_spectrum = eigenspectrum(two_body_operator)
difference = two_body_spectrum - one_body_squared_spectrum
self.assertAlmostEqual(0., numpy.amax(numpy.absolute(difference)))
def test_exception(self):
# Initialize a bad FermionOperator.
n_qubits = 4
random_interaction = random_interaction_operator(n_qubits, seed=36229)
random_fermion = get_fermion_operator(random_interaction)
bad_term = ((1, 1), (2, 1))
random_fermion += FermionOperator(bad_term)
# Check for exception.
with self.assertRaises(TypeError):
fo_constant, fo_one_body_coefficients, fo_chemist_tensor = (
get_chemist_two_body_coefficients(random_fermion))
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_operator_consistency(self):
# Initialize a random two-body FermionOperator.
n_qubits = 4
random_operator = get_fermion_operator(
random_interaction_operator(n_qubits, seed=28644))
# Convert to chemist tensor.
constant, one_body_coefficients, chemist_tensor = (
get_chemist_two_body_coefficients(random_operator))
# 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]
decomposed_operator += FermionOperator(term, coefficient)
# Perform decomposition.
eigenvalues, one_body_squares, trunc_error = (
low_rank_two_body_decomposition(chemist_tensor))
self.assertFalse(trunc_error)
# Check for exception.
with self.assertRaises(ValueError):
eigenvalues, one_body_squares, trunc_error = (
low_rank_two_body_decomposition(chemist_tensor,
truncation_threshold=1.,
final_rank=1))
# Build back two-body component.
for l in range(n_qubits**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_operator)
self.assertAlmostEqual(0., difference.induced_norm())
def test_rank_reduction(self):
# Initialize H2.
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')
molecule = MolecularData(geometry,
basis,
multiplicity,
filename=filename)
molecule.load()
# Get molecular Hamiltonian.
molecular_hamiltonian = molecule.get_molecular_hamiltonian()
# Get fermion Hamiltonian.
fermion_hamiltonian = normal_ordered(
get_fermion_operator(molecular_hamiltonian))
# Get chemist tensor.
constant, one_body_coefficients, chemist_tensor = (
get_chemist_two_body_coefficients(fermion_hamiltonian))
n_qubits = one_body_coefficients.shape[0]
# Rank reduce with threshold.
errors = []
for truncation_threshold in [1., 0.1, 0.01, 0.001]:
# Add back one-body terms and constant.
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]
decomposed_operator += FermionOperator(term, coefficient)
# Rank reduce.
eigenvalues, one_body_squares, trunc_error = (
low_rank_two_body_decomposition(
chemist_tensor, truncation_threshold=truncation_threshold))
# Make sure error is below truncation specification.
self.assertTrue(trunc_error < truncation_threshold)
# Reassemble FermionOperator.
l_max = eigenvalues.size
for l in range(l_max):
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 -
fermion_hamiltonian)
errors += [difference.induced_norm()]
self.assertTrue(errors[-1] <= trunc_error
or abs(errors[-1] - trunc_error) < 1e-6)
self.assertTrue(errors[3] <= errors[2] <= errors[1] <= errors[0])
# Rank reduce by setting final rank.
errors = []
for final_rank in [4, 6, 8, 10, 12]:
# Add back one-body terms and constant.
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]
decomposed_operator += FermionOperator(term, coefficient)
# Rank reduce.
eigenvalues, one_body_squares, trunc_error = (
low_rank_two_body_decomposition(chemist_tensor,
final_rank=final_rank))
# Reassemble FermionOperator.
l_max = eigenvalues.size
for l in range(l_max):
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 -
fermion_hamiltonian)
errors += [difference.induced_norm()]
self.assertTrue(errors[3] <= errors[2] <= errors[1] <= errors[0])
fermionic_hamiltonian = get_fermion_operator(
molecule.get_molecular_hamiltonian())
# matrix for hamiltonian
h = np.array([0, [], [[]], [[[]]], [[[[]]]]])
h[0] = fermionic_hamiltonian.terms[()]
h[2] = np.zeros((nqubit, nqubit))
h[4] = np.zeros((nqubit, nqubit, nqubit, nqubit))
# input hamiltonian into h
for i, j, k, l in itertools.product(range(nqubit), repeat=4):
h[4][i][j][k][l] = fermionic_hamiltonian.terms.get(
((i, 1), (j, 1), (k, 0), (l, 0)), 0)
# get chemist-ordered matrix (h2_correction unused)
h2_correction, V = get_chemist_two_body_coefficients(h[4], spin_basis=True)
# reshape into matrix
Vmat = V.reshape(half_nqubit**2, half_nqubit**2)
# SVD decomposition
u1, lam, u2 = np.linalg.svd(Vmat)
# Record the errors of SVD expansion in each k
V_svd = np.tensordot(u1[:, 0], u2[0, :], 0) * lam[0]
error_svd.append(np.linalg.norm(Vmat - V_svd))
for i in range(1, k_svd):
V_svd += np.tensordot(u1[:, i], u2[i, :], 0) * lam[i]
error_svd.append(np.linalg.norm(Vmat - V_svd))
# 第一添え字をxにするため
