def test_diagonalizing_bogoliubov_transform_particle_conserving(self):
"""Test particle-conserving diagonalizing Bogoliubov transform."""
# Spin-symmetric
quad_ham = random_quadratic_hamiltonian(5,
conserves_particle_number=True,
expand_spin=True)
quad_ham = get_quadratic_hamiltonian(
reorder(get_fermion_operator(quad_ham), up_then_down))
orbital_energies, transformation_matrix, _ = (
quad_ham.diagonalizing_bogoliubov_transform())
max_upper_right = numpy.max(numpy.abs(transformation_matrix[:5, 5:]))
max_lower_left = numpy.max(numpy.abs(transformation_matrix[5:, :5]))
numpy.testing.assert_allclose(orbital_energies[:5],
orbital_energies[5:])
numpy.testing.assert_allclose(transformation_matrix.dot(
quad_ham.combined_hermitian_part.T.dot(
transformation_matrix.T.conj())),
numpy.diag(orbital_energies),
atol=1e-7)
numpy.testing.assert_allclose(max_upper_right, 0.0)
numpy.testing.assert_allclose(max_lower_left, 0.0)
# Specific spin sector
quad_ham = random_quadratic_hamiltonian(5,
conserves_particle_number=True,
expand_spin=True)
quad_ham = get_quadratic_hamiltonian(
reorder(get_fermion_operator(quad_ham), up_then_down))
for spin_sector in range(2):
orbital_energies, transformation_matrix, _ = (
quad_ham.diagonalizing_bogoliubov_transform(
spin_sector=spin_sector))
def index_map(i):
return i + spin_sector * 5
spin_indices = [index_map(i) for i in range(5)]
spin_matrix = quad_ham.combined_hermitian_part[numpy.ix_(
spin_indices, spin_indices)]
numpy.testing.assert_allclose(transformation_matrix.dot(
spin_matrix.T.dot(transformation_matrix.T.conj())),
numpy.diag(orbital_energies),
atol=1e-7)
# Not spin-symmetric
quad_ham = random_quadratic_hamiltonian(5,
conserves_particle_number=True,
expand_spin=False)
orbital_energies, _ = quad_ham.orbital_energies()
_, transformation_matrix, _ = (
quad_ham.diagonalizing_bogoliubov_transform())
numpy.testing.assert_allclose(transformation_matrix.dot(
quad_ham.combined_hermitian_part.T.dot(
transformation_matrix.T.conj())),
numpy.diag(orbital_energies),
atol=1e-7)
def symmetry_conserving_bravyi_kitaev(fermion_hamiltonian, active_orbitals,
active_fermions):
""" Returns the qubit Hamiltonian for the fermionic Hamiltonian
supplied, with two qubits removed using conservation of electron
spin and number, as described in arXiv:1701.08213.
Args:
fermion_hamiltonian: A fermionic hamiltonian obtained
using OpenFermion. An instance
of the FermionOperator class.
active_orbitals: Int type object. The number of active orbitals
being considered for the system.
active_fermions: Int type object. The number of active fermions
being considered for the system (note, this
is less than the number of electrons in a
molecule if some orbitals have been assumed
filled).
Returns:
qubit_hamiltonian: The qubit Hamiltonian corresponding to
the supplied fermionic Hamiltonian, with
two qubits removed using spin symmetries.
WARNING:
Reorders orbitals from the default even-odd ordering to all
spin-up orbitals, then all spin-down orbitals.
Raises:
ValueError if fermion_hamiltonian isn't of the type
FermionOperator, or active_orbitals isn't an integer,
or active_fermions isn't an integer.
Notes: This function reorders the spin orbitals as all spin-up, then
all spin-down. It uses the OpenFermion bravyi_kitaev_tree
mapping, rather than the bravyi-kitaev mapping.
Caution advised when using with a Fermi-Hubbard Hamiltonian;
this technique correctly reduces the Hamiltonian only for the
lowest energy even and odd fermion number states, not states
with an arbitrary number of fermions.
"""
# Catch errors if inputs are of wrong type.
if type(fermion_hamiltonian) is not FermionOperator:
raise ValueError(
"Supplied operator should be an instance of FermionOperator class")
if type(active_orbitals) is not int:
raise ValueError("Number of active orbitals should be an integer.")
if type(active_fermions) is not int:
raise ValueError("Number of active fermions should be an integer.")
# Arrange spins up then down, then BK map to qubit Hamiltonian.
fermion_hamiltonian_reorder = reorder(fermion_hamiltonian,
up_then_down,
num_modes=active_orbitals)
qubit_hamiltonian = bravyi_kitaev_tree(fermion_hamiltonian_reorder,
n_qubits=active_orbitals)
qubit_hamiltonian.compress()
# Allocates the parity factors for the orbitals as in arXiv:1704.05018.
remainder = active_fermions % 4
if remainder == 0:
parity_final_orb = 1
parity_middle_orb = 1
elif remainder == 1:
parity_final_orb = -1
parity_middle_orb = -1
elif remainder == 2:
parity_final_orb = 1
parity_middle_orb = -1
else:
parity_final_orb = -1
parity_middle_orb = 1
# Removes the final qubit, then the middle qubit.
qubit_hamiltonian = edit_hamiltonian_for_spin(qubit_hamiltonian,
active_orbitals,
parity_final_orb)
qubit_hamiltonian = edit_hamiltonian_for_spin(qubit_hamiltonian,
active_orbitals / 2,
parity_middle_orb)
qubit_hamiltonian = remove_indices(qubit_hamiltonian,
(active_orbitals / 2, active_orbitals))
return qubit_hamiltonian