def decompose(hf_file, mapping="jordan_wigner", core=None, active=None):
r"""Decomposes the molecular Hamiltonian into a linear combination of Pauli operators using
OpenFermion tools.
This function uses OpenFermion functions to build the second-quantized electronic Hamiltonian
of the molecule and map it to the Pauli basis using the Jordan-Wigner or Bravyi-Kitaev
transformation.
Args:
hf_file (str): absolute path to the hdf5-formatted file with the
Hartree-Fock electronic structure
mapping (str): Specifies the transformation to map the fermionic Hamiltonian to the
Pauli basis. Input values can be ``'jordan_wigner'`` or ``'bravyi_kitaev'``.
core (list): indices of core orbitals, i.e., the orbitals that are
not correlated in the many-body wave function
active (list): indices of active orbitals, i.e., the orbitals used to
build the correlated many-body wave function
Returns:
QubitOperator: an instance of OpenFermion's ``QubitOperator``
**Example**
>>> decompose('./pyscf/sto-3g/h2', mapping='bravyi_kitaev')
(-0.04207897696293986+0j) [] + (0.04475014401986122+0j) [X0 Z1 X2] +
(0.04475014401986122+0j) [X0 Z1 X2 Z3] +(0.04475014401986122+0j) [Y0 Z1 Y2] +
(0.04475014401986122+0j) [Y0 Z1 Y2 Z3] +(0.17771287459806262+0j) [Z0] +
(0.17771287459806265+0j) [Z0 Z1] +(0.1676831945625423+0j) [Z0 Z1 Z2] +
(0.1676831945625423+0j) [Z0 Z1 Z2 Z3] +(0.12293305054268105+0j) [Z0 Z2] +
(0.12293305054268105+0j) [Z0 Z2 Z3] +(0.1705973832722409+0j) [Z1] +
(-0.2427428049645989+0j) [Z1 Z2 Z3] +(0.1762764080276107+0j) [Z1 Z3] +
(-0.2427428049645989+0j) [Z2]
"""
# loading HF data from the hdf5 file
molecule = MolecularData(filename=hf_file.strip())
# getting the terms entering the second-quantized Hamiltonian
terms_molecular_hamiltonian = molecule.get_molecular_hamiltonian(
occupied_indices=core, active_indices=active
)
# generating the fermionic Hamiltonian
fermionic_hamiltonian = get_fermion_operator(terms_molecular_hamiltonian)
mapping = mapping.strip().lower()
if mapping not in ("jordan_wigner", "bravyi_kitaev"):
raise TypeError(
"The '{}' transformation is not available. \n "
"Please set 'mapping' to 'jordan_wigner' or 'bravyi_kitaev'.".format(mapping)
)
# fermionic-to-qubit transformation of the Hamiltonian
if mapping == "bravyi_kitaev":
return bravyi_kitaev(fermionic_hamiltonian)
return jordan_wigner(fermionic_hamiltonian)
MolecularMeta = {}
molecule = MolecularData(geometry,
basis,
multiplicity,
description=str(round(bond_length, 2)))
molecule = run_pyscf(molecule, run_scf=run_scf)
# Basic information
jim = molecule.name
print("===== Molecule {} =====".format(jim))
MolecularMeta['Name'] = jim
MolecularMeta['Geo'] = bond_length
# Hamiltonian
ham_qubit = jordan_wigner(molecule.get_molecular_hamiltonian())
ham_qubit.compress() # Now in QubitOperator form
ham_sparse = qubit_operator_sparse(ham_qubit, n_qubits=molecule.n_qubits)
print(' HF:', molecule.hf_energy)
MolecularMeta['FCI eigenstates'] = run_FCI(molecule, vqd_maxiter + 8)
# Generate operator pool
if not isinstance(SymbolicAnsatz, Circuit):
pool.init(n_orb=molecule.n_orbitals,
n_occ=molecule.get_n_alpha_electrons(),
n_vir=molecule.n_orbitals - molecule.get_n_alpha_electrons())
opt_eigen_ops = [
] # list of sublists (index of operators used in each eigenstate ansatz)
opt_eigen_params = [
def get_ham_from_psi4(
wfn, mints, ndocc=None, nact=None, nuclear_repulsion_energy=0,
):
"""Get a molecular Hamiltonian from a Psi4 calculation.
Args:
wfn (psi4.core.Wavefunction): Psi4 wavefunction object
mints (psi4.core.MintsHelper): Psi4 molecular integrals helper
ndocc (int): number of doubly occupied molecular orbitals to
include in the saved Hamiltonian.
nact (int): number of active molecular orbitals to include in the
saved Hamiltonian.
nuclear_repulsion_energy (float): The ion-ion interaction energy.
Returns:
hamiltonian (openfermion.ops.InteractionOperator): the electronic
Hamiltonian.
"""
assert wfn.same_a_b_orbs(), (
"Extraction of Hamiltonian from wavefunction"
+ "with different alpha and beta orbitals not yet supported :("
)
orbitals = wfn.Ca().to_array(dense=True)
if nact is None and ndocc is None:
trf_mat = orbitals
ndocc = 0
nact = orbitals.shape[1]
print(
f"Active space selection options were reset to: ndocc = {ndocc} and nact = {nact}"
)
elif nact is not None and ndocc is None:
assert nact <= orbitals.shape[1]
ndocc = 0
trf_mat = orbitals[:, :nact]
print(
f"Active space selection options were reset to: ndocc = {ndocc} and nact = {nact}"
)
elif ndocc is not None and nact is None:
assert ndocc <= orbitals.shape[1]
nact = orbitals.shape[1] - ndocc
trf_mat = orbitals
print(
f"Active space selection options were reset to: ndocc = {ndocc} and nact = {nact}"
)
else:
assert orbitals.shape[1] >= nact + ndocc
trf_mat = orbitals[:, : nact + ndocc]
# Note: code refactored to use Psi4 integral-transformation routines
# no more storing the whole two-electron integral tensor when only an
# active space is needed
one_body_integrals = general_basis_change(
np.asarray(mints.ao_kinetic()), orbitals, (1, 0)
)
one_body_integrals += general_basis_change(
np.asarray(mints.ao_potential()), orbitals, (1, 0)
)
# Build the transformation matrices, i.e. the orbitals for which
# we want the integrals, as Psi4.core.Matrix objects
trf_mat = psi4.core.Matrix.from_array(trf_mat)
two_body_integrals = np.asarray(mints.mo_eri(trf_mat, trf_mat, trf_mat, trf_mat))
n_orbitals = trf_mat.shape[1]
two_body_integrals.reshape((n_orbitals, n_orbitals, n_orbitals, n_orbitals))
two_body_integrals = np.einsum("psqr", two_body_integrals)
# Truncate
one_body_integrals[np.absolute(one_body_integrals) < EQ_TOLERANCE] = 0.0
two_body_integrals[np.absolute(two_body_integrals) < EQ_TOLERANCE] = 0.0
occupied_indices = range(ndocc)
active_indices = range(ndocc, ndocc + nact)
# In order to keep the MolecularData class happy, we need a 'valid' molecule
molecular_data = MolecularData(
geometry=[("H", (0, 0, 0))], basis="", multiplicity=2
)
molecular_data.one_body_integrals = one_body_integrals
molecular_data.two_body_integrals = two_body_integrals
molecular_data.nuclear_repulsion = nuclear_repulsion_energy
hamiltonian = molecular_data.get_molecular_hamiltonian(
occupied_indices, active_indices
)
return hamiltonian
def get_ham_from_psi4(wfn,
mints,
n_active_extract=None,
freeze_core_extract=False,
orbs=None,
nuclear_repulsion_energy=0):
"""Get a molecular Hamiltonian from a Psi4 calculation.
Args:
wfn (psi4.core.Wavefunction): Psi4 wavefunction object
mints (psi4.core.MintsHelper): Psi4 molecular integrals helper
n_active_extract (int): number of molecular orbitals to include in the
saved Hamiltonian. If None, includes all orbitals, else you must provide
active orbitals in orbs.
freeze_core_extract (bool): whether to freeze core orbitals as doubly
occupied in the saved Hamiltonian.
orbs (psi4.core.Matrix): Psi4 orbitals for active space transformations. Must
include all occupied (also core in all cases).
nuclear_repulsion_energy (float): The ion-ion interaction energy.
Returns:
hamiltonian (openfermion.ops.InteractionOperator): the electronic
Hamiltonian. Note that the ion-ion electrostatic energy is not
included.
"""
assert wfn.same_a_b_orbs(), "Extraction of Hamiltonian from wavefunction" + \
"with different alpha and beta orbitals not yet supported :("
# Note: code refactored to use Psi4 integral-transformation routines
# no more storing the whole two-electron integral tensor when only an
# active space is needed
orbitals = wfn.Ca().to_array(dense=True)
one_body_integrals = general_basis_change(np.asarray(mints.ao_kinetic()),
orbitals, (1, 0))
one_body_integrals += general_basis_change(
np.asarray(mints.ao_potential()), orbitals, (1, 0))
# Build the transformation matrices, i.e. the orbitals for which
# we want the integrals, as Psi4.core.Matrix objects
n_core_extract = 0
if freeze_core_extract:
n_core_extract = wfn.nfrzc()
if n_active_extract is None:
trf_mat = wfn.Ca()
n_active_extract = wfn.nmo() - n_core_extract
else:
# If orbs is given, it allows us to perform the two-electron integrals
# transformation only in the space of active orbitals. Otherwise, we
# transform all orbitals and filter them out in the get_ham_from_integrals
# function
if orbs is None:
trf_mat = wfn.Ca()
else:
assert (orbs.to_array(dense=True).shape[1] == n_active_extract +
n_core_extract)
trf_mat = orbs
two_body_integrals = np.asarray(
mints.mo_eri(trf_mat, trf_mat, trf_mat, trf_mat))
n_orbitals = trf_mat.shape[1]
two_body_integrals.reshape(
(n_orbitals, n_orbitals, n_orbitals, n_orbitals))
two_body_integrals = np.einsum('psqr', two_body_integrals)
# Truncate
one_body_integrals[np.absolute(one_body_integrals) < EQ_TOLERANCE] = 0.
two_body_integrals[np.absolute(two_body_integrals) < EQ_TOLERANCE] = 0.
if n_active_extract is None and not freeze_core_extract:
occupied_indices = None
active_indices = None
else:
# Indices of occupied molecular orbitals
occupied_indices = range(n_core_extract)
# Indices of active molecular orbitals
active_indices = range(n_core_extract,
n_core_extract + n_active_extract)
# In order to keep the MolecularData class happy, we need a 'valid' molecule
molecular_data = MolecularData(geometry=[('H', (0, 0, 0))],
basis='',
multiplicity=2)
molecular_data.one_body_integrals = one_body_integrals
molecular_data.two_body_integrals = two_body_integrals
molecular_data.nuclear_repulsion = nuclear_repulsion_energy
hamiltonian = molecular_data.get_molecular_hamiltonian(
occupied_indices, active_indices)
return (hamiltonian)