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)
def build_lih_moleculardata() -> MolecularData:
"""Returns LiH molecular data."""
geometry = [("Li", (0.0, 0.0, 0.0)), ("H", (0.0, 0.0, 1.45))]
basis = "sto-3g"
multiplicity = 1
filename = os.path.join(
fud.__file__.replace("__init__.py", ""),
"H1-Li1_sto-3g_singlet_1.45.hdf5",
)
molecule = MolecularData(geometry, basis, multiplicity, filename=filename)
molecule.load()
return molecule
def _generate_molecule(self, p: IParameter) -> MolecularData:
"""Produce molecule that can be used by the hamiltonian.
Using a singlet state with S = 0 to specify we are looking for the lowest singlet energy state.
multiplicity = 2S + 1
"""
geometry = [('H', (0., 0., 0.)), ('H', (0., 0., p['r0']))]
basis = 'sto-3g'
multiplicity = 1
charge = 0
description = str(p['r0'])
# Change to whatever directory you want
cwd = os.getcwd()
data_directory = cwd+'/mol_data'
if not os.path.exists(data_directory):
os.mkdir(data_directory)
filename = data_directory+'/H2_'+description
run_scf = 1
run_mp2 = 1
run_cisd = 1
run_ccsd = 1
run_fci = 1
delete_input = False
delete_output = False
verbose = False
molecule = MolecularData(
geometry,
basis,
multiplicity,
description=description,
filename=filename)
if os.path.exists('{}.hdf5'.format(filename)):
molecule.load()
else:
molecule = run_psi4(molecule,
verbose=verbose,
run_scf=run_scf,
run_mp2=run_mp2,
run_cisd=run_cisd,
run_ccsd=run_ccsd,
run_fci=run_fci)
# print(f'Reference (Full Configuration Energy: {molecule.fci_energy})')
return molecule
def build_h4square_moleculardata() -> MolecularData:
"""Returns H4 molecular data."""
geometry = [
("H", [0.5, 0.5, 0]),
("H", [0.5, -0.5, 0]),
("H", [-0.5, 0.5, 0]),
("H", [-0.5, -0.5, 0]),
]
basis = "sto-3g"
multiplicity = 1
filename = os.path.join(fud.__file__.replace("__init__.py", ""),
"H4_sto-3g_singlet.hdf5")
molecule = MolecularData(geometry, basis, multiplicity, filename=filename)
molecule.load()
return molecule
def generate_molecular_hamiltonian_mod(guess, geometry, basis, multiplicity,
charge=0, n_active_electrons=None,
n_active_orbitals=None):
"""Function
Old subroutine to get molecular hamiltonian by using pyscf.
Author(s): Takashi Tsuchimochi
"""
# Run electronic structure calculations
molecule, pyscf_mol \
= run_pyscf_mod(guess, n_active_orbitals, n_active_electrons,
MolecularData(geometry, basis, multiplicity, charge,
data_directory=cf.input_dir))
# Freeze core orbitals and truncate to active space
if n_active_electrons is None:
n_core_orbitals = 0
occupied_indices = None
else:
n_core_orbitals = (molecule.n_electrons-n_active_electrons)//2
occupied_indices = list(range(n_core_orbitals))
if n_active_orbitals is None:
active_indices = None
else:
active_indices = list(range(n_core_orbitals,
n_core_orbitals+n_active_orbitals))
return molecule.get_molecular_hamiltonian(occupied_indices=occupied_indices,
active_indices=active_indices)
def test_rhf_min():
filename = os.path.join(DATA_DIRECTORY, "H2_sto-3g_singlet_0.7414.hdf5")
molecule = MolecularData(filename=filename)
overlap = molecule.overlap_integrals
mo_obi = molecule.one_body_integrals
mo_tbi = molecule.two_body_integrals
rotation_mat = molecule.canonical_orbitals.T.dot(overlap)
obi = general_basis_change(mo_obi, rotation_mat, (1, 0))
tbi = general_basis_change(mo_tbi, rotation_mat, (1, 1, 0, 0))
hff = HartreeFockFunctional(one_body_integrals=obi,
two_body_integrals=tbi,
overlap=overlap,
n_electrons=molecule.n_electrons,
model='rhf',
nuclear_repulsion=molecule.nuclear_repulsion)
result = rhf_minimization(hff)
assert isinstance(result, OptimizeResult)
result2 = rhf_minimization(hff,
initial_guess=np.array([0]),
sp_options={
'maxiter': 100,
'disp': False
})
assert isinstance(result2, OptimizeResult)
assert np.isclose(result2.fun, result.fun)
def vqe_fixed(vqe_strategy, vqe_tomography, vqe_method):
"""
Initialize a VQE experiment with a custom hamiltonian
given as constant input
"""
_vqe = None
if vqe_strategy == "custom_program":
custom_ham = PauliSum([PauliTerm(*x) for x in HAMILTONIAN])
_vqe = VQEexperiment(hamiltonian=custom_ham,
method=vqe_method,
strategy=vqe_strategy,
parametric=False,
tomography=vqe_tomography,
shotN=NSHOTS_INT)
elif vqe_strategy == "UCCSD":
cwd = os.path.abspath(os.path.dirname(__file__))
fname = os.path.join(cwd, "resources", "H2.hdf5")
molecule = MolecularData(filename=fname)
_vqe = VQEexperiment(molecule=molecule,
method=vqe_method,
strategy=vqe_strategy,
parametric=False,
tomography=vqe_tomography,
shotN=NSHOTS_INT)
return _vqe
def get_molecule(element_names, bond_len):
geometry = [[element_names[0], [0, 0, 0]],
[element_names[1], [0, 0, bond_len]]]
basis = 'sto-3g'
multiplicity = 1
description = '{:.2}'.format(bond_len)
data_directory = DATA_DIRECTORY
molecule = MolecularData(geometry,
basis,
multiplicity,
description=description,
data_directory=data_directory)
molecule.load()
return molecule
def test_d2_to_g2():
# this should test for correctness
filename = os.path.join(DATA_DIRECTORY, "H1-Li1_sto-3g_singlet_1.45.hdf5")
molecule = MolecularData(filename=filename)
molecule.load()
opdm = molecule.fci_one_rdm
tpdm = molecule.fci_two_rdm
phdm = map_two_pdm_to_particle_hole_dm(tpdm, opdm)
db = tpdm_to_phdm_mapping(molecule.n_qubits)
topdm = Tensor(tensor=opdm, name='ck')
ttpdm = Tensor(tensor=np.einsum('ijlk', tpdm), name='cckk')
tphdm = Tensor(tensor=np.einsum('ijlk', phdm), name='ckck')
mt = MultiTensor(tensors=[topdm, ttpdm, tphdm], dual_basis=db)
A, _, b = mt.synthesize_dual_basis()
vec_rdms = mt.vectorize_tensors()
assert np.isclose(np.linalg.norm(A.dot(vec_rdms) - b), 0)
def test_table_two_particle(name, core, active, v_op_exp):
r"""Test the FermionOperator built by the function `two_particle` of the `obs` module"""
hf_data = MolecularData(filename=os.path.join(ref_dir, name))
v_op = qchem.two_particle(hf_data.two_body_integrals, core=core, active=active)
assert v_op.terms == v_op_exp
def test_table_one_particle(core, active, t_op_exp):
r"""Test the correctness of the FermionOperator built by the `'one_particle'` function
of the `obs` module"""
hf = MolecularData(filename=os.path.join(ref_dir, "h2o_psi4"))
t_op = qchem.one_particle(hf.one_body_integrals, core=core, active=active)
assert t_op.terms == t_op_exp
def test_gradient_lih():
filename = os.path.join(DATA_DIRECTORY, "H1-Li1_sto-3g_singlet_1.45.hdf5")
molecule = MolecularData(filename=filename)
overlap = molecule.overlap_integrals
mo_obi = molecule.one_body_integrals
mo_tbi = molecule.two_body_integrals
rotation_mat = molecule.canonical_orbitals.T.dot(overlap)
obi = general_basis_change(mo_obi, rotation_mat, (1, 0))
tbi = general_basis_change(mo_tbi, rotation_mat, (1, 1, 0, 0))
hff = HartreeFockFunctional(one_body_integrals=obi,
two_body_integrals=tbi,
overlap=overlap,
n_electrons=molecule.n_electrons,
model='rhf',
nuclear_repulsion=molecule.nuclear_repulsion)
params = np.random.randn(hff.nocc * hff.nvirt)
u = sp.linalg.expm(
rhf_params_to_matrix(params,
hff.num_orbitals,
occ=hff.occ,
virt=hff.virt))
grad_dim = hff.nocc * hff.nvirt
initial_opdm = np.diag([1] * hff.nocc + [0] * hff.nvirt)
final_opdm = u.dot(initial_opdm).dot(u.conj().T)
grad = hff.rhf_global_gradient(params, final_opdm)
# get finite difference gradient
finite_diff_grad = np.zeros(grad_dim)
epsilon = 0.0001
for i in range(grad_dim):
params_epsilon = params.copy()
params_epsilon[i] += epsilon
u = sp.linalg.expm(
rhf_params_to_matrix(params_epsilon,
hff.num_orbitals,
occ=hff.occ,
virt=hff.virt))
tfinal_opdm = u.dot(initial_opdm).dot(u.conj().T)
energy_plus_epsilon = hff.energy_from_rhf_opdm(tfinal_opdm)
params_epsilon[i] -= 2 * epsilon
u = sp.linalg.expm(
rhf_params_to_matrix(params_epsilon,
hff.num_orbitals,
occ=hff.occ,
virt=hff.virt))
tfinal_opdm = u.dot(initial_opdm).dot(u.conj().T)
energy_minus_epsilon = hff.energy_from_rhf_opdm(tfinal_opdm)
finite_diff_grad[i] = (energy_plus_epsilon -
energy_minus_epsilon) / (2 * epsilon)
assert np.allclose(finite_diff_grad, grad, atol=epsilon)
def test_generate_hamiltonian():
filename = os.path.join(DATA_DIRECTORY, "H1-Li1_sto-3g_singlet_1.45.hdf5")
molecule = MolecularData(filename=filename)
mo_obi = molecule.one_body_integrals
mo_tbi = molecule.two_body_integrals
mol_ham = generate_hamiltonian(mo_obi, mo_tbi, constant=0)
assert isinstance(mol_ham, InteractionOperator)
assert np.allclose(mol_ham.one_body_tensor[::2, ::2], mo_obi)
assert np.allclose(mol_ham.one_body_tensor[1::2, 1::2], mo_obi)
assert np.allclose(mol_ham.two_body_tensor[::2, ::2, ::2, ::2],
0.5 * mo_tbi)
assert np.allclose(mol_ham.two_body_tensor[1::2, 1::2, 1::2, 1::2],
0.5 * mo_tbi)
def test_inconsistent_active_spaces(mol_name, act_electrons, act_orbitals,
message_match):
r"""Test that an error is raised if an inconsistent active space is generated"""
molecule = MolecularData(filename=os.path.join(ref_dir, mol_name))
with pytest.raises(ValueError, match=message_match):
qchem.active_space(
molecule.n_electrons,
molecule.n_orbitals,
mult=molecule.multiplicity,
active_electrons=act_electrons,
active_orbitals=act_orbitals,
)
def test_moleculardata_to_restricted_hamiltonian(self):
"""
Convert an OpenFermion MolecularData object to a
fqe.RestrictedHamiltonian
"""
h1e, h2e, _ = build_lih_data('energy')
# dummy geometry
geometry = [['Li', [0, 0, 0], ['H', [0, 0, 1.4]]]]
charge = 0
multiplicity = 1
molecule = MolecularData(geometry=geometry,
basis='sto-3g',
charge=charge,
multiplicity=multiplicity)
molecule.one_body_integrals = h1e
molecule.two_body_integrals = numpy.einsum('ijlk', -2 * h2e)
molecule.nuclear_repulsion = 0
restricted_ham = openfermion_utils.molecular_data_to_restricted_fqe_op(
molecule=molecule)
h1e_test, h2e_test = restricted_ham.tensors()
self.assertTrue(numpy.allclose(h1e_test, h1e))
self.assertTrue(numpy.allclose(h2e_test, h2e))
def generate_molecular_hamiltonian(
geometry,
basis,
multiplicity,
charge=0,
n_active_electrons=None,
n_active_orbitals=None):
"""Generate a molecular Hamiltonian with the given properties.
Args:
geometry: A list of tuples giving the coordinates of each atom.
An example is [('H', (0, 0, 0)), ('H', (0, 0, 0.7414))].
Distances in angstrom. Use atomic symbols to
specify atoms.
basis: A string giving the basis set. An example is 'cc-pvtz'.
Only optional if loading from file.
multiplicity: An integer giving the spin multiplicity.
charge: An integer giving the charge.
n_active_electrons: An optional integer specifying the number of
electrons desired in the active space.
n_active_orbitals: An optional integer specifying the number of
spatial orbitals desired in the active space.
Returns:
The Hamiltonian as an InteractionOperator.
"""
# Run electronic structure calculations
molecule = run_pyscf(
MolecularData(geometry, basis, multiplicity, charge)
)
# Freeze core orbitals and truncate to active space
if n_active_electrons is None:
n_core_orbitals = 0
occupied_indices = None
else:
n_core_orbitals = (molecule.n_electrons - n_active_electrons) // 2
occupied_indices = list(range(n_core_orbitals))
if n_active_orbitals is None:
active_indices = None
else:
active_indices = list(range(n_core_orbitals,
n_core_orbitals + n_active_orbitals))
return molecule.get_molecular_hamiltonian(
occupied_indices=occupied_indices,
active_indices=active_indices)
def test_active_spaces(mol_name, act_electrons, act_orbitals, core_ref,
active_ref):
r"""Test the correctness of the generated active spaces"""
molecule = MolecularData(filename=os.path.join(ref_dir, mol_name))
core, active = qchem.active_space(
molecule.n_electrons,
molecule.n_orbitals,
mult=molecule.multiplicity,
active_electrons=act_electrons,
active_orbitals=act_orbitals,
)
assert core == core_ref
assert active == active_ref
def test_hf_calculations(package, tmpdir, psi4_support, tol):
r"""Test the correctness of the HF calculation"""
if package == "Psi4" and not psi4_support:
pytest.skip("Skipped, no Psi4 support")
n_atoms = 2
n_electrons = 2
n_orbitals = 2
hf_energy = -1.1173490350703152
orbital_energies = np.array([-0.59546347, 0.71416528])
one_body_integrals = np.array([[-1.27785300e00, 1.11022302e-16],
[0.00000000e00, -4.48299698e-01]])
two_body_integrals = np.array([
[
[[6.82389533e-01, 0.00000000e00], [6.93889390e-17,
1.79000576e-01]],
[[4.16333634e-17, 1.79000576e-01], [6.70732778e-01,
0.00000000e00]],
],
[
[[5.55111512e-17, 6.70732778e-01],
[1.79000576e-01, 1.11022302e-16]],
[[1.79000576e-01, 0.00000000e00], [2.77555756e-17,
7.05105632e-01]],
],
])
fullpath = qchem.meanfield(symbols,
coordinates,
name=name,
package=package,
outpath=tmpdir.strpath)
molecule = MolecularData(filename=fullpath)
assert molecule.n_atoms == n_atoms
assert molecule.n_electrons == n_electrons
assert molecule.n_orbitals == n_orbitals
assert np.allclose(molecule.hf_energy, hf_energy, **tol)
assert np.allclose(molecule.orbital_energies, orbital_energies, **tol)
assert np.allclose(molecule.one_body_integrals, one_body_integrals, **tol)
assert np.allclose(molecule.two_body_integrals, two_body_integrals, **tol)
def test_rhf_func_generator():
filename = os.path.join(DATA_DIRECTORY, "H1-Li1_sto-3g_singlet_1.45.hdf5")
molecule = MolecularData(filename=filename)
overlap = molecule.overlap_integrals
mo_obi = molecule.one_body_integrals
mo_tbi = molecule.two_body_integrals
rotation_mat = molecule.canonical_orbitals.T.dot(overlap)
obi = general_basis_change(mo_obi, rotation_mat, (1, 0))
tbi = general_basis_change(mo_tbi, rotation_mat, (1, 1, 0, 0))
hff = HartreeFockFunctional(one_body_integrals=obi,
two_body_integrals=tbi,
overlap=overlap,
n_electrons=molecule.n_electrons,
model='rhf',
nuclear_repulsion=molecule.nuclear_repulsion)
unitary, energy, gradient = rhf_func_generator(hff)
assert isinstance(unitary, Callable)
assert isinstance(energy, Callable)
assert isinstance(gradient, Callable)
params = np.random.randn(hff.nocc * hff.nvirt)
u = unitary(params)
assert np.allclose(u.conj().T.dot(u), np.eye(hff.num_orbitals))
assert isinstance(energy(params), float)
assert isinstance(gradient(params), np.ndarray)
_, _, _, opdm_func = rhf_func_generator(hff, get_opdm_func=True)
assert isinstance(opdm_func, Callable)
assert isinstance(opdm_func(params), np.ndarray)
assert np.isclose(opdm_func(params).shape[0], hff.num_orbitals)
_, energy, _ = rhf_func_generator(hff,
init_occ_vec=np.array([1, 1, 1, 1, 0,
0]))
assert isinstance(energy(params), float)
)
print(" VQD")
print(
" --------------------------------------------------------------------------"
)
molecules = []
SymbolicAnsatz = None
for point in [3.0]: #range(1, n_points + 1):
bond_length = point #bond_length_interval * float(point) + 0.2
geometry = [('Li', (0., 0., 0.)), ('H', (0., 0., bond_length))]
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)
def molecular_hamiltonian(
name,
geo_file,
charge=0,
mult=1,
basis="sto-3g",
package="pyscf",
active_electrons=None,
active_orbitals=None,
mapping="jordan_wigner",
outpath=".",
wires=None,
): # pylint:disable=too-many-arguments
r"""Generates the qubit Hamiltonian of a molecule.
This function drives the construction of the second-quantized electronic Hamiltonian
of a molecule and its transformation to the basis of Pauli matrices.
#. The process begins by reading the file containing the geometry of the molecule.
#. OpenFermion-PySCF or OpenFermion-Psi4 plugins are used to launch
the Hartree-Fock (HF) calculation for the polyatomic system using the quantum
chemistry package ``PySCF`` or ``Psi4``, respectively.
- The net charge of the molecule can be given to simulate
cationic/anionic systems. Also, the spin multiplicity can be input
to determine the number of unpaired electrons occupying the HF orbitals
as illustrated in the left panel of the figure below.
- The basis of Gaussian-type *atomic* orbitals used to represent the *molecular* orbitals
can be specified to go beyond the minimum basis approximation. Basis set availability
per element can be found
`here <www.psicode.org/psi4manual/master/basissets_byelement.html#apdx-basiselement>`_
#. An active space can be defined for a given number of *active electrons*
occupying a reduced set of *active orbitals* in the vicinity of the frontier
orbitals as sketched in the right panel of the figure below.
#. Finally, the second-quantized Hamiltonian is mapped to the Pauli basis and
converted to a PennyLane observable.
|
.. figure:: ../../_static/qchem/fig_mult_active_space.png
:align: center
:width: 90%
|
Args:
name (str): name of the molecule
geo_file (str): file containing the geometry of the molecule
charge (int): Net charge of the molecule. If not specified a a neutral system is assumed.
mult (int): Spin multiplicity :math:`\mathrm{mult}=N_\mathrm{unpaired} + 1`
for :math:`N_\mathrm{unpaired}` unpaired electrons occupying the HF orbitals.
Possible values of ``mult`` are :math:`1, 2, 3, \ldots`. If not specified,
a closed-shell HF state is assumed.
basis (str): Atomic basis set used to represent the molecular orbitals. Basis set
availability per element can be found
`here <www.psicode.org/psi4manual/master/basissets_byelement.html#apdx-basiselement>`_
package (str): quantum chemistry package (pyscf or psi4) used to solve the
mean field electronic structure problem
active_electrons (int): Number of active electrons. If not specified, all electrons
are considered to be active.
active_orbitals (int): Number of active orbitals. If not specified, all orbitals
are considered to be active.
mapping (str): transformation (``'jordan_wigner'`` or ``'bravyi_kitaev'``) used to
map the fermionic Hamiltonian to the qubit Hamiltonian
outpath (str): path to the directory containing output files
wires (Wires, list, tuple, dict): Custom wire mapping for connecting to Pennylane ansatz.
For types Wires/list/tuple, each item in the iterable represents a wire label
corresponding to the qubit number equal to its index.
For type dict, only int-keyed dict (for qubit-to-wire conversion) is accepted for
partial mapping. If None, will use identity map.
Returns:
tuple[pennylane.Hamiltonian, int]: the fermionic-to-qubit transformed Hamiltonian
and the number of qubits
**Example**
>>> name = "h2"
>>> geo_file = "h2.xyz"
>>> H, qubits = molecular_hamiltonian(name, geo_file)
>>> print(qubits)
4
>>> print(H)
(-0.04207897647782188) [I0]
+ (0.17771287465139934) [Z0]
+ (0.1777128746513993) [Z1]
+ (-0.24274280513140484) [Z2]
+ (-0.24274280513140484) [Z3]
+ (0.17059738328801055) [Z0 Z1]
+ (0.04475014401535161) [Y0 X1 X2 Y3]
+ (-0.04475014401535161) [Y0 Y1 X2 X3]
+ (-0.04475014401535161) [X0 X1 Y2 Y3]
+ (0.04475014401535161) [X0 Y1 Y2 X3]
+ (0.12293305056183801) [Z0 Z2]
+ (0.1676831945771896) [Z0 Z3]
+ (0.1676831945771896) [Z1 Z2]
+ (0.12293305056183801) [Z1 Z3]
+ (0.176276408043196) [Z2 Z3]
"""
geometry = read_structure(geo_file, outpath)
hf_file = meanfield(name, geometry, charge, mult, basis, package, outpath)
molecule = MolecularData(filename=hf_file)
core, active = active_space(
molecule.n_electrons, molecule.n_orbitals, mult, active_electrons, active_orbitals
)
h_of, qubits = (decompose(hf_file, mapping, core, active), 2 * len(active))
return convert_observable(h_of, wires=wires), qubits
basis = 'sto-3g' # Orbital basis set
multiplicity = 1 # Spin of reference determinant
n_points = 60 # Number of geometries
bond_length_interval = 4.0 / n_points
run_scf = 1
run_ccsd = 1
molecules = []
for point in range(1, n_points + 1):
bond_length = bond_length_interval * float(point) + 0.2
geometry = [('H', (0., 0., 0.)), ('Li', (0., 0., bond_length))]
MolecularMeta = {}
molecule = MolecularData(geometry,
basis,
multiplicity,
description=str(round(bond_length, 2)))
molecule = run_pyscf(molecule, run_scf=run_scf)
MolecularMeta['Geo'] = bond_length
MolecularMeta['FCI eigenstates'] = run_FCI(molecule, roots=8)
molecules.append(MolecularMeta)
with open('FCI_H1-Li1_sto-3g.json', 'w') as json_file:
json.dump(molecules, json_file)
def meanfield(
name, geometry, charge=0, mult=1, basis="sto-3g", package="pyscf", outpath="."
): # pylint: disable=too-many-arguments
r"""Generates a file from which the mean field electronic structure
of the molecule can be retrieved.
This function uses OpenFermion-PySCF and OpenFermion-Psi4 plugins to
perform the Hartree-Fock (HF) calculation for the polyatomic system using the quantum
chemistry packages ``PySCF`` and ``Psi4``, respectively. The mean field electronic
structure is saved in an hdf5-formatted file in the directory
``os.path.join(outpath, package, basis)``.
The charge of the molecule can be given to simulate cationic/anionic systems.
Also, the spin multiplicity can be input to determine the number of unpaired electrons
occupying the HF orbitals as illustrated in the figure below.
|
.. figure:: ../../_static/qchem/hf_references.png
:align: center
:width: 50%
|
Args:
name (str): molecule label
geometry (list): list containing the symbol and Cartesian coordinates for each atom
charge (int): net charge of the system
mult (int): Spin multiplicity :math:`\mathrm{mult}=N_\mathrm{unpaired} + 1` for
:math:`N_\mathrm{unpaired}` unpaired electrons occupying the HF orbitals.
Possible values for ``mult`` are :math:`1, 2, 3, \ldots`. If not specified,
a closed-shell HF state is assumed.
basis (str): Atomic basis set used to represent the HF orbitals. Basis set
availability per element can be found
`here <www.psicode.org/psi4manual/master/basissets_byelement.html#apdx-basiselement>`_
package (str): Quantum chemistry package used to solve the Hartree-Fock equations.
Either ``'pyscf'`` or ``'psi4'`` can be used.
outpath (str): path to output directory
Returns:
str: absolute path to the file containing the mean field electronic structure
**Example**
>>> name = 'h2'
>>> geometry = [['H', (0.0, 0.0, -0.35)], ['H', (0.0, 0.0, 0.35)]]
>>> meanfield(name, geometry)
./pyscf/sto-3g/h2
"""
package = package.strip().lower()
if package not in ("psi4", "pyscf"):
error_message = (
"Integration with quantum chemistry package '{}' is not available. \n Please set"
" 'package' to 'pyscf' or 'psi4'.".format(package)
)
raise TypeError(error_message)
package_dir = os.path.join(outpath.strip(), package)
basis_dir = os.path.join(package_dir, basis.strip())
if not os.path.isdir(package_dir):
os.mkdir(package_dir)
os.mkdir(basis_dir)
elif not os.path.isdir(basis_dir):
os.mkdir(basis_dir)
path_to_file = os.path.join(basis_dir, name.strip())
molecule = MolecularData(geometry, basis, mult, charge, filename=path_to_file)
if package == "psi4":
run_psi4(molecule, run_scf=1, verbose=0, tolerate_error=1)
if package == "pyscf":
run_pyscf(molecule, run_scf=1, verbose=0)
return path_to_file
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)
def vqe_qc(vqe_strategy, vqe_qc_backend, vqe_parametricflag, sample_molecule):
"""
Initialize a VQE experiment with a custom hamiltonian
given as constant input, given a QC-type backend (tomography is always set to True then)
"""
_vqe = None
qc = None
vqe_cq = None
if vqe_strategy == "custom_program":
if vqe_qc_backend == 'Aspen-qvm':
qc = get_qc('Aspen-4-2Q-A-qvm')
vqe_cq = [1, 2]
elif vqe_qc_backend == 'Aspen-pyqvm':
qc = get_qc('Aspen-4-2Q-A-pyqvm')
vqe_cq = [1, 2]
elif vqe_qc_backend == 'Nq-qvm':
qc = get_qc('2q-qvm')
elif vqe_qc_backend == 'Nq-pyqvm':
qc = get_qc('2q-pyqvm')
custom_ham = PauliSum([PauliTerm(*x) for x in HAMILTONIAN])
_vqe = VQEexperiment(hamiltonian=custom_ham,
qc=qc,
custom_qubits=vqe_cq,
method='QC',
strategy=vqe_strategy,
parametric=True,
tomography=True,
shotN=NSHOTS_SMALL)
elif vqe_strategy == "HF":
if vqe_qc_backend == 'Aspen-qvm':
qc = get_qc('Aspen-4-2Q-A-qvm')
vqe_cq = [1, 2]
elif vqe_qc_backend == 'Aspen-pyqvm':
qc = get_qc('Aspen-4-2Q-A-pyqvm')
vqe_cq = [1, 2]
elif vqe_qc_backend == 'Nq-qvm':
qc = get_qc('2q-qvm')
elif vqe_qc_backend == 'Nq-pyqvm':
qc = get_qc('2q-pyqvm')
cwd = os.path.abspath(os.path.dirname(__file__))
fname = os.path.join(cwd, "resources", "H.hdf5")
molecule = MolecularData(filename=fname)
_vqe = VQEexperiment(molecule=molecule,
qc=qc,
custom_qubits=vqe_cq,
method='QC',
strategy=vqe_strategy,
parametric=vqe_parametricflag,
tomography=True,
shotN=NSHOTS_SMALL)
elif vqe_strategy == "UCCSD":
if vqe_qc_backend == 'Aspen-qvm':
qc = get_qc('Aspen-4-4Q-A-qvm')
vqe_cq = [7, 0, 1, 2]
elif vqe_qc_backend == 'Aspen-pyqvm':
qc = get_qc('Aspen-4-4Q-A-pyqvm')
vqe_cq = [7, 0, 1, 2]
elif vqe_qc_backend == 'Nq-qvm':
qc = get_qc('4q-qvm')
elif vqe_qc_backend == 'Nq-pyqvm':
qc = get_qc('4q-pyqvm')
_vqe = VQEexperiment(molecule=sample_molecule,
qc=qc,
custom_qubits=vqe_cq,
method='QC',
strategy=vqe_strategy,
parametric=vqe_parametricflag,
tomography=True,
shotN=NSHOTS_SMALL)
return _vqe
def sample_molecule():
cwd = os.path.abspath(os.path.dirname(__file__))
fname = os.path.join(cwd, "resources", "H2.hdf5")
molecule = MolecularData(filename=fname)
return molecule
def do_make_molecule(self, *args, **kwargs) -> MolecularData:
energy = self.compute_energy(method="hf", *args, **kwargs)
wfn = self.logs['hf'].wfn
molecule = MolecularData(**self.parameters.molecular_data_param)
if wfn.nirrep() != 1:
wfn = wfn.c1_deep_copy(wfn.basisset())
molecule.one_body_integrals = self.compute_one_body_integrals(
ref_wfn=wfn)
if "two_body_ordering" not in kwargs:
molecule.two_body_integrals = self.compute_two_body_integrals(
ref_wfn=wfn)
else:
molecule.two_body_integrals = self.compute_two_body_integrals(
ref_wfn=wfn, ordering=kwargs["two_body_ordering"])
molecule.hf_energy = energy
molecule.nuclear_repulsion = wfn.variables(
)['NUCLEAR REPULSION ENERGY']
molecule.canonical_orbitals = numpy.asarray(wfn.Ca())
molecule.overlap_integrals = numpy.asarray(wfn.S())
molecule.n_orbitals = molecule.canonical_orbitals.shape[0]
molecule.n_qubits = 2 * molecule.n_orbitals
molecule.orbital_energies = numpy.asarray(wfn.epsilon_a())
molecule.fock_matrix = numpy.asarray(wfn.Fa())
molecule.save()
return molecule
def do_make_molecule(self, molecule=None) -> MolecularData:
if molecule is None:
molecule = MolecularData(**self.parameters.molecular_data_param)
return run_pyscf(molecule, **self.parameters_pyscf.__dict__)
def meanfield(
symbols,
coordinates,
name="molecule",
charge=0,
mult=1,
basis="sto-3g",
package="pyscf",
outpath=".",
): # pylint: disable=too-many-arguments
r"""Generates a file from which the mean field electronic structure
of the molecule can be retrieved.
This function uses OpenFermion-PySCF and OpenFermion-Psi4 plugins to
perform the Hartree-Fock (HF) calculation for the polyatomic system using the quantum
chemistry packages ``PySCF`` and ``Psi4``, respectively. The mean field electronic
structure is saved in an hdf5-formatted file in the directory
``os.path.join(outpath, package, basis)``.
The charge of the molecule can be given to simulate cationic/anionic systems.
Also, the spin multiplicity can be input to determine the number of unpaired electrons
occupying the HF orbitals as illustrated in the figure below.
|
.. figure:: ../../_static/qchem/hf_references.png
:align: center
:width: 50%
|
Args:
symbols (list[str]): symbols of the atomic species in the molecule
coordinates (array[float]): 1D array with the atomic positions in Cartesian
coordinates. The coordinates must be given in atomic units and the size of the array
should be ``3*N`` where ``N`` is the number of atoms.
name (str): molecule label
charge (int): net charge of the system
mult (int): Spin multiplicity :math:`\mathrm{mult}=N_\mathrm{unpaired} + 1` for
:math:`N_\mathrm{unpaired}` unpaired electrons occupying the HF orbitals.
Possible values for ``mult`` are :math:`1, 2, 3, \ldots`. If not specified,
a closed-shell HF state is assumed.
basis (str): Atomic basis set used to represent the HF orbitals. Basis set
availability per element can be found
`here <www.psicode.org/psi4manual/master/basissets_byelement.html#apdx-basiselement>`_
package (str): Quantum chemistry package used to solve the Hartree-Fock equations.
Either ``'pyscf'`` or ``'psi4'`` can be used.
outpath (str): path to output directory
Returns:
str: absolute path to the file containing the mean field electronic structure
**Example**
>>> symbols, coordinates = (['H', 'H'], np.array([0., 0., -0.66140414, 0., 0., 0.66140414]))
>>> meanfield(symbols, coordinates, name="h2")
./pyscf/sto-3g/h2
"""
if coordinates.size != 3 * len(symbols):
raise ValueError(
"The size of the array 'coordinates' has to be 3*len(symbols) = {};"
" got 'coordinates.size' = {}".format(3 * len(symbols),
coordinates.size))
package = package.strip().lower()
if package not in ("psi4", "pyscf"):
error_message = (
"Integration with quantum chemistry package '{}' is not available. \n Please set"
" 'package' to 'pyscf' or 'psi4'.".format(package))
raise TypeError(error_message)
package_dir = os.path.join(outpath.strip(), package)
basis_dir = os.path.join(package_dir, basis.strip())
if not os.path.isdir(package_dir):
os.mkdir(package_dir)
os.mkdir(basis_dir)
elif not os.path.isdir(basis_dir):
os.mkdir(basis_dir)
path_to_file = os.path.join(basis_dir, name.strip())
geometry = [[symbol,
tuple(coordinates[3 * i:3 * i + 3] * bohr_angs)]
for i, symbol in enumerate(symbols)]
molecule = MolecularData(geometry,
basis,
mult,
charge,
filename=path_to_file)
if package == "psi4":
run_psi4(molecule, run_scf=1, verbose=0, tolerate_error=1)
if package == "pyscf":
run_pyscf(molecule, run_scf=1, verbose=0)
return path_to_file