def _fourier_transform_helper(hamiltonian, grid, spinless, phase_factor,
vec_func_1, vec_func_2):
hamiltonian_t = FermionOperator.zero()
normalize_factor = numpy.sqrt(1.0 / float(grid.num_points()))
for term in hamiltonian.terms:
transformed_term = FermionOperator.identity()
for ladder_op_mode, ladder_op_type in term:
indices_1 = grid_indices(ladder_op_mode, grid, spinless)
vec1 = vec_func_1(indices_1, grid)
new_basis = FermionOperator.zero()
for indices_2 in grid.all_points_indices():
vec2 = vec_func_2(indices_2, grid)
spin = None if spinless else ladder_op_mode % 2
orbital = orbital_id(grid, indices_2, spin)
exp_index = phase_factor * 1.0j * numpy.dot(vec1, vec2)
if ladder_op_type == 1:
exp_index *= -1.0
element = FermionOperator(((orbital, ladder_op_type), ),
numpy.exp(exp_index))
new_basis += element
new_basis *= normalize_factor
transformed_term *= new_basis
# Coefficient.
transformed_term *= hamiltonian.terms[term]
hamiltonian_t += transformed_term
return hamiltonian_t
def __init__(self, a=7.72, n=3, n_active_el=2, n_active_orb=4):
self.a = a
self.n = n
self.n_active_el = n_active_el
self.n_active_orb = n_active_orb
self.N_units = 4
self.opt_energy = None
self.opt_amplitudes = None
species_a = 'H'
species_b = 'Li'
# Construct a fermion Hamiltonian
grid = Grid(3, self.n, self.a)
geometry = [(species_a, (0, 0, 0)), (species_a, (0, 0.5, 0.5)),
(species_a, (0.5, 0, 0.5)), (species_a, (0.5, 0.5, 0)),
(species_b, (0.5, 0.5, 0.5)), (species_b, (0.5, 0, 0)),
(species_b, (0, 0.5, 0)), (species_b, (0, 0, 0.5))]
self.fermion_hamiltonian = plane_wave_hamiltonian(
grid,
geometry=geometry,
spinless=False,
plane_wave=False,
include_constant=False,
e_cutoff=None)
# Freeze specified orbitals
n_qubits = 2 * n * n * n
n_electrons = 4 * 3 + 4 * 1
# Determine the indices of occupied orbitals to be frozen
if self.n == 3:
to_fill = ((1, 1, 1), (0, 1, 1), (2, 1, 1), (1, 0, 1), (1, 2, 1),
(1, 1, 0), (1, 1, 2), (0, 0, 1))
else:
to_fill = range(n_electrons - self.n_active_el)
to_fill_ids = []
for s in to_fill:
to_fill_ids.append(orbital_id(grid, s, 0))
to_fill_ids.append(orbital_id(grid, s, 1))
to_fill_ids = to_fill_ids[0:(n_electrons - self.n_active_el)]
#print(to_fill_ids)
#print('# of terms: {}'.format(len(self.fermion_hamiltonian.terms)))
self.fermion_hamiltonian = freeze_orbitals(self.fermion_hamiltonian,
to_fill_ids)
#print('# of terms: {}'.format(len(self.fermion_hamiltonian.terms)))
# Freeze unoccupied orbitals
to_freeze_ids = range(self.n_active_orb,
n_qubits - (n_electrons - self.n_active_el))
#print(to_freeze_ids)
self.fermion_hamiltonian = freeze_orbitals(self.fermion_hamiltonian,
[], to_freeze_ids)
print('# of terms: {}'.format(len(self.fermion_hamiltonian.terms)))
# Construct qubit Hamiltonian
self.qubit_hamiltonian = jordan_wigner(self.fermion_hamiltonian)
# Initialize com;iler engine
self.compiler_engine = uccsd_trotter_engine()