def test_plane_wave_period_cutoff(self):
# TODO: After figuring out the correct formula for period cutoff for
# dual basis, change period_cutoff to default, and change
# h_1 to also accept period_cutoff for real integration test.
geometry = [('H', (0, )), ('H', (0.8, ))]
grid = Grid(dimensions=1, scale=1.1, length=5)
period_cutoff = 50.0
h_1 = plane_wave_hamiltonian(grid, geometry, True, True, False, None)
jw_1 = jordan_wigner(h_1)
spectrum_1 = eigenspectrum(jw_1)
h_2 = plane_wave_hamiltonian(grid, geometry, True, True, False, None,
True, period_cutoff)
jw_2 = jordan_wigner(h_2)
spectrum_2 = eigenspectrum(jw_2)
max_diff = numpy.amax(numpy.absolute(spectrum_1 - spectrum_2))
self.assertGreater(max_diff, 0.)
# TODO: This is only for code coverage. Remove after having real
# integration test.
h_3 = plane_wave_hamiltonian(grid, geometry, True, True, False, None,
True)
def test_plane_wave_hamiltonian_integration(self):
length_set = [3, 4]
spinless_set = [True, False]
geometry = [('H', (0, )), ('H', (0.8, ))]
length_scale = 1.1
for l in length_set:
for spinless in spinless_set:
grid = Grid(dimensions=1, scale=length_scale, length=l)
h_plane_wave = plane_wave_hamiltonian(grid,
geometry,
spinless,
True,
include_constant=True)
h_dual_basis = plane_wave_hamiltonian(grid, geometry, spinless,
False)
jw_h_plane_wave = jordan_wigner(h_plane_wave)
jw_h_dual_basis = jordan_wigner(h_dual_basis)
h_plane_wave_spectrum = eigenspectrum(jw_h_plane_wave)
h_dual_basis_spectrum = eigenspectrum(jw_h_dual_basis)
max_diff = numpy.amax(h_plane_wave_spectrum -
h_dual_basis_spectrum)
min_diff = numpy.amin(h_plane_wave_spectrum -
h_dual_basis_spectrum)
self.assertAlmostEqual(max_diff, 2.8372 / length_scale)
self.assertAlmostEqual(min_diff, 2.8372 / length_scale)
def test_model_integration_with_constant(self):
# Compute Hamiltonian in both momentum and position space.
length_scale = 0.7
for length in [2, 3]:
grid = Grid(dimensions=2, length=length, scale=length_scale)
spinless = True
# Include Madelung constant in the momentum but not the position
# Hamiltonian.
momentum_hamiltonian = jellium_model(grid,
spinless,
True,
include_constant=True)
position_hamiltonian = jellium_model(grid, spinless, False)
# Confirm they are Hermitian
momentum_hamiltonian_operator = (
get_sparse_operator(momentum_hamiltonian))
self.assertTrue(is_hermitian(momentum_hamiltonian_operator))
position_hamiltonian_operator = (
get_sparse_operator(position_hamiltonian))
self.assertTrue(is_hermitian(position_hamiltonian_operator))
# Diagonalize and confirm the same energy.
jw_momentum = jordan_wigner(momentum_hamiltonian)
jw_position = jordan_wigner(position_hamiltonian)
momentum_spectrum = eigenspectrum(jw_momentum)
position_spectrum = eigenspectrum(jw_position)
# Confirm momentum spectrum is shifted 2.8372/length_scale higher.
max_difference = numpy.amax(momentum_spectrum - position_spectrum)
min_difference = numpy.amax(momentum_spectrum - position_spectrum)
self.assertAlmostEqual(max_difference, 2.8372 / length_scale)
self.assertAlmostEqual(min_difference, 2.8372 / length_scale)
def test_plane_wave_hamiltonian_integration(self):
length_set = [2, 3, 4]
spinless_set = [True, False]
length_scale = 1.1
for geometry in [[('H', (0, )), ('H', (0.8, ))], [('H', (0.1, ))],
[('H', (0.1, ))]]:
for l in length_set:
for spinless in spinless_set:
grid = Grid(dimensions=1, scale=length_scale, length=l)
h_plane_wave = plane_wave_hamiltonian(
grid, geometry, spinless, True, include_constant=False)
h_dual_basis = plane_wave_hamiltonian(
grid,
geometry,
spinless,
False,
include_constant=False)
# Test for Hermiticity
plane_wave_operator = get_sparse_operator(h_plane_wave)
dual_operator = get_sparse_operator(h_dual_basis)
self.assertTrue(is_hermitian((plane_wave_operator)))
self.assertTrue(is_hermitian(dual_operator))
jw_h_plane_wave = jordan_wigner(h_plane_wave)
jw_h_dual_basis = jordan_wigner(h_dual_basis)
h_plane_wave_spectrum = eigenspectrum(jw_h_plane_wave)
h_dual_basis_spectrum = eigenspectrum(jw_h_dual_basis)
max_diff = numpy.amax(h_plane_wave_spectrum -
h_dual_basis_spectrum)
min_diff = numpy.amin(h_plane_wave_spectrum -
h_dual_basis_spectrum)
self.assertAlmostEqual(max_diff, 0)
self.assertAlmostEqual(min_diff, 0)
def test_plane_wave_energy_cutoff(self):
spinless = True
# [[spatial dimension, fieldline dimension]]
dims = [[2, 2], [2, 3], [3, 3]]
e_cutoff = 20.0
for dim in dims:
# If dim[0] == 2, get range(2, 4).
# If dim[0] == 3, get range(2, 3).
for length in range(2, 6 - dim[0]):
grid = Grid(dimensions=dim[0], length=length, scale=1.0)
hamiltonian_1 = jellium_model(grid,
spinless,
True,
False,
fieldlines=dim[1])
jw_1 = jordan_wigner(hamiltonian_1)
spectrum_1 = eigenspectrum(jw_1)
hamiltonian_2 = jellium_model(grid,
spinless,
True,
False,
e_cutoff,
fieldlines=dim[1])
jw_2 = jordan_wigner(hamiltonian_2)
spectrum_2 = eigenspectrum(jw_2)
max_diff = numpy.amax(numpy.absolute(spectrum_1 - spectrum_2))
self.assertGreater(max_diff, 0.)
def test_model_integration(self):
# Compute Hamiltonian in both momentum and position space.
for length in [2, 3]:
grid = Grid(dimensions=2, length=length, scale=1.0)
spinless = True
momentum_hamiltonian = jellium_model(grid, spinless, True)
position_hamiltonian = jellium_model(grid, spinless, False)
# Confirm they are Hermitian
momentum_hamiltonian_operator = (
get_sparse_operator(momentum_hamiltonian))
self.assertTrue(is_hermitian(momentum_hamiltonian_operator))
position_hamiltonian_operator = (
get_sparse_operator(position_hamiltonian))
self.assertTrue(is_hermitian(position_hamiltonian_operator))
# Diagonalize and confirm the same energy.
jw_momentum = jordan_wigner(momentum_hamiltonian)
jw_position = jordan_wigner(position_hamiltonian)
momentum_spectrum = eigenspectrum(jw_momentum)
position_spectrum = eigenspectrum(jw_position)
# Confirm spectra are the same.
difference = numpy.amax(
numpy.absolute(momentum_spectrum - position_spectrum))
self.assertAlmostEqual(difference, 0.)
def test_potential_integration(self):
# Compute potential energy operator in momentum and position space.
for length in [2, 3]:
grid = Grid(dimensions=2, length=length, scale=2.)
spinless = True
momentum_potential = plane_wave_potential(grid, spinless)
position_potential = dual_basis_potential(grid, spinless)
# Confirm they are Hermitian
momentum_potential_operator = (
get_sparse_operator(momentum_potential))
self.assertTrue(is_hermitian(momentum_potential_operator))
position_potential_operator = (
get_sparse_operator(position_potential))
self.assertTrue(is_hermitian(position_potential_operator))
# Diagonalize and confirm the same energy.
jw_momentum = jordan_wigner(momentum_potential)
jw_position = jordan_wigner(position_potential)
momentum_spectrum = eigenspectrum(jw_momentum)
position_spectrum = eigenspectrum(jw_position)
# Confirm spectra are the same.
difference = numpy.amax(
numpy.absolute(momentum_spectrum - position_spectrum))
self.assertAlmostEqual(difference, 0.)
def test_plane_wave_energy_cutoff(self):
'''
Key: Spatial dimension.
Value: List of geometries.
'''
geometry_sets = {
2: [[('H', (0., 0.)), ('H', (0.8, 0.))],
[('H', (0.1, 0.))]],
3: [[('H', (0., 0., 0.)), ('H', (0.8, 0., 0.))],
[('H', (0.1, 0., 0.))]]
}
# [[spatial dimension, fieldline dimension]]
dims = [[2, 2], [2, 3], [3, 3]]
spinless_set = [True, False]
e_cutoff = 20.0
for dim in dims:
for geometry in geometry_sets[dim[0]]:
for spinless in spinless_set:
grid = Grid(dimensions=dim[0], scale=1.1, length=2)
h_1 = plane_wave_hamiltonian(grid, geometry, True, True, False, fieldlines=dim[1])
jw_1 = jordan_wigner(h_1)
spectrum_1 = eigenspectrum(jw_1)
h_2 = plane_wave_hamiltonian(grid, geometry, True, True, False,
e_cutoff, fieldlines=dim[1])
jw_2 = jordan_wigner(h_2)
spectrum_2 = eigenspectrum(jw_2)
max_diff = numpy.amax(numpy.absolute(spectrum_1 - spectrum_2))
self.assertGreater(max_diff, 0.)
def test_bk_jw_majoranas(self):
# Check if the Majorana operators have the same spectrum
# irrespectively of the transform.
n_qubits = 7
a = FermionOperator(((1, 0),))
a_dag = FermionOperator(((1, 1),))
c = a + a_dag
d = 1j * (a_dag - a)
c_spins = [jordan_wigner(c), bravyi_kitaev_tree(c)]
d_spins = [jordan_wigner(d), bravyi_kitaev_tree(d)]
c_sparse = [get_sparse_operator(c_spins[0]),
get_sparse_operator(c_spins[1])]
d_sparse = [get_sparse_operator(d_spins[0]),
get_sparse_operator(d_spins[1])]
c_spectrum = [eigenspectrum(c_spins[0]),
eigenspectrum(c_spins[1])]
d_spectrum = [eigenspectrum(d_spins[0]),
eigenspectrum(d_spins[1])]
self.assertAlmostEqual(0., numpy.amax(numpy.absolute(d_spectrum[0] -
d_spectrum[1])))
def test_plane_wave_period_cutoff(self):
# TODO: After figuring out the correct formula for period cutoff for
# dual basis, change period_cutoff to default, and change
# hamiltonian_1 to a real jellium_model for real integration test.
grid = Grid(dimensions=2, length=2, scale=1.0)
spinless = True
period_cutoff = 0.
hamiltonian_1 = FermionOperator()
jw_1 = jordan_wigner(hamiltonian_1)
spectrum_1 = eigenspectrum(jw_1)
hamiltonian_2 = jellium_model(grid, spinless, True, False, None, True,
period_cutoff)
jw_2 = jordan_wigner(hamiltonian_2)
spectrum_2 = eigenspectrum(jw_2)
max_diff = numpy.amax(numpy.absolute(spectrum_1 - spectrum_2))
self.assertGreater(max_diff, 0.)
# TODO: This is only for code coverage. Remove after having real
# integration test.
jellium_model(grid, spinless, True, False, None, True)
jellium_model(grid, spinless, False, False, None, True)
def test_tapering_qubits_manual_input(self):
"""
Test taper_off_qubits function using LiH Hamiltonian.
Checks different qubits inputs to remove manually.
Test the lowest eigenvalue against the full Hamiltonian,
and the full spectrum between them.
"""
hamiltonian, spectrum = lih_hamiltonian()
qubit_hamiltonian = jordan_wigner(hamiltonian)
stab1 = QubitOperator('Z0 Z2', -1.0)
stab2 = QubitOperator('Z1 Z3', -1.0)
tapered_ham_0_3 = taper_off_qubits(qubit_hamiltonian, [stab1, stab2],
manual_input=True,
fixed_positions=[0, 3])
tapered_ham_2_1 = taper_off_qubits(qubit_hamiltonian, [stab1, stab2],
manual_input=True,
fixed_positions=[2, 1])
tapered_spectrum_0_3 = eigenspectrum(tapered_ham_0_3)
tapered_spectrum_2_1 = eigenspectrum(tapered_ham_2_1)
self.assertAlmostEqual(spectrum[0], tapered_spectrum_0_3[0])
self.assertAlmostEqual(spectrum[0], tapered_spectrum_2_1[0])
self.assertTrue(
numpy.allclose(tapered_spectrum_0_3, tapered_spectrum_2_1))
def test_bravyi_kitaev(self):
hamiltonian, gs_energy = lih_hamiltonian()
code = bravyi_kitaev_code(4)
qubit_hamiltonian = binary_code_transform(hamiltonian, code)
self.assertAlmostEqual(gs_energy, eigenspectrum(qubit_hamiltonian)[0])
qubit_spectrum = eigenspectrum(qubit_hamiltonian)
fenwick_spectrum = eigenspectrum(bravyi_kitaev(hamiltonian))
for eigen_idx, eigenvalue in enumerate(qubit_spectrum):
self.assertAlmostEqual(eigenvalue, fenwick_spectrum[eigen_idx])
def test_one_body_square_decomposition(self):
# Initialize H2 InteractionOperator.
n_qubits = 4
n_orbitals = 2
filename = os.path.join(THIS_DIRECTORY, 'data',
'H2_sto-3g_singlet_0.7414')
molecule = MolecularData(filename=filename)
molecule_interaction = molecule.get_molecular_hamiltonian()
fermion_operator = get_fermion_operator(molecule_interaction)
two_body_coefficients = molecule_interaction.two_body_tensor
# Decompose.
eigenvalues, one_body_squares, one_body_correction, error = (
low_rank_two_body_decomposition(two_body_coefficients))
rank = eigenvalues.size
for l in range(rank):
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.
if abs(eigenvalues[l]) < 1e-6:
with self.assertRaises(ValueError):
prepare_one_body_squared_evolution(one_body_squares[l])
continue
else:
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_eigenspectrum(self):
fermion_eigenspectrum = eigenspectrum(self.fermion_operator)
qubit_eigenspectrum = eigenspectrum(self.qubit_operator)
interaction_eigenspectrum = eigenspectrum(self.interaction_operator)
for i in range(2**self.n_qubits):
self.assertAlmostEqual(fermion_eigenspectrum[i],
qubit_eigenspectrum[i])
self.assertAlmostEqual(fermion_eigenspectrum[i],
interaction_eigenspectrum[i])
def test_nonperiodic_external_potential_integration(self):
# Compute potential energy operator in momentum and position space.
# Non-periodic test.
'''
Key: Spatial dimension.
Value: List of geometries.
'''
geometry_sets = {
2: [[('H', (0., 0.)), ('H', (0.8, 0.))],
[('H', (0.1, 0.))]],
3: [[('H', (0., 0., 0.)), ('H', (0.8, 0., 0.))],
[('H', (0.1, 0., 0.))]]
}
# [[spatial dimension, fieldline dimension]]
dims = [[2, 2], [2, 3], [3, 3]]
scale = 8 * 1.
spinless = True
for dim in dims:
# If dim[0] == 2, get range(2, 4).
# If dim[0] == 3, get range(2, 3).
for length in range(2, 6 - dim[0]):
for geometry in geometry_sets[dim[0]]:
grid = Grid(dimensions=dim[0], scale=scale, length=length)
period_cutoff = grid.volume_scale() ** (1. / grid.dimensions)
momentum_external_potential = plane_wave_external_potential(grid, geometry, spinless, e_cutoff=None,
non_periodic=True, period_cutoff=period_cutoff,
fieldlines=dim[1])
position_external_potential = dual_basis_external_potential(grid, geometry, spinless,
non_periodic=True, period_cutoff=period_cutoff,
fieldlines=dim[1])
# Confirm they are Hermitian
momentum_external_potential_operator = (
get_sparse_operator(momentum_external_potential))
self.assertTrue(is_hermitian(momentum_external_potential_operator))
position_external_potential_operator = (
get_sparse_operator(position_external_potential))
self.assertTrue(is_hermitian(position_external_potential_operator))
# Diagonalize.
jw_momentum = jordan_wigner(momentum_external_potential)
jw_position = jordan_wigner(position_external_potential)
momentum_spectrum = eigenspectrum(jw_momentum)
position_spectrum = eigenspectrum(jw_position)
# Confirm spectra are the same.
difference = numpy.amax(
numpy.absolute(momentum_spectrum - position_spectrum))
self.assertAlmostEqual(difference, 0.)
def test_bravyi_kitaev_fast_number_excitation_operator(self):
# using hydrogen Hamiltonian and introducing some number operator terms
constant = 0
one_body = numpy.zeros((4, 4))
one_body[(0, 0)] = .4
one_body[(1, 1)] = .5
one_body[(2, 2)] = .6
one_body[(3, 3)] = .7
two_body = self.molecular_hamiltonian.two_body_tensor
# initiating number operator terms for all the possible cases
two_body[(1, 2, 3, 1)] = 0.1
two_body[(1, 3, 2, 1)] = 0.1
two_body[(1, 2, 1, 3)] = 0.15
two_body[(3, 1, 2, 1)] = 0.15
two_body[(0, 2, 2, 1)] = 0.09
two_body[(1, 2, 2, 0)] = 0.09
two_body[(1, 2, 3, 2)] = 0.11
two_body[(2, 3, 2, 1)] = 0.11
two_body[(2, 2, 2, 2)] = 0.1
molecular_hamiltonian = InteractionOperator(constant, one_body,
two_body)
# comparing the eigenspectrum of Hamiltonian
n_qubits = count_qubits(molecular_hamiltonian)
bravyi_kitaev_fast_H = _bksf.bravyi_kitaev_fast(molecular_hamiltonian)
jw_H = jordan_wigner(molecular_hamiltonian)
bravyi_kitaev_fast_H_eig = eigenspectrum(bravyi_kitaev_fast_H)
jw_H_eig = eigenspectrum(jw_H)
bravyi_kitaev_fast_H_eig = bravyi_kitaev_fast_H_eig.round(5)
jw_H_eig = jw_H_eig.round(5)
evensector_H = 0
for i in range(numpy.size(jw_H_eig)):
if bool(
numpy.size(
numpy.where(jw_H_eig[i] == bravyi_kitaev_fast_H_eig))):
evensector_H += 1
# comparing eigenspectrum of number operator
bravyi_kitaev_fast_n = _bksf.number_operator(molecular_hamiltonian)
jw_n = QubitOperator()
n_qubits = count_qubits(molecular_hamiltonian)
for i in range(n_qubits):
jw_n += jordan_wigner_one_body(i, i)
jw_eig_spec = eigenspectrum(jw_n)
bravyi_kitaev_fast_eig_spec = eigenspectrum(bravyi_kitaev_fast_n)
evensector_n = 0
for i in range(numpy.size(jw_eig_spec)):
if bool(
numpy.size(
numpy.where(
jw_eig_spec[i] == bravyi_kitaev_fast_eig_spec))):
evensector_n += 1
self.assertEqual(evensector_H, 2**(n_qubits - 1))
self.assertEqual(evensector_n, 2**(n_qubits - 1))
def test_energy_reduce_symmetry_qubits(self):
# Generate the fermionic Hamiltonians,
# number of orbitals and number of electrons.
lih_sto_hamil, lih_sto_numorb, lih_sto_numel = LiH_sto3g()
# Use test function to reduce the qubits.
lih_sto_qbt = (symmetry_conserving_bravyi_kitaev(
lih_sto_hamil, lih_sto_numorb, lih_sto_numel))
self.assertAlmostEqual(
eigenspectrum(lih_sto_qbt)[0],
eigenspectrum(lih_sto_hamil)[0])
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_bk_jw_number_operator(self):
# Check if number operator has the same spectrum in both
# BK and JW representations
n = number_operator(1, 0)
jw_n = jordan_wigner(n)
bk_n = bravyi_kitaev(n)
# Diagonalize and make sure the spectra are the same.
jw_spectrum = eigenspectrum(jw_n)
bk_spectrum = eigenspectrum(bk_n)
self.assertAlmostEqual(0., numpy.amax(
numpy.absolute(jw_spectrum - bk_spectrum)))
def test_bk_jw_hopping_operator(self):
# Check if the spectrum fits for a single hoppping operator
ho = FermionOperator(((1, 1), (4, 0))) + FermionOperator(
((4, 1), (1, 0)))
jw_ho = jordan_wigner(ho)
bk_ho = bravyi_kitaev(ho)
# Diagonalize and make sure the spectra are the same.
jw_spectrum = eigenspectrum(jw_ho)
bk_spectrum = eigenspectrum(bk_ho)
self.assertAlmostEqual(0., numpy.amax(
numpy.absolute(jw_spectrum - bk_spectrum)))
def test_model_integration_with_constant(self):
# Compute Hamiltonian in both momentum and position space.
length_scale = 0.7
spinless = True
# [[spatial dimension, fieldline dimension]]
dims = [[2, 2], [2, 3], [3, 3]]
for dim in dims:
# If dim[0] == 2, get range(2, 4).
# If dim[0] == 3, get range(2, 3).
for length in range(2, 6 - dim[0]):
grid = Grid(dimensions=dim[0],
length=length,
scale=length_scale)
# Include Madelung constant in the momentum but not the position
# Hamiltonian.
momentum_hamiltonian = jellium_model(grid,
spinless,
True,
include_constant=True,
fieldlines=dim[1])
position_hamiltonian = jellium_model(grid,
spinless,
False,
fieldlines=dim[1])
# Confirm they are Hermitian.
momentum_hamiltonian_operator = (
get_sparse_operator(momentum_hamiltonian))
self.assertTrue(is_hermitian(momentum_hamiltonian_operator))
position_hamiltonian_operator = (
get_sparse_operator(position_hamiltonian))
self.assertTrue(is_hermitian(position_hamiltonian_operator))
# Diagonalize and confirm the same energy.
jw_momentum = jordan_wigner(momentum_hamiltonian)
jw_position = jordan_wigner(position_hamiltonian)
momentum_spectrum = eigenspectrum(jw_momentum)
position_spectrum = eigenspectrum(jw_position)
# Confirm momentum spectrum is shifted 2.8372/length_scale higher.
max_difference = numpy.amax(momentum_spectrum -
position_spectrum)
min_difference = numpy.amax(momentum_spectrum -
position_spectrum)
self.assertAlmostEqual(max_difference, 2.8372 / length_scale)
self.assertAlmostEqual(min_difference, 2.8372 / length_scale)
def test_nonperiodic_potential_integration(self):
# Compute potential energy operator in momentum and position space.
# Non-periodic test.
spinless = True
# [[spatial dimension, fieldline dimension]]
dims = [[2, 2], [2, 3], [3, 3]]
for dim in dims:
# If dim[0] == 2, get range(2, 4).
# If dim[0] == 3, get range(2, 3).
for length in range(2, 6 - dim[0]):
grid = Grid(dimensions=dim[0], length=length, scale=1.)
period_cutoff = grid.volume_scale()**(1. /
grid.dimensions) / 2.
momentum_potential = plane_wave_potential(
grid,
spinless=spinless,
e_cutoff=None,
non_periodic=True,
period_cutoff=period_cutoff,
fieldlines=dim[1])
position_potential = dual_basis_potential(
grid,
spinless=spinless,
non_periodic=True,
period_cutoff=period_cutoff,
fieldlines=dim[1])
# Confirm they are Hermitian
momentum_potential_operator = (
get_sparse_operator(momentum_potential))
self.assertTrue(is_hermitian(momentum_potential_operator))
position_potential_operator = (
get_sparse_operator(position_potential))
self.assertTrue(is_hermitian(position_potential_operator))
# Diagonalize and confirm the same energy.
jw_momentum = jordan_wigner(momentum_potential)
jw_position = jordan_wigner(position_potential)
momentum_spectrum = eigenspectrum(jw_momentum)
position_spectrum = eigenspectrum(jw_position)
# Confirm spectra are the same.
difference = numpy.amax(
numpy.absolute(momentum_spectrum - position_spectrum))
self.assertAlmostEqual(difference, 0.)
def test_bk_jw_number_operator_scaled(self):
# Check if number operator has the same spectrum in both
# JW and BK representations
n_qubits = 1
n = number_operator(n_qubits, 0, coefficient=2) # eigenspectrum (0,2)
jw_n = jordan_wigner(n)
bk_n = bravyi_kitaev(n)
# Diagonalize and make sure the spectra are the same.
jw_spectrum = eigenspectrum(jw_n)
bk_spectrum = eigenspectrum(bk_n)
self.assertAlmostEqual(0., numpy.amax(
numpy.absolute(jw_spectrum - bk_spectrum)))
def test_bk_jw_integration(self):
# This is a legacy test, which was a minimal failing example when
# optimization for hermitian operators was used.
# Minimal failing example:
fo = FermionOperator(((3, 1),))
jw = jordan_wigner(fo)
bk = bravyi_kitaev(fo)
jw_spectrum = eigenspectrum(jw)
bk_spectrum = eigenspectrum(bk)
self.assertAlmostEqual(0., numpy.amax(numpy.absolute(jw_spectrum -
bk_spectrum)))
def test_plane_wave_energy_cutoff(self):
grid = Grid(dimensions=1, length=5, scale=1.0)
spinless = True
e_cutoff = 20.0
hamiltonian_1 = jellium_model(grid, spinless, True, False)
jw_1 = jordan_wigner(hamiltonian_1)
spectrum_1 = eigenspectrum(jw_1)
hamiltonian_2 = jellium_model(grid, spinless, True, False, e_cutoff)
jw_2 = jordan_wigner(hamiltonian_2)
spectrum_2 = eigenspectrum(jw_2)
max_diff = numpy.amax(numpy.absolute(spectrum_1 - spectrum_2))
self.assertGreater(max_diff, 0.)
def lih_hamiltonian():
"""
Generate test Hamiltonian from LiH.
Args:
None
Return:
hamiltonian: FermionicOperator
spectrum: List of energies.
"""
geometry = [('Li', (0., 0., 0.)), ('H', (0., 0., 1.45))]
active_space_start = 1
active_space_stop = 3
molecule = MolecularData(geometry, 'sto-3g', 1, description="1.45")
molecule.load()
molecular_hamiltonian = molecule.get_molecular_hamiltonian(
occupied_indices=range(active_space_start),
active_indices=range(active_space_start, active_space_stop))
hamiltonian = get_fermion_operator(molecular_hamiltonian)
spectrum = eigenspectrum(hamiltonian)
return hamiltonian, spectrum
def test_weight_one_binary_addressing_code(self):
hamiltonian, gs_energy = lih_hamiltonian()
code = interleaved_code(8) * (
2 * weight_one_binary_addressing_code(2))
qubit_hamiltonian = binary_code_transform(hamiltonian, code)
self.assertAlmostEqual(gs_energy,
eigenspectrum(qubit_hamiltonian)[0])
def test_jordan_wigner(self):
hamiltonian, gs_energy = lih_hamiltonian()
code = jordan_wigner_code(4)
qubit_hamiltonian = binary_code_transform(hamiltonian, code)
self.assertAlmostEqual(gs_energy, eigenspectrum(qubit_hamiltonian)[0])
self.assertDictEqual(qubit_hamiltonian.terms,
jordan_wigner(hamiltonian).terms)
def test_plane_wave_energy_cutoff(self):
geometry = [('H', (0, )), ('H', (0.8, ))]
grid = Grid(dimensions=1, scale=1.1, length=5)
e_cutoff = 50.0
h_1 = plane_wave_hamiltonian(grid, geometry, True, True, False)
jw_1 = jordan_wigner(h_1)
spectrum_1 = eigenspectrum(jw_1)
h_2 = plane_wave_hamiltonian(grid, geometry, True, True, False,
e_cutoff)
jw_2 = jordan_wigner(h_2)
spectrum_2 = eigenspectrum(jw_2)
max_diff = numpy.amax(numpy.absolute(spectrum_1 - spectrum_2))
self.assertGreater(max_diff, 0.)
def test_bk_jw_number_operators(self):
# Check if a number operator has the same spectrum in both
# JW and BK representations
n_qubits = 2
n1 = number_operator(n_qubits, 0)
n2 = number_operator(n_qubits, 1)
n = n1 + n2
jw_n = jordan_wigner(n)
bk_n = bravyi_kitaev(n)
# Diagonalize and make sure the spectra are the same.
jw_spectrum = eigenspectrum(jw_n)
bk_spectrum = eigenspectrum(bk_n)
self.assertAlmostEqual(0., numpy.amax(
numpy.absolute(jw_spectrum - bk_spectrum)))
