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 = np.amax(h_plane_wave_spectrum -
h_dual_basis_spectrum)
min_diff = np.amin(h_plane_wave_spectrum -
h_dual_basis_spectrum)
self.assertAlmostEqual(max_diff, 0)
self.assertAlmostEqual(min_diff, 0)
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_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_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_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_interaction_operator(self):
for n_orbitals, real, _ in itertools.product((1, 2, 5), (True, False),
range(5)):
operator = random_interaction_operator(n_orbitals, real=real)
normal_ordered_operator = normal_ordered(operator)
expected_qubit_operator = jordan_wigner(operator)
actual_qubit_operator = jordan_wigner(normal_ordered_operator)
assert expected_qubit_operator == actual_qubit_operator
two_body_tensor = normal_ordered_operator.two_body_tensor
n_orbitals = len(two_body_tensor)
ones = numpy.ones((n_orbitals,) * 2)
triu = numpy.triu(ones, 1)
shape = (n_orbitals**2, 1)
mask = (triu.reshape(shape) * ones.reshape(shape[::-1]) +
ones.reshape(shape) * triu.reshape(shape[::-1])).reshape(
(n_orbitals,) * 4)
assert numpy.allclose(mask * two_body_tensor,
numpy.zeros((n_orbitals,) * 4))
for term in normal_ordered_operator:
order = len(term) // 2
left_term, right_term = term[:order], term[order:]
assert all(i[1] == 1 for i in left_term)
assert all(i[1] == 0 for i in right_term)
assert left_term == tuple(sorted(left_term, reverse=True))
assert right_term == tuple(sorted(right_term, reverse=True))
def test_hermitian_conjugated_interaction_operator(self):
for n_orbitals, _ in itertools.product((1, 2, 5), range(5)):
operator = random_interaction_operator(n_orbitals)
qubit_operator = jordan_wigner(operator)
conjugate_operator = hermitian_conjugated(operator)
conjugate_qubit_operator = jordan_wigner(conjugate_operator)
assert hermitian_conjugated(qubit_operator) == \
conjugate_qubit_operator
def test_hermitian_conjugated_qubit_op_consistency(self):
"""Some consistency checks for conjugating QubitOperators."""
ferm_op = (FermionOperator('1^ 2') + FermionOperator('2 3 4') +
FermionOperator('2^ 7 9 11^'))
# Check that hermitian conjugation commutes with transforms
self.assertEqual(jordan_wigner(hermitian_conjugated(ferm_op)),
hermitian_conjugated(jordan_wigner(ferm_op)))
self.assertEqual(bravyi_kitaev(hermitian_conjugated(ferm_op)),
hermitian_conjugated(bravyi_kitaev(ferm_op)))
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 setUp(self):
geometry = [('H', (0., 0., 0.)), ('H', (0., 0., 0.7414))]
basis = 'sto-3g'
multiplicity = 1
filename = os.path.join(THIS_DIRECTORY, 'data',
'H2_sto-3g_singlet_0.7414')
self.molecule = MolecularData(geometry,
basis,
multiplicity,
filename=filename)
self.molecule.load()
# Get molecular Hamiltonian.
self.molecular_hamiltonian = self.molecule.get_molecular_hamiltonian()
# Get FCI RDM.
self.fci_rdm = self.molecule.get_molecular_rdm(use_fci=1)
# Get explicit coefficients.
self.nuclear_repulsion = self.molecular_hamiltonian.constant
self.one_body = self.molecular_hamiltonian.one_body_tensor
self.two_body = self.molecular_hamiltonian.two_body_tensor
# Get fermion Hamiltonian.
self.fermion_hamiltonian = normal_ordered(
get_fermion_operator(self.molecular_hamiltonian))
# Get qubit Hamiltonian.
self.qubit_hamiltonian = jordan_wigner(self.fermion_hamiltonian)
# Get the sparse matrix.
self.hamiltonian_matrix = get_sparse_operator(
self.molecular_hamiltonian)
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_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 = np.amax(np.absolute(spectrum_1 - spectrum_2))
self.assertGreater(max_diff, 0.)
def test_jordan_wigner_dual_basis_jellium(self):
# Parameters.
grid = Grid(dimensions=2, length=3, scale=1.)
spinless = True
# Compute fermionic Hamiltonian. Include then subtract constant.
fermion_hamiltonian = dual_basis_jellium_model(grid,
spinless,
include_constant=True)
qubit_hamiltonian = jordan_wigner(fermion_hamiltonian)
qubit_hamiltonian -= QubitOperator((), 2.8372)
# Compute Jordan-Wigner Hamiltonian.
test_hamiltonian = jordan_wigner_dual_basis_jellium(grid, spinless)
# Make sure Hamiltonians are the same.
self.assertTrue(test_hamiltonian == qubit_hamiltonian)
# Check number of terms.
n_qubits = count_qubits(qubit_hamiltonian)
if spinless:
paper_n_terms = 1 - .5 * n_qubits + 1.5 * (n_qubits**2)
num_nonzeros = sum(
1 for coeff in qubit_hamiltonian.terms.values() if coeff != 0.0)
self.assertTrue(num_nonzeros <= paper_n_terms)
def test_identity(self):
n_qubits = 5
transmed_i = reverse_jordan_wigner(self.identity, n_qubits)
expected_i = FermionOperator(())
self.assertTrue(transmed_i == expected_i)
retransmed_i = jordan_wigner(transmed_i)
self.assertTrue(self.identity == retransmed_i)
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 setUp(self):
self.n_qubits = 5
self.majorana_operator = MajoranaOperator((1, 4, 9))
self.fermion_term = FermionOperator('1^ 2^ 3 4', -3.17)
self.fermion_operator = self.fermion_term + hermitian_conjugated(
self.fermion_term)
self.qubit_operator = jordan_wigner(self.fermion_operator)
self.interaction_operator = get_interaction_operator(
self.fermion_operator)
def test_zero(self):
n_qubits = 5
transmed_i = reverse_jordan_wigner(QubitOperator(), n_qubits)
expected_i = FermionOperator()
self.assertTrue(transmed_i == expected_i)
retransmed_i = jordan_wigner(transmed_i)
expected_i = QubitOperator()
self.assertTrue(expected_i == retransmed_i)
def test_get_qubit_expectations(self):
qubit_operator = jordan_wigner(self.hamiltonian)
qubit_expectations = self.rdm.get_qubit_expectations(qubit_operator)
test_energy = 0.0
for qubit_term in qubit_expectations.terms:
term_coefficient = qubit_operator.terms[qubit_term]
test_energy += (term_coefficient *
qubit_expectations.terms[qubit_term])
self.assertLess(abs(test_energy - self.cisd_energy), EQ_TOLERANCE)
def test_z(self):
pauli_z = QubitOperator(((2, 'Z'), ))
transmed_z = reverse_jordan_wigner(pauli_z)
expected = (FermionOperator(()) + FermionOperator(
((2, 1), (2, 0)), -2.))
self.assertTrue(transmed_z == expected)
retransmed_z = jordan_wigner(transmed_z)
self.assertTrue(pauli_z == retransmed_z)
def test_reduce_terms(self):
"""Test reduce_terms function using LiH Hamiltonian."""
hamiltonian, spectrum = lih_hamiltonian()
qubit_hamiltonian = jordan_wigner(hamiltonian)
stab1 = QubitOperator('Z0 Z2', -1.0)
stab2 = QubitOperator('Z1 Z3', -1.0)
red_eigenspectrum = eigenspectrum(
reduce_number_of_terms(qubit_hamiltonian, stab1 + stab2))
self.assertAlmostEqual(spectrum[0], red_eigenspectrum[0])
def test_interaction_operator_mapping(self):
# Make sure mapping of FermionOperator to InteractionOperator works.
molecular_hamiltonian = get_interaction_operator(
self.fermion_hamiltonian)
fermion_hamiltonian = get_fermion_operator(molecular_hamiltonian)
self.assertTrue(self.fermion_hamiltonian == fermion_hamiltonian)
# Make sure mapping of InteractionOperator to QubitOperator works.
qubit_hamiltonian = jordan_wigner(self.molecular_hamiltonian)
self.assertTrue(self.qubit_hamiltonian == qubit_hamiltonian)
def test_bk_jw_majoranas(self):
# Check if the Majorana operators have the same spectrum
# irrespectively of the transform.
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(c)]
d_spins = [jordan_wigner(d), bravyi_kitaev(d)]
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(c_spectrum[0] - c_spectrum[1])))
self.assertAlmostEqual(
0., numpy.amax(numpy.absolute(d_spectrum[0] - d_spectrum[1])))
def test_jordan_wigner_dual_basis_hamiltonian(self):
grid = Grid(dimensions=2, length=3, scale=1.)
spinless_set = [True, False]
geometry = [('H', (0, 0)), ('H', (0.5, 0.8))]
for spinless in spinless_set:
fermion_hamiltonian = plane_wave_hamiltonian(
grid, geometry, spinless, False, include_constant=False)
qubit_hamiltonian = jordan_wigner(fermion_hamiltonian)
test_hamiltonian = jordan_wigner_dual_basis_hamiltonian(
grid, geometry, spinless, include_constant=False)
self.assertTrue(test_hamiltonian == qubit_hamiltonian)
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_kinetic_integration(self):
# Compute kinetic energy operator in both momentum and position space.
grid = Grid(dimensions=2, length=2, scale=3.)
spinless = False
momentum_kinetic = plane_wave_kinetic(grid, spinless)
position_kinetic = dual_basis_kinetic(grid, spinless)
# Confirm they are Hermitian
momentum_kinetic_operator = get_sparse_operator(momentum_kinetic)
self.assertTrue(is_hermitian(momentum_kinetic_operator))
position_kinetic_operator = get_sparse_operator(position_kinetic)
self.assertTrue(is_hermitian(position_kinetic_operator))
# Confirm spectral match and hermiticity
for length in [2, 3, 4]:
grid = Grid(dimensions=1, length=length, scale=2.1)
spinless = False
momentum_kinetic = plane_wave_kinetic(grid, spinless)
position_kinetic = dual_basis_kinetic(grid, spinless)
# Confirm they are Hermitian
momentum_kinetic_operator = get_sparse_operator(momentum_kinetic)
self.assertTrue(is_hermitian(momentum_kinetic_operator))
position_kinetic_operator = get_sparse_operator(position_kinetic)
self.assertTrue(is_hermitian(position_kinetic_operator))
# Diagonalize and confirm the same energy.
jw_momentum = jordan_wigner(momentum_kinetic)
jw_position = jordan_wigner(position_kinetic)
momentum_spectrum = eigenspectrum(jw_momentum, 2 * length)
position_spectrum = eigenspectrum(jw_position, 2 * length)
# Confirm spectra are the same.
difference = numpy.amax(
numpy.absolute(momentum_spectrum - position_spectrum))
self.assertAlmostEqual(difference, 0.)
def test_reduce_terms_manual_input(self):
"""Test reduce_terms function using LiH Hamiltonian."""
hamiltonian, spectrum = lih_hamiltonian()
qubit_hamiltonian = jordan_wigner(hamiltonian)
stab1 = QubitOperator('Z0 Z2', -1.0)
stab2 = QubitOperator('Z1 Z3', -1.0)
red_eigenspectrum = eigenspectrum(
reduce_number_of_terms(qubit_hamiltonian, [stab1, stab2],
manual_input=True,
fixed_positions=[0, 1]))
self.assertAlmostEqual(spectrum[0], red_eigenspectrum[0])
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_xy(self):
xy = QubitOperator(((4, 'X'), (5, 'Y')), -2.j)
transmed_xy = reverse_jordan_wigner(xy)
retransmed_xy = jordan_wigner(transmed_xy)
expected1 = -2j * (FermionOperator(((4, 1), ), 1j) - FermionOperator(
((4, 0), ), 1j))
expected2 = (FermionOperator(((5, 1), )) - FermionOperator(((5, 0), )))
expected = expected1 * expected2
self.assertTrue(xy == retransmed_xy)
self.assertTrue(
normal_ordered(transmed_xy) == normal_ordered(expected))
def test_yy(self):
yy = QubitOperator(((2, 'Y'), (3, 'Y')), 2.)
transmed_yy = reverse_jordan_wigner(yy)
retransmed_yy = jordan_wigner(transmed_yy)
expected1 = -(FermionOperator(((2, 1), ), 2.) + FermionOperator(
((2, 0), ), 2.))
expected2 = (FermionOperator(((3, 1), )) - FermionOperator(((3, 0), )))
expected = expected1 * expected2
self.assertTrue(yy == retransmed_yy)
self.assertTrue(
normal_ordered(transmed_yy) == normal_ordered(expected))
def test_xx(self):
xx = QubitOperator(((3, 'X'), (4, 'X')), 2.)
transmed_xx = reverse_jordan_wigner(xx)
retransmed_xx = jordan_wigner(transmed_xx)
expected1 = (FermionOperator(((3, 1), ), 2.) - FermionOperator(
((3, 0), ), 2.))
expected2 = (FermionOperator(((4, 1), ), 1.) + FermionOperator(
((4, 0), ), 1.))
expected = expected1 * expected2
self.assertTrue(xx == retransmed_xx)
self.assertTrue(
normal_ordered(transmed_xx) == normal_ordered(expected))
