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_inverse_fourier_transform_2d(self):
grid = Grid(dimensions=2, scale=1.5, length=3)
spinless = True
geometry = [('H', (0, 0)), ('H', (0.5, 0.8))]
h_plane_wave = plane_wave_hamiltonian(grid, geometry, spinless, True)
h_dual_basis = plane_wave_hamiltonian(grid, geometry, spinless, False)
h_dual_basis_t = inverse_fourier_transform(h_dual_basis, grid,
spinless)
self.assertTrue(
normal_ordered(h_dual_basis_t).isclose(
normal_ordered(h_plane_wave)))
def test_fourier_transform(self):
grid = Grid(dimensions=1, scale=1.5, length=3)
spinless_set = [True, False]
geometry = [('H', (0, )), ('H', (0.5, ))]
for spinless in spinless_set:
h_plane_wave = plane_wave_hamiltonian(grid, geometry, spinless,
True)
h_dual_basis = plane_wave_hamiltonian(grid, geometry, spinless,
False)
h_plane_wave_t = fourier_transform(h_plane_wave, grid, spinless)
self.assertTrue(
normal_ordered(h_plane_wave_t).isclose(
normal_ordered(h_dual_basis)))
def test_jordan_wigner_dual_basis_hamiltonian(self):
grid = Grid(dimensions=2, length=3, scale=1.)
spinless = True
geometry = [('H', (0, 0)), ('H', (0.5, 0.8))]
fermion_hamiltonian = plane_wave_hamiltonian(grid,
geometry,
spinless,
False,
include_constant=True)
qubit_hamiltonian = jordan_wigner(fermion_hamiltonian)
test_hamiltonian = jordan_wigner_dual_basis_hamiltonian(
grid, geometry, spinless, include_constant=True)
self.assertTrue(test_hamiltonian.isclose(qubit_hamiltonian))
def test_plane_wave_hamiltonian_bad_element(self):
grid = Grid(dimensions=3, scale=1.0, length=4)
with self.assertRaises(ValueError):
plane_wave_hamiltonian(grid, geometry=[('Unobtainium', (0, 0, 0))])
def test_plane_wave_hamiltonian_bad_geometry(self):
grid = Grid(dimensions=1, scale=1.0, length=4)
with self.assertRaises(ValueError):
plane_wave_hamiltonian(grid, geometry=[('H', (0, 0, 0))])
def test_plane_wave_hamiltonian_default_to_jellium_with_no_geometry(self):
grid = Grid(dimensions=1, scale=1.0, length=4)
self.assertTrue(
plane_wave_hamiltonian(grid).isclose(jellium_model(grid)))