def test_too_many_terms(self):
"""Test exception raised for wrong number of terms"""
with pytest.raises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 0.1, 0.2)
H -= BosonOperator('0^ 0^ 0^ 0^')
extract_onsite_chemical(H)
with pytest.raises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 0.1, 0.2)
H -= BosonOperator('5^ 5 5^ 5')
extract_onsite_chemical(H)
def test_too_many_terms(self):
"""Test exception raised for wrong number of terms"""
with pytest.raises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 0)
H -= BosonOperator('0^ 1^')
extract_tunneling(H)
with pytest.raises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 0)
H -= BosonOperator('0^ 1')
H -= BosonOperator('1^ 0')
extract_tunneling(H)
def test_tunneling_2x2(self):
"""Test extracted tunneling on 2x2 grid"""
H = bose_hubbard(2, 2, 0.5, 0)
res = extract_tunneling(H)
res[0] = sorted(res[0], key=lambda x: x[1])
expected = [[(0, 1), (0, 2), (1, 3), (2, 3)], 0.5]
assert res == expected
def test_1x2_tf(self, hbar, tol):
"""Test a 1x2 lattice Bose-Hubbard model using TF"""
try:
import tensorflow as tf
except (ImportError, ModuleNotFoundError):
pytest.skip("TensorFlow not installed.")
if tf.__version__[:3] != "1.3":
pytest.skip("Incorrect TensorFlow version")
sf.hbar = hbar
prog = sf.Program(2)
H = bose_hubbard(1, 2, self.J, self.U)
with prog.context as q:
Fock(2) | q[0]
BoseHubbardPropagation(H, self.t, self.k) | q
eng = sf.Engine("tf", backend_options={"cutoff_dim": 7})
state = eng.run(prog).state
Hm = -self.J*np.sqrt(2)*np.array([[0, 1, 0], [1, 0, 1], [0, 1, 0]]) \
+ self.U*np.diag([1, 0, 1])
init_state = np.array([1, 0, 0])
exp = np.abs(np.dot(expm(-1j * self.t * Hm), init_state))**2
assert np.allclose(state.fock_prob([2, 0]), exp[0], rtol=tol)
assert np.allclose(state.fock_prob([1, 1]), exp[1], rtol=tol)
assert np.allclose(state.fock_prob([0, 2]), exp[2], rtol=tol)
def test_ladder_wrong_form(self):
"""Test exception raised for wrong ladder operators"""
with pytest.raises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 1, 1, 0.5)
H += BosonOperator('5^ 5 6^ 6^')
H -= BosonOperator('6 5')
extract_dipole(H)
def test_wrong_term_length(self):
"""Test exception raised for wrong terms"""
with pytest.raises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 0.1, 0.2)
H -= BosonOperator('5^ 5 5^')
H += BosonOperator('5^ 5')
extract_onsite_chemical(H)
def test_ladder_wrong_form(self):
"""Test exception raised for wrong ladder operators"""
with self.assertRaises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 0)
H -= BosonOperator('5^ 6^')
H -= BosonOperator('6 5')
extract_tunneling(H)
def test_incorrect_ladders(self):
"""Test exception raised for wrong ladder operators"""
with pytest.raises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 0.1, 0.2)
H -= BosonOperator('5^ 5^ 5^ 5^')
H -= BosonOperator('5 5^ 5 5^')
extract_onsite_chemical(H)
def test_both(self):
"""Test case where there is non-zero mu and non-zero U"""
self.logTestName()
H = bose_hubbard(2, 2, 1, 0.1, 0.2)
res = extract_onsite_chemical(H)
expected = ([[0, 1, 2, 3], 0.1], [[0, 1, 2, 3], 0.2])
self.assertEqual(res, expected)
def test_2x2(self):
"""Test extracted dipole terms on 2x2 grid"""
H = bose_hubbard(2, 2, 1, 0, 0, 0.5)
res = extract_dipole(H)
res[0] = sorted(res[0], key=lambda x: x[0])
expected = [[(0, 1), (0, 2), (1, 3), (2, 3)], 0.5]
assert res == expected
def test_too_many_terms(self):
"""Test exception raised for wrong number of terms"""
self.logTestName()
with self.assertRaises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 1, 1, 0.5)
H += BosonOperator('0^ 0 1^ 2', 0.5)
extract_dipole(H)
def test_tunneling_1x2(self):
"""Test extracted tunneling on 1x2 grid"""
self.logTestName()
H = bose_hubbard(1, 2, 0.5, 0)
res = extract_tunneling(H)
expected = [[(0, 1)], 0.5]
self.assertEqual(res, expected)
def test_differing_chemical_potential(self):
"""Test exception raised for differing coefficients"""
self.logTestName()
with self.assertRaises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 0.1, 0.2)
H -= BosonOperator('5^ 5')
extract_onsite_chemical(H)
def test_bose_hubbard_2x2_aperiodic():
hubbard_model = bose_hubbard(2,
2,
1.0,
4.0,
chemical_potential=0.5,
dipole=0.3,
periodic=False)
assert str(hubbard_model).strip() == """
-1.0 [0 1^] +
-1.0 [0 2^] +
-2.5 [0^ 0] +
2.0 [0^ 0 0^ 0] +
0.3 [0^ 0 1^ 1] +
0.3 [0^ 0 2^ 2] +
-1.0 [0^ 1] +
-1.0 [0^ 2] +
-1.0 [1 3^] +
-2.5 [1^ 1] +
2.0 [1^ 1 1^ 1] +
0.3 [1^ 1 3^ 3] +
-1.0 [1^ 3] +
-1.0 [2 3^] +
-2.5 [2^ 2] +
2.0 [2^ 2 2^ 2] +
0.3 [2^ 2 3^ 3] +
-1.0 [2^ 3] +
-2.5 [3^ 3] +
2.0 [3^ 3 3^ 3]
""".strip()
def test_differing_onsite(self):
"""Test exception raised for differing coefficients"""
with pytest.raises(BoseHubbardError):
H = bose_hubbard(2, 2, 1, 0.1, 0.2)
H -= BosonOperator('5^ 5 5^ 5')
H += BosonOperator('5^ 5')
extract_onsite_chemical(H)
def test_2x2(self):
"""Test extracted dipole terms on 2x2 grid"""
self.logTestName()
H = bose_hubbard(2, 2, 1, 0, 0, 0.5)
res = extract_dipole(H)
res[0] = sorted(res[0], key=lambda x: x[0])
expected = [[(0, 1), (0, 2), (1, 3), (2, 3)], 0.5]
self.assertEqual(res, expected)
def test_tunneling_2x2(self):
"""Test extracted tunneling on 2x2 grid"""
self.logTestName()
H = bose_hubbard(2, 2, 0.5, 0)
res = extract_tunneling(H)
res[0] = sorted(res[0], key=lambda x: x[1])
expected = [[(0, 1), (0, 2), (1, 3), (2, 3)], 0.5]
self.assertEqual(res, expected)
def test_two_by_two_periodic_rudimentary(self):
hubbard_model = bose_hubbard(self.x_dimension,
self.y_dimension,
self.tunneling,
self.interaction,
self.chemical_potential,
self.dipole,
periodic=True)
def test_tunneling_2x2(self):
"""Test non-interacting 2x2 grid"""
H = bose_hubbard(2, 2, self.J, 0, 0)
res = trotter_layer(H, self.t, self.k)
theta = -self.t * self.J / self.k
phi = np.pi / 2
expected = {'BS': (theta, phi, [(0, 1), (0, 2), (1, 3), (2, 3)])}
self.assertEqual(res, expected)
def setUp(self):
self.hbar = 2.
self.eng, _ = sf.Engine(3, hbar=self.hbar)
self.J = -1
self.U = 1.5
self.t = 1.086
self.k = 20
self.tol = 1e-2
self.H = bose_hubbard(1, 2, self.J, self.U)
def test_tunneling_2x2(self):
"""Test non-interacting 2x2 grid"""
H = bose_hubbard(2, 2, self.J, 0, 0)
res = trotter_layer(H, self.t, self.k)
theta = -self.t * self.J / self.k
phi = np.pi / 2
expected = {'BS': (theta, phi, [(0, 1), (0, 2), (1, 3), (2, 3)])}
res['BS'] = res['BS'][:2] + (sorted(res['BS'][2],
key=lambda x: x[0]), )
assert res == expected
def test_three_by_two_periodic_rudimentary(self):
hubbard_model = bose_hubbard(3,
2,
self.tunneling,
self.interaction,
self.chemical_potential,
self.dipole,
periodic=True)
# Check up top/bottom hopping terms.
self.assertAlmostEqual(hubbard_model.terms[((0, 0), (2, 1))],
-self.tunneling)
def setUp(self):
"""parameters"""
self.hbar = 2.
self.eng, _ = sf.Engine(2, hbar=self.hbar)
self.J = -1
self.U = 1.5
self.t = 1.086
self.k = 20
self.tol = 1e-2
self.H = bose_hubbard(1, 2, self.J, self.U)
self.Hquad = get_quad_operator(self.H, hbar=self.hbar)
def test_chemical_potential_2x2(self):
"""Test on-site interacting and chemical potential on a 2x2 grid"""
H = bose_hubbard(2, 2, self.J, self.U, self.mu)
res = trotter_layer(H, self.t, self.k)
theta = -self.t * self.J / self.k
phi = np.pi / 2
kappa = -self.t * self.U / (2 * self.k)
r = self.t * (0.5 * self.U + self.mu) / (2 * self.k)
expected = {
'BS': (theta, phi, [(0, 1), (0, 2), (1, 3), (2, 3)]),
'K': (kappa, [0, 1, 2, 3]),
'R': (r, [0, 1, 2, 3]),
}
self.assertEqual(res, expected)
def test_onsite_2x2(self):
"""Test on-site interacting 2x2 grid"""
H = bose_hubbard(2, 2, self.J, self.U, 0)
res = trotter_layer(H, self.t, self.k)
theta = -self.t * self.J / self.k
phi = np.pi / 2
kappa = -self.t * self.U / (2 * self.k)
r = -kappa
expected = {
'BS': (theta, phi, [(0, 1), (0, 2), (1, 3), (2, 3)]),
'K': (kappa, [0, 1, 2, 3]),
'R': (r, [0, 1, 2, 3]),
}
self.assertEqual(res, expected)
def test_bose_hubbard_3x2():
hubbard_model = bose_hubbard(3,
2,
1.0,
4.0,
chemical_potential=0.5,
dipole=0.3)
assert str(hubbard_model).strip() == """
-1.0 [0 1^] +
-1.0 [0 2^] +
-1.0 [0 3^] +
-2.5 [0^ 0] +
2.0 [0^ 0 0^ 0] +
0.3 [0^ 0 1^ 1] +
0.3 [0^ 0 3^ 3] +
-1.0 [0^ 1] +
-1.0 [0^ 2] +
-1.0 [0^ 3] +
-1.0 [1 2^] +
-1.0 [1 4^] +
-2.5 [1^ 1] +
2.0 [1^ 1 1^ 1] +
0.3 [1^ 1 2^ 2] +
0.3 [1^ 1 4^ 4] +
-1.0 [1^ 2] +
-1.0 [1^ 4] +
-1.0 [2 5^] +
-2.5 [2^ 2] +
0.3 [2^ 2 0^ 0] +
2.0 [2^ 2 2^ 2] +
0.3 [2^ 2 5^ 5] +
-1.0 [2^ 5] +
-1.0 [3 4^] +
-1.0 [3 5^] +
-2.5 [3^ 3] +
2.0 [3^ 3 3^ 3] +
0.3 [3^ 3 4^ 4] +
-1.0 [3^ 4] +
-1.0 [3^ 5] +
-1.0 [4 5^] +
-2.5 [4^ 4] +
2.0 [4^ 4 4^ 4] +
0.3 [4^ 4 5^ 5] +
-1.0 [4^ 5] +
-2.5 [5^ 5] +
0.3 [5^ 5 3^ 3] +
2.0 [5^ 5 5^ 5]
""".strip()
def test_bose_hubbard_2x3():
hubbard_model = bose_hubbard(2,
3,
1.0,
4.0,
chemical_potential=0.5,
dipole=0.3)
assert str(hubbard_model).strip() == """
-1.0 [0 1^] +
-1.0 [0 2^] +
-1.0 [0 4^] +
-2.5 [0^ 0] +
2.0 [0^ 0 0^ 0] +
0.3 [0^ 0 1^ 1] +
0.3 [0^ 0 2^ 2] +
-1.0 [0^ 1] +
-1.0 [0^ 2] +
-1.0 [0^ 4] +
-1.0 [1 3^] +
-1.0 [1 5^] +
-2.5 [1^ 1] +
2.0 [1^ 1 1^ 1] +
0.3 [1^ 1 3^ 3] +
-1.0 [1^ 3] +
-1.0 [1^ 5] +
-1.0 [2 3^] +
-1.0 [2 4^] +
-2.5 [2^ 2] +
2.0 [2^ 2 2^ 2] +
0.3 [2^ 2 3^ 3] +
0.3 [2^ 2 4^ 4] +
-1.0 [2^ 3] +
-1.0 [2^ 4] +
-1.0 [3 5^] +
-2.5 [3^ 3] +
2.0 [3^ 3 3^ 3] +
0.3 [3^ 3 5^ 5] +
-1.0 [3^ 5] +
-1.0 [4 5^] +
-2.5 [4^ 4] +
0.3 [4^ 4 0^ 0] +
2.0 [4^ 4 4^ 4] +
0.3 [4^ 4 5^ 5] +
-1.0 [4^ 5] +
-2.5 [5^ 5] +
0.3 [5^ 5 1^ 1] +
2.0 [5^ 5 5^ 5]
""".strip()
def test_chemical_potential_2x2(self):
"""Test on-site interacting and chemical potential on a 2x2 grid"""
H = bose_hubbard(2, 2, self.J, self.U, self.mu)
res = trotter_layer(H, self.t, self.k)
theta = -self.t * self.J / self.k
phi = np.pi / 2
kappa = -self.t * self.U / (2 * self.k)
r = self.t * (0.5 * self.U + self.mu) / (2 * self.k)
expected = {
'BS': (theta, phi, [(0, 1), (0, 2), (1, 3), (2, 3)]),
'K': (kappa, [0, 1, 2, 3]),
'R': (r, [0, 1, 2, 3]),
}
res['BS'] = res['BS'][:2] + (sorted(res['BS'][2],
key=lambda x: x[0]), )
assert res == expected
def test_onsite_2x2(self):
"""Test on-site interacting 2x2 grid"""
H = bose_hubbard(2, 2, self.J, self.U, 0)
res = trotter_layer(H, self.t, self.k)
theta = -self.t * self.J / self.k
phi = np.pi / 2
kappa = -self.t * self.U / (2 * self.k)
r = -kappa
expected = {
'BS': (theta, phi, [(0, 1), (0, 2), (1, 3), (2, 3)]),
'K': (kappa, [0, 1, 2, 3]),
'R': (r, [0, 1, 2, 3]),
}
res['BS'] = res['BS'][:2] + (sorted(res['BS'][2],
key=lambda x: x[0]), )
assert res == expected
def test_two_by_two(self):
# Initialize the Hamiltonian.
hubbard_model = bose_hubbard(self.x_dimension, self.y_dimension,
self.tunneling, self.interaction,
self.chemical_potential, self.dipole,
self.periodic)
# Check on on-site interaction and chemical-potential terms.
chem_coeff = -self.interaction / 2 - self.chemical_potential
on_site_coeff = self.interaction / 2
for i in range(4):
self.assertAlmostEqual(hubbard_model.terms[((i, 1), (i, 0))],
chem_coeff)
self.assertAlmostEqual(
hubbard_model.terms[((i, 1), (i, 0), (i, 1), (i, 0))],
on_site_coeff)
# Check right/left hopping terms.
t_coeff = -self.tunneling
self.assertAlmostEqual(hubbard_model.terms[((0, 1), (1, 0))], t_coeff)
self.assertAlmostEqual(hubbard_model.terms[((0, 0), (1, 1))], t_coeff)
self.assertAlmostEqual(hubbard_model.terms[((2, 0), (3, 1))], t_coeff)
self.assertAlmostEqual(hubbard_model.terms[((2, 1), (3, 0))], t_coeff)
# Check top/bottom hopping terms.
self.assertAlmostEqual(hubbard_model.terms[((0, 1), (2, 0))], t_coeff)
self.assertAlmostEqual(hubbard_model.terms[((0, 0), (2, 1))], t_coeff)
self.assertAlmostEqual(hubbard_model.terms[((1, 0), (3, 1))], t_coeff)
self.assertAlmostEqual(hubbard_model.terms[((1, 1), (3, 0))], t_coeff)
# Check left/right dipole interaction terms.
d_coeff = self.dipole
self.assertAlmostEqual(
hubbard_model.terms[((0, 1), (0, 0), (1, 1), (1, 0))], d_coeff)
self.assertAlmostEqual(
hubbard_model.terms[((2, 1), (2, 0), (3, 1), (3, 0))], d_coeff)
# Check top/bottom interaction terms.
self.assertAlmostEqual(
hubbard_model.terms[((0, 1), (0, 0), (2, 1), (2, 0))], d_coeff)
self.assertAlmostEqual(
hubbard_model.terms[((1, 1), (1, 0), (3, 1), (3, 0))], d_coeff)
# Check that there are no other interaction terms.
self.assertNotIn(((0, 1), (0, 0), (3, 1), (3, 0)), hubbard_model.terms)
self.assertNotIn(((1, 1), (1, 0), (2, 1), (2, 0)), hubbard_model.terms)
