def test_tile_0():
r"""Generate the Tile state for index = 0:
.. math::
|\psi_0 \rangle = \frac{1}{\sqrt{2}} |0 \rangle
\left(|0\rangle - |1\rangle \right).
"""
e_0, e_1 = basis(3, 0), basis(3, 1)
expected_res = 1 / np.sqrt(2) * e_0 * (e_0 - e_1)
res = tile(0)
bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)
def test_tile_3():
r"""Generate the Tile state for index = 3:
.. math::
|\psi_3\rangle = \frac{1}{\sqrt{2}}
\left(|1\rangle - |2\rangle \right) |0\rangle
"""
e_0, e_1, e_2 = basis(3, 0), basis(3, 1), basis(3, 2)
expected_res = 1 / np.sqrt(2) * (e_1 - e_2) * e_0
res = tile(3)
bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)
def test_tile_2():
r"""Generate the Tile state for index = 2:
.. math::
|\psi_2\rangle = \frac{1}{\sqrt{2}} |2\rangle
\left(|1\rangle - |2\rangle \right)
"""
e_1, e_2 = basis(3, 1), basis(3, 2)
expected_res = 1 / np.sqrt(2) * np.kron(e_2, (e_1 - e_2))
res = tile(2)
bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)
def test_tile_4():
r"""Generate the Tile state for index = 4:
.. math::
|\psi_4\rangle = \frac{1}{3}
\left(|0\rangle + |1\rangle + |2\rangle)\right)
\left(|0\rangle + |1\rangle + |2\rangle.
"""
e_0, e_1, e_2 = basis(3, 0), basis(3, 1), basis(3, 2)
expected_res = 1 / 3 * (e_0 + e_1 + e_2) * (e_0 + e_1 + e_2)
res = tile(4)
bool_mat = np.isclose(res, expected_res)
np.testing.assert_equal(np.all(bool_mat), True)
def test_tile_invalid():
"""Ensures that an integer above 4 is error-checked."""
with np.testing.assert_raises(ValueError):
tile(5)