def test_quantum_state_product_state():
q0, q1, q2 = cirq.LineQubit.range(3)
product_state_1 = cirq.KET_PLUS(q0) * cirq.KET_PLUS(q1) * cirq.KET_ONE(q2)
state = cirq.quantum_state(product_state_1)
np.testing.assert_allclose(state.data, product_state_1.state_vector())
assert state.qid_shape == (2, 2, 2)
assert state.dtype == np.complex64
with pytest.raises(ValueError, match='qid shape'):
_ = cirq.quantum_state(product_state_1, qid_shape=(2, 2))
def test_quantum_state_density_matrix():
density_matrix_1 = np.eye(4, dtype=np.complex64) / 4
state = cirq.quantum_state(density_matrix_1, qid_shape=(4,), copy=True)
assert state.data is not density_matrix_1
np.testing.assert_array_equal(state.data, density_matrix_1)
assert state.qid_shape == (4,)
assert state.dtype == np.complex64
with pytest.raises(ValueError, match='not compatible'):
_ = cirq.quantum_state(density_matrix_1, qid_shape=(8,))
def test_quantum_state_state_vector_state_tensor():
state_vector_1 = cirq.one_hot(shape=(4,), dtype=np.complex128)
state_tensor_1 = np.reshape(state_vector_1, (2, 2))
state = cirq.quantum_state(state_vector_1, dtype=np.complex64, qid_shape=(2, 2))
np.testing.assert_array_equal(state.data, state_vector_1)
assert state.qid_shape == (2, 2)
assert state.dtype == np.complex64
state = cirq.quantum_state(state_tensor_1, qid_shape=(2, 2))
assert state.data is state_tensor_1
assert state.qid_shape == (2, 2)
assert state.dtype == np.complex128
def test_von_neumann_entropy():
# 1x1 matrix
assert cirq.von_neumann_entropy(np.array([[1]])) == 0
# An EPR pair state (|00> + |11>)(<00| + <11|)
assert (
cirq.von_neumann_entropy(0.5 * np.array([1, 0, 0, 1] * np.array([[1], [0], [0], [1]]))) == 0
)
# Maximally mixed state
# yapf: disable
assert cirq.von_neumann_entropy(np.array(
[[0.5, 0],
[0, 0.5]])) == 1
# yapf: enable
# 2x2 random unitary, each column as a ket, each ket as a density matrix,
# linear combination of the two with coefficients 0.1 and 0.9
res = cirq.testing.random_unitary(2)
first_column = res[:, 0]
first_density_matrix = 0.1 * np.outer(first_column, np.conj(first_column))
second_column = res[:, 1]
second_density_matrix = 0.9 * np.outer(second_column, np.conj(second_column))
assert np.isclose(
cirq.von_neumann_entropy(first_density_matrix + second_density_matrix), 0.4689, atol=1e-04
)
assert np.isclose(
cirq.von_neumann_entropy(np.diag([0, 0, 0.1, 0, 0.2, 0.3, 0.4, 0])), 1.8464, atol=1e-04
)
# Random NxN matrix
probs = np.random.exponential(size=N)
probs /= np.sum(probs)
mat = U @ (probs * U).T.conj()
np.testing.assert_allclose(
cirq.von_neumann_entropy(mat), -np.sum(probs * np.log(probs) / np.log(2))
)
# QuantumState object
assert (
cirq.von_neumann_entropy(cirq.quantum_state(np.array([[0.5, 0], [0, 0.5]]), qid_shape=(2,)))
== 1
)
assert (
cirq.von_neumann_entropy(
cirq.quantum_state(np.array([[0.5, 0.5], [0.5, 0.5]]), qid_shape=(2, 2))
)
== 0
)
def test_quantum_state_computational_basis_state():
state = cirq.quantum_state(7, qid_shape=(3, 4))
np.testing.assert_allclose(
state.data, cirq.one_hot(index=7, shape=(12, ), dtype=np.complex64))
assert state.qid_shape == (3, 4)
assert state.dtype == np.complex64
state = cirq.quantum_state((0, 1, 2, 3),
qid_shape=(1, 2, 3, 4),
dtype=np.complex128)
np.testing.assert_allclose(
state.data,
cirq.one_hot(index=(0, 1, 2, 3),
shape=(1, 2, 3, 4),
dtype=np.complex64))
assert state.qid_shape == (1, 2, 3, 4)
assert state.dtype == np.complex128
with pytest.raises(ValueError, match='ambiguous'):
_ = cirq.quantum_state(7)
with pytest.raises(ValueError, match='out of range'):
_ = cirq.quantum_state(7, qid_shape=(2, 2))
with pytest.raises(ValueError, match='ambiguous'):
_ = cirq.quantum_state((0, 1, 2, 3))
with pytest.raises(ValueError, match='out of bounds'):
_ = cirq.quantum_state((0, 1, 2, 3), qid_shape=(2, 2, 2, 2))
with pytest.raises(ValueError, match='ambiguous'):
_ = cirq.quantum_state((0, 0, 1, 1), qid_shape=(1, 1, 2, 2))
def test_quantum_state_state_vector_state_tensor():
state_vector_1 = cirq.one_hot(shape=(4, ), dtype=np.complex128)
state_tensor_1 = np.reshape(state_vector_1, (2, 2))
state = cirq.quantum_state(state_vector_1, dtype=np.complex64)
np.testing.assert_array_equal(state.data, state_vector_1)
assert state.qid_shape == (2, 2)
assert state.dtype == np.complex64
state = cirq.quantum_state(state_tensor_1, qid_shape=(2, 2))
assert state.data is state_tensor_1
assert state.qid_shape == (2, 2)
assert state.dtype == np.complex128
with pytest.raises(ValueError, match='ambiguous'):
_ = cirq.quantum_state(state_tensor_1)
with pytest.raises(ValueError, match='not compatible'):
_ = cirq.quantum_state(state_tensor_1, qid_shape=(2, 3))
def test_quantum_state_quantum_state():
state_vector_1 = cirq.one_hot(shape=(4,), dtype=np.complex128)
quantum_state = cirq.QuantumState(state_vector_1, qid_shape=(2, 2))
state = cirq.quantum_state(quantum_state)
assert state is quantum_state
assert state.data is quantum_state.data
assert state.dtype == np.complex128
state = cirq.quantum_state(quantum_state, copy=True)
assert state is not quantum_state
assert state.data is not quantum_state.data
assert state.dtype == np.complex128
state = cirq.quantum_state(quantum_state, dtype=np.complex64)
assert state is not quantum_state
assert state.data is not quantum_state.data
assert state.dtype == np.complex64
with pytest.raises(ValueError, match='qid shape'):
state = cirq.quantum_state(quantum_state, qid_shape=(4,))
