def test_quadratic_form_parameterized(self):
"""Test the quadratic form circuit with parameters."""
theta = ParameterVector("th", 7)
p_quadratic = [[theta[0], theta[1]], [theta[2], theta[3]]]
p_linear = [theta[4], theta[5]]
p_offset = theta[6]
quadratic = np.array([[2, 1], [-1, -2]])
linear = np.array([2, 0])
offset = 0
m = 2
circuit = QuadraticForm(m, p_quadratic, p_linear, p_offset)
param_dict = dict(zip(theta, [*quadratic[0]] + [*quadratic[1]] + [*linear] + [offset]))
circuit.assign_parameters(param_dict, inplace=True)
self.assertQuadraticFormIsCorrect(m, quadratic, linear, offset, circuit)
def test_required_result_qubits(self):
"""Test getting the number of required result qubits."""
with self.subTest("positive bound"):
quadratic = [[1, -50], [100, 0]]
linear = [-5, 5]
offset = 0
num_result_qubits = QuadraticForm.required_result_qubits(quadratic, linear, offset)
self.assertEqual(num_result_qubits, 1 + int(np.ceil(np.log2(106 + 1))))
with self.subTest("negative bound"):
quadratic = [[1, -50], [10, 0]]
linear = [-5, 5]
offset = 0
num_result_qubits = QuadraticForm.required_result_qubits(quadratic, linear, offset)
self.assertEqual(num_result_qubits, 1 + int(np.ceil(np.log2(55))))
with self.subTest("empty"):
num_result_qubits = QuadraticForm.required_result_qubits([[]], [], 0)
self.assertEqual(num_result_qubits, 1)
def _get_a_operator(self, qr_key_value, problem):
quadratic = problem.objective.quadratic.to_array()
linear = problem.objective.linear.to_array()
offset = problem.objective.constant
# Get circuit requirements from input.
quadratic_form = QuadraticForm(self._num_value_qubits, quadratic, linear, offset,
little_endian=False)
a_operator = QuantumCircuit(qr_key_value)
a_operator.h(list(range(self._num_key_qubits)))
a_operator.compose(quadratic_form, inplace=True)
return a_operator
def test_quadratic_form(self):
"""Test the quadratic form circuit."""
with self.subTest("empty"):
circuit = QuadraticForm()
self.assertQuadraticFormIsCorrect(1, [[0]], [0], 0, circuit)
with self.subTest("1d case"):
quadratic = np.array([[1]])
linear = np.array([2])
offset = -1
circuit = QuadraticForm(quadratic=quadratic,
linear=linear,
offset=offset)
self.assertQuadraticFormIsCorrect(3, quadratic, linear, offset,
circuit)
with self.subTest("negative"):
quadratic = np.array([[-2]])
linear = np.array([0])
offset = -1
m = 2
circuit = QuadraticForm(m, quadratic, linear, offset)
self.assertQuadraticFormIsCorrect(m, quadratic, linear, offset,
circuit)
with self.subTest("missing quadratic"):
quadratic = np.zeros((3, 3))
linear = np.array([-2, 0, 1])
offset = -1
circuit = QuadraticForm(linear=linear, offset=offset)
self.assertQuadraticFormIsCorrect(3, quadratic, linear, offset,
circuit)
with self.subTest("missing linear"):
quadratic = np.array([[1, 2, 3], [3, 1, 2], [2, 3, 1]])
linear = np.zeros(3)
offset = -1
m = 2
circuit = QuadraticForm(m, quadratic, None, offset)
self.assertQuadraticFormIsCorrect(m, quadratic, linear, offset,
circuit)
with self.subTest("missing offset"):
quadratic = np.array([[2, 1], [-1, -2]])
linear = np.array([2, 0])
offset = 0
m = 2
circuit = QuadraticForm(m, quadratic, linear)
self.assertQuadraticFormIsCorrect(m, quadratic, linear, offset,
circuit)
def test_endian(self, little_endian):
"""Test the outcome for different endianness."""
qform = QuadraticForm(2, linear=[0, 1], little_endian=little_endian)
circuit = QuantumCircuit(4)
circuit.x(1)
circuit.compose(qform, inplace=True)
# the result is x_0 linear_0 + x_1 linear_1 = 1 = '0b01'
result = "01"
# the state is encoded as |q(x)>|x>, |x> = |x_1 x_0> = |10>
index = (result if little_endian else result[::-1]) + "10"
ref = np.zeros(2 ** 4, dtype=complex)
ref[int(index, 2)] = 1
self.assertTrue(Statevector.from_instruction(circuit).equiv(ref))