def test_superposition(self):
x = qc.positive_superposition()
y1 = (qc.zeros() + qc.ones()) / np.sqrt(2)
y2 = (qc.zeros() + qc.ones()) * (1 / np.sqrt(2))
y3 = (1 / np.sqrt(2)) * (qc.ones() + qc.zeros())
y4 = (1 / np.sqrt(2)) * qc.ones() + qc.zeros() / np.sqrt(2)
self.assertLess(max_absolute_difference(y1, x), epsilon)
self.assertLess(max_absolute_difference(y2, x), epsilon)
self.assertLess(max_absolute_difference(y3, x), epsilon)
self.assertLess(max_absolute_difference(y4, x), epsilon)
self.assertLess(
max_absolute_difference(np.sqrt(2) * x - qc.ones(), qc.zeros()),
epsilon)
def deutsch_algorithm(f):
U_f = qc.U_f(f, d=2)
H = qc.Hadamard()
phi = H(qc.zeros()) * H(qc.ones())
phi = U_f(phi)
phi = H(phi, qubit_indices=[0])
measurement = phi.measure(qubit_indices=0)
return measurement
def deutsch_jozsa_algorithm(d, f):
# The operators we will need
U_f = qc.U_f(f, d=d + 1)
H_d = qc.Hadamard(d)
H = qc.Hadamard()
state = qc.zeros(d) * qc.ones(1)
state = (H_d * H)(state)
state = U_f(state)
state = H_d(state, qubit_indices=range(d))
measurements = state.measure(qubit_indices=range(d))
return measurements
def grover_algorithm(d, f):
# The operators we will need
Oracle = qc.U_f(f, d=d+1)
H_d = qc.Hadamard(d)
H = qc.Hadamard()
N = 2**d
zero_projector = np.zeros((N, N))
zero_projector[0, 0] = 1
Inversion = H_d((2 * qc.Operator.from_matrix(zero_projector) - qc.Identity(d))(H_d))
Grover = Inversion(Oracle, qubit_indices=range(d))
# Initial state
state = qc.zeros(d) * qc.ones(1)
state = (H_d * H)(state)
# Number of Grover iterations
angle_to_rotate = np.arccos(np.sqrt(1 / N))
rotation_angle = 2 * np.arcsin(np.sqrt(1 / N))
iterations = int(round(angle_to_rotate / rotation_angle))
for i in range(iterations):
state = Grover(state)
measurements = state.measure(qubit_indices=range(d))
return measurements