def modifiedGramSchmidt(A):
# assuming A is a square matrix
dim = A.shape[0]
Q = np.zeros(A.shape, dtype=A.dtype)
for j in range(0, dim):
q = A[:, j]
for i in range(0, j):
rij = np.vdot(Q[:, i], q)
q = q - rij * Q[:, i]
rjj = np.linalg.norm(q, ord=2)
if np.isclose(rjj, 0.0):
raise ValueError("invalid input matrix")
else:
Q[:, j] = q / rjj
return Q
def test_multiple_expectation_different_wires(self):
"Tests that qnodes return multiple expectation values."
self.logTestName()
a, b, c = 0.5, 0.54, 0.3
@qml.qnode(self.dev2)
def circuit(x, y, z):
qml.RX(x, [0])
qml.RZ(y, [0])
qml.CNOT([0, 1])
qml.RY(y, [0])
qml.RX(z, [0])
return qml.expval.PauliY(0), qml.expval.PauliZ(1)
res = circuit(a, b, c)
out_state = np.kron(Rotx(c), I) @ np.kron(Roty(b), I) @ CNOT \
@ np.kron(Rotz(b), I) @ np.kron(Rotx(a), I) @ np.array([1, 0, 0, 0])
ex0 = np.vdot(out_state, np.kron(Y, I) @ out_state)
ex1 = np.vdot(out_state, np.kron(I, Z) @ out_state)
ex = np.array([ex0, ex1])
self.assertAllAlmostEqual(ex, res, delta=self.tol)
def real_ip(u, v):
"""Real inner product of complex vectors."""
ip = np.real(np.vdot(u, v))
return ip