def Quantum_system(mat, click, state):
start = mat
for i in range(click):
state_click = mat_op.mult_mat(start, mat_op.transpuesta(state))
start = mat_op.mult_mat(start, mat)
state_click = [[round((state_click[i][0].mod())**2, 2)]
for i in range(len(state_click))]
Plot(len(state_click), mat_op.transpuesta(state_click))
return state_click
def Dynamics(n, U_n, state):
if mat_op.unitary(U_n):
U = U_n
for i in range(n):
ans = mat_op.mult_mat(U, state)
U = mat_op.mult_mat(U, U_n)
prob = ans
prob = [round(ans[i][0].mod()**2, 2) for i in range(len(ans))]
return prob
else:
return 'Matriz no unitaria'
def exp_complex_slit(mat):
A = mat
V = [complex_cart(0, 0) for i in range(len(mat))]
V[0] = complex_cart(1, 0)
V = mat_op.transpuesta(V)
for i in range(2):
C = mat_op.mult_mat(A, V)
A = mat_op.mult_mat(A, mat)
B = mat_op.transpuesta(C[:])
for i in range(len(B)):
B[i] = round(B[i].mod()**2, 2)
Plot(len(B), B)
return mat_op.transpuesta(B)
def test_mult_mat(self):
self.assertEqual(
str(mat_op.mult_mat(self.mat_comp_b, self.mat_comp_a)),
'[[-6 + 18i, -6 + 18i], [-6 + 18i, -6 + 18i], [-6 + 18i, -6 + 18i]]'
)
self.assertEqual(
str(
mat_op.mult_mat(self.mat_comp_b,
mat_op.transpuesta(self.mat_comp_b))),
'[[0 + 28i, 0 + 28i, 0 + 28i], [0 + 28i, 0 + 28i, 0 + 28i], [0 + 28i, 0 + 28i, 0 + 28i]]'
)
self.assertEqual(
str(
mat_op.mult_mat(self.mat_comp_a,
mat_op.transpuesta(self.mat_comp_a))),
'[[-6 + 8i, -6 + 8i, -6 + 8i], [-6 + 8i, -6 + 8i, -6 + 8i], [-6 + 8i, -6 + 8i, -6 + 8i]]'
)
def Observables(observable, ket):
if mat_op.hermitian(observable):
ans = mat_op.mult_mat(observable, ket)
media = mat_op.product_in(mat_op.transpuesta(ans),
mat_op.transpuesta(ket))
identy = mat_op.mult_esc_mat(media, Identy(len(observable)))
operador = mat_op.sum_mat_com(observable, mat_op.inv_adit_mat(identy))
operador_1 = mat_op.mult_mat(operador, operador)
ket_operador = mat_op.transpuesta(mat_op.mult_mat(operador_1, ket))
var = mat_op.product_in(mat_op.transpuesta(ket), ket_operador)
return var.a
else:
return None
def Problem(x):
if x == '4.3.1':
observable = [[complex_cart(0, 0),
complex_cart(1, 0)],
[complex_cart(1, 0),
complex_cart(0, 0)]]
ket = [[complex_cart(1, 0)], [complex_cart(0, 0)]]
ans = Measuring(observable, ket)
return ans[1]
elif x == '4.3.2':
observable = [[complex_cart(0, 0),
complex_cart(1, 0)],
[complex_cart(1, 0),
complex_cart(0, 0)]]
ket = [[complex_cart(1, 0)], [complex_cart(0, 0)]]
ans = Measuring(observable, ket)
value = ans[0][0] * complex_cart(
ans[2][0], 0) + ans[0][1] * complex_cart(ans[2][1], 0)
print(value)
ans_1 = mat_op.mult_mat(observable, ket)
media = mat_op.product_in(mat_op.transpuesta(ans_1),
mat_op.transpuesta(ket))
print(media)
print(
'El valor de la distribucion hallado es igual al que se obtiene en el calculo de la media'
)
return (media)
elif x == '4.4.1':
U_1 = [[complex_cart(0, 0), complex_cart(1, 0)],
[complex_cart(1, 0), complex_cart(0, 0)]]
U_2 = [[
complex_cart(math.sqrt(2 / 4), 0),
complex_cart(math.sqrt(2 / 4), 0)
],
[
complex_cart(math.sqrt(2 / 4), 0),
complex_cart(-math.sqrt(2 / 4), 0)
]]
print(mat_op.unitary(U_1, ), mat_op.unitary(U_2))
print('Las dos matrices son unitarias')
U_3 = mat_op.mult_mat(U_1, U_2)
print(mat_op.unitary(U_3))
print('El producto de las matrices es unitario')
return [mat_op.unitary(U_3)]
elif x == '4.4.2':
U_n = [[
complex_cart(0, 0),
complex_cart(1 / math.sqrt(2), 0),
complex_cart(1 / math.sqrt(2), 0),
complex_cart(0, 0)
],
[
complex_cart(0, 1 / math.sqrt(2)),
complex_cart(0, 0),
complex_cart(0, 0),
complex_cart(1 / math.sqrt(2), 0)
],
[
complex_cart(1 / math.sqrt(2), 0),
complex_cart(0, 0),
complex_cart(0, 0),
complex_cart(0, 1 / math.sqrt(2))
],
[
complex_cart(0, 0),
complex_cart(1 / math.sqrt(2), 0),
complex_cart(-1 / math.sqrt(2), 0),
complex_cart(0, 0)
]]
state = state = mat_op.transpuesta([
complex_cart(1, 0),
complex_cart(0, 0),
complex_cart(0, 0),
complex_cart(0, 0)
])
ans = Dynamics(3, U_n, state)
return ans[3]
elif x == '4.5.2':
return 'hola'
else:
return 'EL ejercicio no fue propuesto'