def test_keywordarg_not_differentiated(self, tol):
"""Tests that qnodes do not differentiate w.r.t. keyword arguments."""
par = np.array([0.5, 0.54])
def circuit1(weights, x=0.3):
qml.QubitStateVector(np.array([1, 0, 1, 1]) / np.sqrt(3),
wires=[0, 1])
qml.Rot(weights[0], weights[1], x, wires=0)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliY(1))
dev = qml.device("default.qubit", wires=2)
circuit1 = QubitQNode(circuit1, dev)
def circuit2(weights):
qml.QubitStateVector(np.array([1, 0, 1, 1]) / np.sqrt(3),
wires=[0, 1])
qml.Rot(weights[0], weights[1], 0.3, wires=0)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliY(1))
circuit2 = QubitQNode(circuit2, dev)
res1 = circuit1.jacobian([par])
res2 = circuit2.jacobian([par])
assert res1 == pytest.approx(res2, abs=tol)
def test_array_parameters_evaluate(self, tol):
"""Tests that array parameters gives same result as positional arguments."""
a, b, c = 0.5, 0.54, 0.3
dev = qml.device("default.qubit", wires=2)
def ansatz(x, y, z):
qml.QubitStateVector(np.array([1, 0, 1, 1]) / np.sqrt(3),
wires=[0, 1])
qml.Rot(x, y, z, wires=0)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliY(1))
def circuit1(x, y, z):
return ansatz(x, y, z)
def circuit2(x, array):
return ansatz(x, array[0], array[1])
def circuit3(array):
return ansatz(*array)
circuit1 = QubitQNode(circuit1, dev)
circuit2 = QubitQNode(circuit2, dev)
circuit3 = QubitQNode(circuit3, dev)
positional_res = circuit1(a, b, c)
positional_grad = circuit1.jacobian([a, b, c])
array_res = circuit2(a, np.array([b, c]))
array_grad = circuit2.jacobian([a, np.array([b, c])])
assert positional_res == pytest.approx(array_res, abs=tol)
assert positional_grad == pytest.approx(array_grad, abs=tol)
list_res = circuit2(a, [b, c])
list_grad = circuit2.jacobian([a, [b, c]])
assert positional_res == pytest.approx(list_res, abs=tol)
assert positional_grad == pytest.approx(list_grad, abs=tol)
array_res = circuit3(np.array([a, b, c]))
array_grad = circuit3.jacobian([np.array([a, b, c])])
list_res = circuit3([a, b, c])
list_grad = circuit3.jacobian([[a, b, c]])
assert positional_res == pytest.approx(array_res, abs=tol)
assert positional_grad == pytest.approx(array_grad, abs=tol)
def test_fanout_multiple_params(self, reused_p, other_p, tol):
"""Tests that the correct gradient is computed for qnodes which
use the same parameter in multiple gates."""
from pennylane.plugins.default_qubit import Rotx as Rx, Roty as Ry, Rotz as Rz
def expZ(state):
return np.abs(state[0])**2 - np.abs(state[1])**2
extra_param = 0.31
def circuit(reused_param, other_param):
qml.RX(extra_param, wires=[0])
qml.RY(reused_param, wires=[0])
qml.RZ(other_param, wires=[0])
qml.RX(reused_param, wires=[0])
return qml.expval(qml.PauliZ(0))
dev = qml.device("default.qubit", wires=1)
f = QubitQNode(circuit, dev)
zero_state = np.array([1., 0.])
# analytic gradient
grad_A = f.jacobian([reused_p, other_p])
# manual gradient
grad_true0 = (expZ(Rx(reused_p) @ Rz(other_p) @ Ry(reused_p + np.pi / 2) @ Rx(extra_param) @ zero_state) \
-expZ(Rx(reused_p) @ Rz(other_p) @ Ry(reused_p - np.pi / 2) @ Rx(extra_param) @ zero_state)) / 2
grad_true1 = (expZ(Rx(reused_p + np.pi / 2) @ Rz(other_p) @ Ry(reused_p) @ Rx(extra_param) @ zero_state) \
-expZ(Rx(reused_p - np.pi / 2) @ Rz(other_p) @ Ry(reused_p) @ Rx(extra_param) @ zero_state)) / 2
grad_true = grad_true0 + grad_true1 # product rule
assert grad_A[0, 0] == pytest.approx(grad_true, abs=tol)
def test_differentiate_positional_multidim(self, tol):
"""Tests that all positional arguments are differentiated
when they are multidimensional."""
def circuit(a, b):
qml.RX(a[0], wires=0)
qml.RX(a[1], wires=1)
qml.RX(b[2, 1], wires=2)
return qml.expval(qml.PauliZ(0)), qml.expval(
qml.PauliZ(1)), qml.expval(qml.PauliZ(2))
dev = qml.device("default.qubit", wires=3)
circuit = QubitQNode(circuit, dev)
a = np.array([-np.sqrt(2), -0.54])
b = np.array([np.pi / 7] * 6).reshape([3, 2])
circuit_output = circuit(a, b)
expected_output = np.cos(np.array([a[0], a[1], b[-1, 0]]))
assert circuit_output == pytest.approx(expected_output, abs=tol)
# circuit jacobians
circuit_jacobian = circuit.jacobian([a, b])
expected_jacobian = np.array([
[-np.sin(a[0])] + [0.0] * 7, # expval 0
[0.0, -np.sin(a[1])] + [0.0] * 6, # expval 1
[0.0] * 2 + [0.0] * 5 + [-np.sin(b[2, 1])],
]) # expval 2
assert circuit_jacobian == pytest.approx(expected_jacobian, abs=tol)
def test_multidim_array_parameter(self, shape, tol):
"""Tests that arguments which are multidimensional arrays are
properly evaluated and differentiated in QubitQNodes."""
n = np.prod(shape)
base_array = np.linspace(-1.0, 1.0, n)
multidim_array = np.reshape(base_array, shape)
def circuit(w):
for k in range(n):
qml.RX(w[np.unravel_index(k, shape)], wires=k) # base_array[k]
return tuple(qml.expval(qml.PauliZ(idx)) for idx in range(n))
dev = qml.device("default.qubit", wires=n)
circuit = QubitQNode(circuit, dev)
# circuit evaluations
circuit_output = circuit(multidim_array)
expected_output = np.cos(base_array)
assert circuit_output == pytest.approx(expected_output, abs=tol)
# circuit jacobians
circuit_jacobian = circuit.jacobian([multidim_array])
expected_jacobian = -np.diag(np.sin(base_array))
assert circuit_jacobian == pytest.approx(expected_jacobian, abs=tol)
def test_controlled_RZ_gradient(self, tol):
"""Test gradient of controlled RZ gate"""
dev = qml.device("default.qubit", wires=2)
def circuit(x):
qml.PauliX(wires=0)
qml.CRZ(x, wires=[0, 1])
return qml.expval(qml.PauliZ(0))
circuit = QubitQNode(circuit, dev)
a = 0.542 # any value of a should give zero gradient
# get the analytic gradient
gradA = circuit.jacobian([a], method="A")
# get the finite difference gradient
gradF = circuit.jacobian([a], method="F")
# the expected gradient
expected = 0
assert gradF == pytest.approx(expected, abs=tol)
assert gradA == pytest.approx(expected, abs=tol)
def circuit1(x):
qml.RX(x, wires=0)
qml.CRZ(x, wires=[0, 1])
return qml.expval(qml.PauliZ(0))
circuit1 = QubitQNode(circuit1, dev)
b = 0.123 # gradient is -sin(x)
# get the analytic gradient
gradA = circuit1.jacobian([b], method="A")
# get the finite difference gradient
gradF = circuit1.jacobian([b], method="F")
# the expected gradient
expected = -np.sin(b)
assert gradF == pytest.approx(expected, abs=tol)
assert gradA == pytest.approx(expected, abs=tol)
def test_gradient_parameters_inside_array(self, tol):
"""Tests that free parameters inside an array passed to
an Operation yield correct gradients."""
par = [0.8, 1.3]
def qf(x, y):
qml.RX(x, wires=[0])
qml.RY(x, wires=[0])
return qml.expval(qml.Hermitian(np.diag([y, 1]), 0))
dev = qml.device("default.qubit", wires=1)
q = QubitQNode(qf, dev)
grad = q.jacobian(par)
grad_F = q.jacobian(par, method="F")
# par[0] can use the "A" method, par[1] cannot
assert q.par_to_grad_method == {0: "A", 1: "F"}
# the different methods agree
assert grad == pytest.approx(grad_F, abs=tol)
def test_pauli_rotation_gradient(self, G, theta, tol):
"""Tests that the automatic gradients of Pauli rotations are correct."""
def circuit(x):
qml.RX(x, wires=[0])
return qml.expval(qml.PauliZ(0))
dev = qml.device("default.qubit", wires=1)
circuit = QubitQNode(circuit, dev)
autograd_val = circuit.jacobian([theta])
manualgrad_val = (circuit(theta + np.pi / 2) -
circuit(theta - np.pi / 2)) / 2
assert autograd_val == pytest.approx(manualgrad_val, abs=tol)
def test_gradient_repeated_gate_parameters(self, tol):
"""Tests that repeated use of a free parameter in a
multi-parameter gate yield correct gradients."""
par = [0.8, 1.3]
def qf(x, y):
qml.RX(np.pi / 4, wires=[0])
qml.Rot(y, x, 2 * x, wires=[0])
return qml.expval(qml.PauliX(0))
dev = qml.device("default.qubit", wires=1)
q = QubitQNode(qf, dev)
grad_A = q.jacobian(par, method="A")
grad_F = q.jacobian(par, method="F")
# the different methods agree
assert grad_A == pytest.approx(grad_F, abs=tol)
def test_expval_and_variance(self, tol):
"""Test that the qnode works for a combination of expectation
values and variances"""
dev = qml.device("default.qubit", wires=3)
def circuit(a, b, c):
qml.RX(a, wires=0)
qml.RY(b, wires=1)
qml.CNOT(wires=[1, 2])
qml.RX(c, wires=2)
qml.CNOT(wires=[0, 1])
qml.RZ(c, wires=2)
return qml.var(qml.PauliZ(0)), qml.expval(qml.PauliZ(1)), qml.var(
qml.PauliZ(2))
circuit = QubitQNode(circuit, dev)
a = 0.54
b = -0.423
c = 0.123
var = circuit(a, b, c)
expected = np.array([
np.sin(a)**2,
np.cos(a) * np.cos(b),
0.25 * (3 - 2 * np.cos(b)**2 * np.cos(2 * c) - np.cos(2 * b)),
])
assert var == pytest.approx(expected, abs=tol)
# # circuit jacobians
gradA = circuit.jacobian([a, b, c], method="A")
gradF = circuit.jacobian([a, b, c], method="F")
expected = np.array([
[2 * np.cos(a) * np.sin(a), -np.cos(b) * np.sin(a), 0],
[
0,
-np.cos(a) * np.sin(b),
0.5 *
(2 * np.cos(b) * np.cos(2 * c) * np.sin(b) + np.sin(2 * b)),
],
[0, 0, np.cos(b)**2 * np.sin(2 * c)],
]).T
assert gradF == pytest.approx(expected, abs=tol)
assert gradA == pytest.approx(expected, abs=tol)
def test_differentiate_second_positional(self, tol):
"""Tests that the second positional arguments are differentiated."""
def circuit3(a, b):
qml.RX(b, wires=0)
return qml.expval(qml.PauliZ(0))
dev = qml.device("default.qubit", wires=2)
circuit3 = QubitQNode(circuit3, dev)
a = 0.7418
b = -5.0
circuit_output = circuit3(a, b)
expected_output = np.cos(b)
assert circuit_output == pytest.approx(expected_output, abs=tol)
# circuit jacobians
circuit_jacobian = circuit3.jacobian([a, b])
expected_jacobian = np.array([[0, -np.sin(b)]])
assert circuit_jacobian == pytest.approx(expected_jacobian, abs=tol)
def test_involutory_variance(self, tol):
"""Tests qubit observable that are involutory"""
def circuit(a):
qml.RX(a, wires=0)
return qml.var(qml.PauliZ(0))
dev = qml.device("default.qubit", wires=1)
circuit = QubitQNode(circuit, dev)
a = 0.54
var = circuit(a)
expected = 1 - np.cos(a)**2
assert var == pytest.approx(expected, abs=tol)
# circuit jacobians
gradA = circuit.jacobian([a], method="A")
gradF = circuit.jacobian([a], method="F")
expected = 2 * np.sin(a) * np.cos(a)
assert gradF == pytest.approx(expected, abs=tol)
assert gradA == pytest.approx(expected, abs=tol)
def test_differentiate_all_positional(self, tol):
"""Tests that all positional arguments are differentiated."""
def circuit1(a, b, c):
qml.RX(a, wires=0)
qml.RX(b, wires=1)
qml.RX(c, wires=2)
return tuple(qml.expval(qml.PauliZ(idx)) for idx in range(3))
dev = qml.device("default.qubit", wires=3)
circuit1 = QubitQNode(circuit1, dev)
vals = np.array([np.pi, np.pi / 2, np.pi / 3])
circuit_output = circuit1(*vals)
expected_output = np.cos(vals)
assert circuit_output == pytest.approx(expected_output, abs=tol)
# circuit jacobians
circuit_jacobian = circuit1.jacobian(vals)
expected_jacobian = -np.diag(np.sin(vals))
assert circuit_jacobian == pytest.approx(expected_jacobian, abs=tol)
def test_fanout(self, tol):
"""Tests qubit observable with repeated parameters"""
def circuit(a):
qml.RX(a, wires=0)
qml.RY(a, wires=0)
return qml.var(qml.PauliZ(0))
dev = qml.device("default.qubit", wires=2)
circuit = QubitQNode(circuit, dev)
a = 0.54
var = circuit(a)
expected = 0.5 * np.sin(a)**2 * (np.cos(2 * a) + 3)
assert var == pytest.approx(expected, abs=tol)
# circuit jacobians
gradA = circuit.jacobian([a], method="A")
gradF = circuit.jacobian([a], method="F")
expected = 4 * np.sin(a) * np.cos(a)**3
assert gradA == pytest.approx(expected, abs=tol)
assert gradF == pytest.approx(expected, abs=tol)
def test_Rot_gradient(self, theta, tol):
"""Tests that the automatic gradient of a arbitrary Euler-angle-parameterized gate is correct."""
def circuit(x, y, z):
qml.Rot(x, y, z, wires=[0])
return qml.expval(qml.PauliZ(0))
dev = qml.device("default.qubit", wires=1)
circuit = QubitQNode(circuit, dev)
eye = np.eye(3)
angle_inputs = np.array([theta, theta**3, np.sqrt(2) * theta])
autograd_val = circuit.jacobian(angle_inputs)
manualgrad_val = np.zeros((1, 3))
for idx in range(3):
onehot_idx = eye[idx]
param1 = angle_inputs + np.pi / 2 * onehot_idx
param2 = angle_inputs - np.pi / 2 * onehot_idx
manualgrad_val[0, idx] = (circuit(*param1) - circuit(*param2)) / 2
assert autograd_val == pytest.approx(manualgrad_val, abs=tol)
def test_non_involutory_variance(self, tol):
"""Tests a qubit Hermitian observable that is not involutory"""
A = np.array([[4, -1 + 6j], [-1 - 6j, 2]])
def circuit(a):
qml.RX(a, wires=0)
return qml.var(qml.Hermitian(A, 0))
dev = qml.device("default.qubit", wires=1)
circuit = QubitQNode(circuit, dev)
a = 0.54
var = circuit(a)
expected = (39 / 2) - 6 * np.sin(2 * a) + (35 / 2) * np.cos(2 * a)
assert var == pytest.approx(expected, abs=tol)
# circuit jacobians
gradA = circuit.jacobian([a], method="A")
gradF = circuit.jacobian([a], method="F")
expected = -35 * np.sin(2 * a) - 12 * np.cos(2 * a)
assert gradA == pytest.approx(expected, abs=tol)
assert gradF == pytest.approx(expected, abs=tol)
def test_differentiate_second_third_positional(self, tol):
"""Tests that the second and third positional arguments are differentiated."""
def circuit4(a, b, c):
qml.RX(b, wires=0)
qml.RX(c, wires=1)
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliZ(1))
dev = qml.device("default.qubit", wires=2)
circuit4 = QubitQNode(circuit4, dev)
a = 0.7418
b = -5.0
c = np.pi / 7
circuit_output = circuit4(a, b, c)
expected_output = np.array([np.cos(b), np.cos(c)])
assert circuit_output == pytest.approx(expected_output, abs=tol)
# circuit jacobians
circuit_jacobian = circuit4.jacobian([a, b, c])
expected_jacobian = np.array([[0.0, -np.sin(b), 0.0],
[0.0, 0.0, -np.sin(c)]])
assert circuit_jacobian == pytest.approx(expected_jacobian, abs=tol)
def test_gradient_gate_with_multiple_parameters(self, tol):
"""Tests that gates with multiple free parameters yield correct gradients."""
par = [0.5, 0.3, -0.7]
def qf(x, y, z):
qml.RX(0.4, wires=[0])
qml.Rot(x, y, z, wires=[0])
qml.RY(-0.2, wires=[0])
return qml.expval(qml.PauliZ(0))
dev = qml.device("default.qubit", wires=1)
q = QubitQNode(qf, dev)
value = q(*par)
grad_A = q.jacobian(par, method="A")
grad_F = q.jacobian(par, method="F")
# analytic method works for every parameter
assert q.par_to_grad_method == {0: "A", 1: "A", 2: "A"}
# gradient has the correct shape and every element is nonzero
assert grad_A.shape == (1, 3)
assert np.count_nonzero(grad_A) == 3
# the different methods agree
assert grad_A == pytest.approx(grad_F, abs=tol)