def test_hybrid_gradients(self, qubit_device_2_wires, tol):
"Tests that the various ways of computing the gradient of a hybrid computation all agree."
# input data is the first parameter
def classifier_circuit(in_data, x):
qml.RX(in_data, wires=[0])
qml.CNOT(wires=[0, 1])
qml.RY(-1.6, wires=[0])
qml.RY(in_data, wires=[1])
qml.CNOT(wires=[1, 0])
qml.RX(x, wires=[0])
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(0))
classifier = to_autograd(
QubitQNode(classifier_circuit, qubit_device_2_wires))
param = -0.1259
in_data = np.array([-0.1, -0.88, np.exp(0.5)])
out_data = np.array([1.5, np.pi / 3, 0.0])
def error(p):
"Total square error of classifier predictions."
ret = 0
for d_in, d_out in zip(in_data, out_data):
square_diff = (classifier(d_in, p) - d_out)**2
ret = ret + square_diff
return ret
def d_error(p, grad_method):
"Gradient of error, computed manually."
ret = 0
for d_in, d_out in zip(in_data, out_data):
args = (d_in, p)
diff = (classifier(*args) - d_out)
ret = ret + 2 * diff * classifier.jacobian(
args, wrt=[1], method=grad_method)
return ret
y0 = error(param)
grad = autograd.grad(error)
grad_auto = grad(param)
grad_fd1 = d_error(param, 'F')
grad_angle = d_error(param, 'A')
# gradients computed with different methods must agree
assert grad_fd1 == pytest.approx(grad_angle, abs=tol)
assert grad_fd1 == pytest.approx(grad_auto, abs=tol)
assert grad_angle == pytest.approx(grad_auto, 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)
def test_rotation_gradient(self, theta, tol):
"""Tests that the automatic gradient of a phase space rotation is correct."""
def circuit(y):
qml.Displacement(alpha, 0., wires=[0])
qml.Rotation(y, wires=[0])
return qml.expval(qml.X(0))
dev = qml.device('default.gaussian', wires=1)
circuit = to_autograd(QubitQNode(circuit, dev))
grad_fn = autograd.grad(circuit)
autograd_val = grad_fn(theta)
# qfunc evalutes to hbar * alpha * cos(theta)
manualgrad_val = -hbar * alpha * np.sin(theta)
assert autograd_val == pytest.approx(manualgrad_val, 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_multiple_expectation_jacobian_array(self, tol, qubit_device_2_wires):
"""Tests that qnodes using an array argument return correct gradients
for multiple expectation values."""
par = np.array([0.5, 0.54, 0.3])
def circuit(weights):
qml.QubitStateVector(np.array([1, 0, 1, 1]) / np.sqrt(3), wires=[0, 1])
qml.Rot(weights[0], weights[1], weights[2], wires=0)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(0)), qml.expval(qml.PauliY(1))
circuit = to_autograd(QubitQNode(circuit, qubit_device_2_wires))
expected_jac = self.expected_jacobian(*par)
res = circuit.jacobian([par])
assert expected_jac == pytest.approx(res, abs=tol)
jac = autograd.jacobian(circuit, 0)
res = jac(par)
assert expected_jac == pytest.approx(res, abs=tol)
def sample_circuit(self):
"""Sample variational circuit fixture used in the
next couple of tests"""
dev = qml.device("default.qubit", wires=3)
def non_parametrized_layer(a, b, c):
qml.RX(a, wires=0)
qml.RX(b, wires=1)
qml.RX(c, wires=1)
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[1, 2])
qml.RZ(a, wires=0)
qml.Hadamard(wires=1)
qml.CNOT(wires=[0, 1])
qml.RZ(b, wires=1)
qml.Hadamard(wires=0)
a = 0.5
b = 0.1
c = 0.5
def final(x, y, z, h, g, f):
non_parametrized_layer(a, b, c)
qml.RX(x, wires=0)
qml.RY(y, wires=1)
qml.RZ(z, wires=2)
non_parametrized_layer(a, b, c)
qml.RY(f, wires=1)
qml.RZ(g, wires=2)
qml.RX(h, wires=1)
return qml.expval(qml.PauliX(0)), qml.expval(
qml.PauliX(1)), qml.expval(qml.PauliX(2))
final = QubitQNode(final, dev)
return dev, final, non_parametrized_layer, a, b, c
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_construct_subcircuit_layers(self):
"""Test correct subcircuits constructed
when a layer structure exists"""
dev = qml.device("default.qubit", wires=3)
def circuit(params):
# section 1
qml.RX(params[0], wires=0)
# section 2
qml.RY(params[1], wires=0)
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[1, 2])
# section 3
qml.RX(params[2], wires=0)
qml.RY(params[3], wires=1)
qml.RZ(params[4], wires=2)
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[1, 2])
# section 4
qml.RX(params[5], wires=0)
qml.RY(params[6], wires=1)
qml.RZ(params[7], wires=2)
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[1, 2])
return qml.expval(qml.PauliX(0)), qml.expval(
qml.PauliX(1)), qml.expval(qml.PauliX(2))
circuit = QubitQNode(circuit, dev)
params = np.ones([8])
circuit.metric_tensor([params], only_construct=True)
res = circuit._metric_tensor_subcircuits
# this circuit should split into 4 independent
# sections or layers when constructing subcircuits
assert len(res) == 4
# first layer subcircuit
layer = res[(0, )]
assert len(layer["queue"]) == 0
assert len(layer["observable"]) == 1
assert isinstance(layer["observable"][0], qml.PauliX)
# second layer subcircuit
layer = res[(1, )]
assert len(layer["queue"]) == 1
assert len(layer["observable"]) == 1
assert isinstance(layer["queue"][0], qml.RX)
assert isinstance(layer["observable"][0], qml.PauliY)
# third layer subcircuit
layer = res[(2, 3, 4)]
assert len(layer["queue"]) == 4
assert len(layer["observable"]) == 3
assert isinstance(layer["queue"][0], qml.RX)
assert isinstance(layer["queue"][1], qml.RY)
assert isinstance(layer["queue"][2], qml.CNOT)
assert isinstance(layer["queue"][3], qml.CNOT)
assert isinstance(layer["observable"][0], qml.PauliX)
assert isinstance(layer["observable"][1], qml.PauliY)
assert isinstance(layer["observable"][2], qml.PauliZ)
# fourth layer subcircuit
layer = res[(5, 6, 7)]
assert len(layer["queue"]) == 9
assert len(layer["observable"]) == 3
assert isinstance(layer["queue"][0], qml.RX)
assert isinstance(layer["queue"][1], qml.RY)
assert isinstance(layer["queue"][2], qml.CNOT)
assert isinstance(layer["queue"][3], qml.CNOT)
assert isinstance(layer["queue"][4], qml.RX)
assert isinstance(layer["queue"][5], qml.RY)
assert isinstance(layer["queue"][6], qml.RZ)
assert isinstance(layer["queue"][7], qml.CNOT)
assert isinstance(layer["queue"][8], qml.CNOT)
assert isinstance(layer["observable"][0], qml.PauliX)
assert isinstance(layer["observable"][1], qml.PauliY)
assert isinstance(layer["observable"][2], qml.PauliZ)
def test_evaluate_diag_approx_metric_tensor(self, sample_circuit, tol):
"""Test that a metric tensor under the
diagonal approximation evaluates correctly."""
dev, circuit, non_parametrized_layer, a, b, c = sample_circuit
params = [-0.282203, 0.145554, 0.331624, -0.163907, 0.57662, 0.081272]
x, y, z, h, g, f = params
G = circuit.metric_tensor(params, diag_approx=True)
# ============================================
# Test block diag metric tensor of first layer is correct.
# We do this by comparing against the known analytic result.
# First layer includes the non_parametrized_layer,
# followed by observables corresponding to generators of:
# qml.RX(x, wires=0)
# qml.RY(y, wires=1)
# qml.RZ(z, wires=2)
G1 = np.zeros([3, 3])
# diag elements
G1[0, 0] = np.sin(a)**2 / 4
G1[1,
1] = (16 * np.cos(a)**2 * np.sin(b)**3 * np.cos(b) * np.sin(2 * c) +
np.cos(2 * b) *
(2 - 8 * np.cos(a)**2 * np.sin(b)**2 * np.cos(2 * c)) +
np.cos(2 * (a - b)) + np.cos(2 * (a + b)) -
2 * np.cos(2 * a) + 14) / 64
G1[2,
2] = (3 - np.cos(2 * a) - 2 * np.cos(a)**2 * np.cos(2 *
(b + c))) / 16
assert np.allclose(G[:3, :3], G1, atol=tol, rtol=0)
# =============================================
# Test metric tensor of second layer is correct.
# We do this by computing the required expectation values
# numerically.
# The second layer includes the non_parametrized_layer,
# RX, RY, RZ gates (x, y, z params), a 2nd non_parametrized_layer,
# followed by the qml.RY(f, wires=2) operation.
#
# Observable is simply generator of:
# qml.RY(f, wires=2)
#
# Note: since this layer only consists of a single parameter,
# only need to compute a single diagonal element.
def layer2_diag(x, y, z, h, g, f):
non_parametrized_layer(a, b, c)
qml.RX(x, wires=0)
qml.RY(y, wires=1)
qml.RZ(z, wires=2)
non_parametrized_layer(a, b, c)
qml.RY(f, wires=2)
return qml.var(qml.PauliX(1))
layer2_diag = QubitQNode(layer2_diag, dev)
G2 = layer2_diag(x, y, z, h, g, f) / 4
assert np.allclose(G[3:4, 3:4], G2, atol=tol, rtol=0)
# =============================================
# Test block diag metric tensor of third layer is correct.
# We do this by computing the required expectation values
# numerically using multiple circuits.
# The second layer includes the non_parametrized_layer,
# RX, RY, RZ gates (x, y, z params), and a 2nd non_parametrized_layer.
#
# Observables are the generators of:
# qml.RY(f, wires=1)
# qml.RZ(g, wires=2)
G3 = np.zeros([2, 2])
def layer3_diag(x, y, z, h, g, f):
non_parametrized_layer(a, b, c)
qml.RX(x, wires=0)
qml.RY(y, wires=1)
qml.RZ(z, wires=2)
non_parametrized_layer(a, b, c)
return qml.var(qml.PauliZ(2)), qml.var(qml.PauliY(1))
layer3_diag = QubitQNode(layer3_diag, dev)
# calculate the diagonal terms
varK0, varK1 = layer3_diag(x, y, z, h, g, f)
G3[0, 0] = varK0 / 4
G3[1, 1] = varK1 / 4
assert np.allclose(G[4:6, 4:6], G3, atol=tol, rtol=0)
# ============================================
# Finally, double check that the entire metric
# tensor is as computed.
G_expected = block_diag(G1, G2, G3)
assert np.allclose(G, G_expected, atol=tol, rtol=0)