def test_cv_gradients_multiple_gate_parameters(self, tol):
"""Tests that gates with multiple free parameters yield correct gradients."""
gaussian_dev = qml.device("default.gaussian", wires=2)
par = [0.4, -0.3, -0.7, 0.2]
def qf(r0, phi0, r1, phi1):
qml.Squeezing(r0, phi0, wires=[0])
qml.Squeezing(r1, phi1, wires=[0])
return qml.expval(qml.NumberOperator(0))
q = CVQNode(qf, gaussian_dev)
grad_F = q.jacobian(par, method="F")
grad_A = q.jacobian(par, method="A")
grad_A2 = q.jacobian(par, method="A", options={'force_order2': True})
# analytic method works for every parameter
assert q.par_to_grad_method == {i:"A" for i in range(4)}
# the different methods agree
assert grad_A == pytest.approx(grad_F, abs=tol)
assert grad_A2 == pytest.approx(grad_F, abs=tol)
# check against the known analytic formula
r0, phi0, r1, phi1 = par
dn = np.zeros([4])
dn[0] = np.cosh(2 * r1) * np.sinh(2 * r0) + np.cos(phi0 - phi1) * np.cosh(2 * r0) * np.sinh(2 * r1)
dn[1] = -0.5 * np.sin(phi0 - phi1) * np.sinh(2 * r0) * np.sinh(2 * r1)
dn[2] = np.cos(phi0 - phi1) * np.cosh(2 * r1) * np.sinh(2 * r0) + np.cosh(2 * r0) * np.sinh(2 * r1)
dn[3] = 0.5 * np.sin(phi0 - phi1) * np.sinh(2 * r0) * np.sinh(2 * r1)
assert dn[np.newaxis, :] == pytest.approx(grad_F, abs=tol)
def test_first_order_cv(self, tol):
"""Test variance of a first order CV expectation value"""
dev = qml.device("default.gaussian", wires=1)
def circuit(r, phi):
qml.Squeezing(r, 0, wires=0)
qml.Rotation(phi, wires=0)
return qml.var(qml.X(0))
circuit = CVQNode(circuit, dev)
r = 0.543
phi = -0.654
var = circuit(r, phi)
expected = np.exp(2 * r) * np.sin(phi) ** 2 + np.exp(-2 * r) * np.cos(phi) ** 2
assert var == pytest.approx(expected, abs=tol)
# circuit jacobians
gradA = circuit.jacobian([r, phi], method="A")
gradF = circuit.jacobian([r, phi], method="F")
expected = np.array(
[[
2 * np.exp(2 * r) * np.sin(phi) ** 2 - 2 * np.exp(-2 * r) * np.cos(phi) ** 2,
2 * np.sinh(2 * r) * np.sin(2 * phi),
]]
)
assert gradA == pytest.approx(expected, abs=tol)
assert gradF == pytest.approx(expected, abs=tol)
def test_cv_gradients_parameters_inside_array(self, tol):
"""Tests that free parameters inside an array passed to an Operation yield correct gradients."""
gaussian_dev = qml.device("default.gaussian", wires=2)
par = [0.4, 1.3]
def qf(x, y):
qml.Displacement(0.5, 0, wires=[0])
qml.Squeezing(x, 0, wires=[0])
M = np.zeros((5, 5), dtype=object)
M[1,1] = y
M[1,2] = 1.0
M[2,1] = 1.0
return qml.expval(qml.PolyXP(M, [0, 1]))
q = CVQNode(qf, gaussian_dev)
grad_best = q.jacobian(par)
grad_best2 = q.jacobian(par, options={"force_order2": True})
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_best == pytest.approx(grad_F, abs=tol)
assert grad_best2 == pytest.approx(grad_F, abs=tol)
def test_error_analytic_second_order_cv(self):
"""Test exception raised if attempting to use a second
order observable to compute the variance derivative analytically"""
dev = qml.device("default.gaussian", wires=1)
def circuit(a):
qml.Displacement(a, 0, wires=0)
return qml.var(qml.NumberOperator(0))
circuit = CVQNode(circuit, dev)
with pytest.raises(ValueError, match=r"cannot be used with the parameters \{0\}"):
circuit.jacobian([1.0], method="A")
def test_correct_method_non_gaussian_observable(self, operable_mock_CV_device_2_wires):
"""Tests that a non-Gaussian observable one parameter fallsback to finite-diff"""
par = [0.4, -2.3]
def qf(x, y):
qml.Displacement(x, 0, wires=[0]) # followed by nongaussian observable
qml.Beamsplitter(0.2, 1.7, wires=[0, 1])
qml.Displacement(y, 0, wires=[1]) # followed by order-2 observable
return qml.expval(qml.FockStateProjector(np.array([2]), 0)), qml.expval(qml.NumberOperator(1))
q = CVQNode(qf, operable_mock_CV_device_2_wires)
q._construct(par, {})
assert q.par_to_grad_method == {0: "F", 1: "A"}
def test_correct_method_non_gaussian_preceeding_one_param(self, operable_mock_CV_device_2_wires):
"""Tests that a non-Gaussian preceeding one parameter fallsback to finite-diff"""
par = [0.4, -2.3]
def qf(x, y):
qml.Kerr(y, wires=[1])
qml.Displacement(x, 0, wires=[0])
qml.Beamsplitter(0.2, 1.7, wires=[0, 1])
return qml.expval(qml.X(0)), qml.expval(qml.X(1))
q = CVQNode(qf, operable_mock_CV_device_2_wires)
q._construct(par, {})
assert q.par_to_grad_method == {0: "A", 1: "F"}
def test_param_no_observables(self, operable_mock_CV_device_2_wires):
"""Tests that a parameter has 0 gradient if it is not followed by any observables"""
par = [0.4]
def qf(x):
qml.Displacement(x, 0, wires=[0])
qml.Squeezing(0.3, x, wires=[0])
qml.Rotation(1.3, wires=[1])
return qml.expval(qml.X(1))
q = CVQNode(qf, operable_mock_CV_device_2_wires)
q._construct(par, {})
assert q.par_to_grad_method == {0: "0"}
def test_param_not_differentiable(self, operable_mock_CV_device_2_wires):
"""Tests that a parameter is not differentiable if used in an operation
where grad_method=None"""
par = [0.4]
def qf(x):
qml.FockState(x, wires=[0])
qml.Rotation(1.3, wires=[0])
return qml.expval(qml.X(0))
q = CVQNode(qf, operable_mock_CV_device_2_wires)
q._construct(par, {})
assert q.par_to_grad_method == {0: None}
def test_correct_method_non_gaussian_successor_unused_param(self, operable_mock_CV_device_2_wires):
"""Tests that a non-Gaussian succeeding a parameter fallsback to finite-diff
alongside an unused parameter"""
par = [0.4, -2.3]
def qf(x, y):
qml.Displacement(x, 0, wires=[0])
qml.CubicPhase(0.2, wires=[0]) # nongaussian succeeding x
qml.Squeezing(0.3, x, wires=[1]) # x affects gates on both wires, y unused
qml.Rotation(1.3, wires=[1])
return qml.expval(qml.X(0)), qml.expval(qml.X(1))
q = CVQNode(qf, operable_mock_CV_device_2_wires)
q._construct(par, {})
assert q.par_to_grad_method == {0: "F", 1: "0"}
def test_correct_method_non_gaussian_successor_all_params(self, operable_mock_CV_device_2_wires):
"""Tests that a non-Gaussian succeeding all parameters fallsback to finite-diff"""
par = [0.4, -2.3]
def qf(x, y):
qml.Displacement(x, 0, wires=[0])
qml.Displacement(1.2, y, wires=[1])
qml.Beamsplitter(0.2, 1.7, wires=[0, 1])
qml.Rotation(1.9, wires=[0])
qml.Kerr(0.3, wires=[1]) # nongaussian succeeding both x and y due to the beamsplitter
return qml.expval(qml.X(0)), qml.expval(qml.X(1))
q = CVQNode(qf, operable_mock_CV_device_2_wires)
q._construct(par, {})
assert q.par_to_grad_method == {0: "F", 1: "F"}
def test_gaussian_successors_fails(self, operable_mock_CV_device_2_wires):
"""Tests that the parameter-shift differentiation method is not allowed
if a non-gaussian gate is between a differentiable gaussian gate and an observable."""
def circuit(x):
qml.Squeezing(x, 0, wires=[0])
qml.Beamsplitter(np.pi/4, 0, wires=[0, 1])
qml.Kerr(0.54, wires=[1])
return qml.expval(qml.NumberOperator(1))
node = CVQNode(circuit, operable_mock_CV_device_2_wires)
with pytest.raises(ValueError, match="analytic gradient method cannot be used with"):
node.jacobian([0.321], method="A")
assert node.par_to_grad_method == {0: "F"}
def test_non_gaussian_successors(self, gaussian_device, tol):
"""Tests that the analytic differentiation method is allowed and matches numerical
differentiation if a non-Gaussian gate is not succeeded by an observable."""
def circuit(x):
qml.Squeezing(x, 0, wires=[0])
qml.Beamsplitter(np.pi/4, 0, wires=[0, 1])
qml.Kerr(0.54, wires=[1])
return qml.expval(qml.NumberOperator(0))
node = CVQNode(circuit, gaussian_device)
res = node.jacobian([0.321], wrt=[0], method="A")
expected = node.jacobian([0.321], method="F")
assert res == pytest.approx(expected, abs=tol)
assert node.par_to_grad_method == {0: "A"}
def test_keywordarg_with_positional_arg_immutable_second_order_cv(self, tol):
"""Non-differentiable keyword arguments appear in the same op with differentiable arguments,
qfunc is immutable so kwargs are passed as Variables."""
dev = qml.device("default.gaussian", wires=1)
def circuit(x, *, k=0.0):
qml.Displacement(0.5, 0, wires=0)
qml.Squeezing(x, k, wires=0)
return qml.expval(qml.X(0))
node = CVQNode(circuit, dev, mutable=False)
par = [0.39]
aux = {'k': -0.7}
# circuit jacobians
grad_A = node.jacobian(par, aux, method="A", options={'force_order2': True})
grad_F = node.jacobian(par, aux, method="F")
assert grad_A == pytest.approx(grad_F, abs=tol)
def test_gradient_gate_with_two_parameters(self, tol):
"""Test that a gate with two parameters yields
correct gradients"""
def qf(r0, phi0, r1, phi1):
qml.Squeezing(r0, phi0, wires=[0])
qml.Squeezing(r1, phi1, wires=[0])
return qml.expval(qml.NumberOperator(0))
dev = qml.device("default.gaussian", wires=1)
q = CVQNode(qf, dev)
par = [0.543, 0.123, 0.654, -0.629]
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_keywordarg_second_order_cv(self, tol):
"""Non-differentiable keyword arguments with a second order CV expectation value."""
dev = qml.device("default.gaussian", wires=3)
def circuit(x, *, k=0.0):
qml.Displacement(x, 0, wires=0)
qml.Rotation(k, wires=0)
return qml.expval(qml.PolyXP(np.diag([0, 1, 0]), wires=0)) # X^2
node = CVQNode(circuit, dev)
par = [0.62]
aux = {'k': 0.4}
# circuit jacobians
grad_A = node.jacobian(par, aux, method="A")
grad_F = node.jacobian(par, aux, method="F")
expected = np.array([[8 * par[0] * np.cos(aux['k']) ** 2]])
assert grad_A == pytest.approx(grad_F, abs=tol)
assert grad_A == pytest.approx(expected, abs=tol)
def test_quadoperator(self, tol):
"""Test the differentiation of CV observables that depend on positional qfunc parameters."""
def circuit(a):
qml.Displacement(1.0, 0, wires=0)
return qml.expval(qml.QuadOperator(a, 0))
gaussian_dev = qml.device("default.gaussian", wires=1)
qnode = CVQNode(circuit, gaussian_dev)
par = [0.6]
grad_F = qnode.jacobian(par, method='F')
grad_A = qnode.jacobian(par, method='A')
grad_A2 = qnode.jacobian(par, method='A', options={'force_order2': True})
# par 0 can use the 'A' method
assert qnode.par_to_grad_method == {0: 'A'}
# the different methods agree
assert grad_A == pytest.approx(grad_F, abs=tol)
assert grad_A2 == pytest.approx(grad_F, abs=tol)
def test_cv_gradients_repeated_gate_parameters(self, tol):
"""Tests that repeated use of a free parameter in a multi-parameter gate yield correct gradients."""
gaussian_dev = qml.device("default.gaussian", wires=2)
par = [0.2, 0.3]
def qf(x, y):
qml.Displacement(x, 0, wires=[0])
qml.Squeezing(y, -1.3*y, wires=[0])
return qml.expval(qml.X(0))
q = CVQNode(qf, gaussian_dev)
grad_F = q.jacobian(par, method="F")
grad_A = q.jacobian(par, method="A")
grad_A2 = q.jacobian(par, method="A", options={'force_order2': True})
# analytic method works for every parameter
assert q.par_to_grad_method == {0:"A", 1:"A"}
# the different methods agree
assert grad_A == pytest.approx(grad_F, abs=tol)
assert grad_A2 == pytest.approx(grad_F, abs=tol)
def test_expval_and_variance_cv(self, tol):
"""Test that the qnode works for a combination of CV expectation
values and variances"""
dev = qml.device("default.gaussian", wires=3)
def circuit(a, b):
qml.Displacement(0.5, 0, wires=0)
qml.Squeezing(a, 0, wires=0)
qml.Squeezing(b, 0, wires=1)
qml.Beamsplitter(0.6, -0.3, wires=[0, 1])
qml.Squeezing(-0.3, 0, wires=2)
qml.Beamsplitter(1.4, 0.5, wires=[1, 2])
return qml.var(qml.X(0)), qml.expval(qml.X(1)), qml.var(qml.X(2))
node = CVQNode(circuit, dev)
par = [0.54, -0.423]
# jacobians must match
gradA = node.jacobian(par, method="A")
gradF = node.jacobian(par, method="F")
assert gradA == pytest.approx(gradF, abs=tol)
def test_second_order_cv(self, tol):
"""Test variance of a second order CV expectation value"""
dev = qml.device("default.gaussian", wires=1)
def circuit(n, a):
qml.ThermalState(n, wires=0)
qml.Displacement(a, 0, wires=0)
return qml.var(qml.NumberOperator(0))
circuit = CVQNode(circuit, dev)
n = 0.12
a = 0.765
var = circuit(n, a)
expected = n ** 2 + n + np.abs(a) ** 2 * (1 + 2 * n)
assert var == pytest.approx(expected, abs=tol)
# circuit jacobians
gradF = circuit.jacobian([n, a], method="F")
expected = np.array([[2 * a ** 2 + 2 * n + 1, 2 * a * (2 * n + 1)]])
assert gradF == pytest.approx(expected, abs=tol)
def test_cv_gradients_gaussian_circuit(self, G, O, tol):
"""Tests that the gradients of circuits of gaussian gates match between the finite difference and analytic methods."""
gaussian_dev = qml.device("default.gaussian", wires=2)
tol = 1e-5
par = [0.4]
def circuit(x):
args = [0.3] * G.num_params
args[0] = x
qml.Displacement(0.5, 0, wires=0)
G(*args, wires=range(G.num_wires))
qml.Beamsplitter(1.3, -2.3, wires=[0, 1])
qml.Displacement(-0.5, 0.1, wires=0)
qml.Squeezing(0.5, -1.5, wires=0)
qml.Rotation(-1.1, wires=0)
return qml.expval(O(wires=0))
q = CVQNode(circuit, gaussian_dev)
val = q.evaluate(par, {})
grad_F = q.jacobian(par, method="F")
grad_A2 = q.jacobian(par, method="A", options={'force_order2': True})
if O.ev_order == 1:
grad_A = q.jacobian(par, method="A")
# the different methods agree
assert grad_A == pytest.approx(grad_F, abs=tol)
# analytic method works for every parameter
assert q.par_to_grad_method == {0:"A"}
# the different methods agree
assert grad_A2 == pytest.approx(grad_F, abs=tol)
def test_CVOperation_with_heisenberg_and_no_parshift(self, name, tol):
"""An integration test for Gaussian CV gates that have a Heisenberg representation
but cannot be differentiated using the parameter-shift method themselves
(for example, they may accept no parameters, or have no gradient recipe).
Tests that the parameter-shift method can still be used with other gates in the circuit.
"""
gaussian_dev = qml.device("default.gaussian", wires=2)
cls = getattr(qml.ops, name)
if cls.supports_heisenberg and (not cls.supports_parameter_shift):
U = np.array([[0.51310276+0.81702166j, 0.13649626+0.22487759j],
[0.26300233+0.00556194j, -0.96414101-0.03508489j]])
if cls.num_wires <= 0:
w = list(range(2))
else:
w = list(range(cls.num_wires))
def circuit(x):
qml.Displacement(x, 0, wires=0)
if cls.par_domain == "A":
cls(U, wires=w)
else:
cls(wires=w)
return qml.expval(qml.X(0))
qnode = CVQNode(circuit, gaussian_dev)
grad_F = qnode.jacobian(0.5, method="F")
grad_A = qnode.jacobian(0.5, method="A")
grad_A2 = qnode.jacobian(0.5, method="A", options={'force_order2': True})
# par[0] can use the "A" method
assert qnode.par_to_grad_method == {0: "A"}
# the different methods agree
assert grad_A == pytest.approx(grad_F, abs=tol)
assert grad_A2 == pytest.approx(grad_F, abs=tol)
def test_cv_gradient_fanout(self, tol):
"""Tests that CV qnodes can compute the correct gradient when the same parameter is used
in multiple gates."""
gaussian_dev = qml.device("default.gaussian", wires=2)
par = [0.5, 1.3]
def circuit(x, y):
qml.Displacement(x, 0, wires=[0])
qml.Rotation(y, wires=[0])
qml.Displacement(0, x, wires=[0])
return qml.expval(qml.X(0))
q = CVQNode(circuit, gaussian_dev)
grad_F = q.jacobian(par, method="F")
grad_A = q.jacobian(par, method="A")
grad_A2 = q.jacobian(par, method="A", options={'force_order2': True})
# analytic method works for every parameter
assert q.par_to_grad_method == {0:"A", 1:"A"}
# the different methods agree
assert grad_A == pytest.approx(grad_F, abs=tol)
assert grad_A2 == pytest.approx(grad_F, abs=tol)
def test_displacement_gradient(self, mag, theta, tol):
"""Tests that the automatic gradient of a phase space displacement is correct."""
def circuit(r, phi):
qml.Displacement(r, phi, wires=[0])
return qml.expval(qml.X(0))
dev = qml.device('default.gaussian', wires=1)
circuit = to_autograd(CVQNode(circuit, dev))
grad_fn = autograd.grad(circuit)
#alpha = mag * np.exp(1j * theta)
autograd_val = grad_fn(mag, theta)
# qfunc evalutes to hbar * Re(alpha)
manualgrad_val = hbar * np.cos(theta)
assert autograd_val == pytest.approx(manualgrad_val, abs=tol)
def test_beamsplitter_gradient(self, theta, tol):
"""Tests that the automatic gradient of a beamsplitter is correct."""
def circuit(y):
qml.Displacement(alpha, 0., wires=[0])
qml.Beamsplitter(y, 0, wires=[0, 1])
return qml.expval(qml.X(0))
dev = qml.device('default.gaussian', wires=2)
circuit = to_autograd(CVQNode(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_squeeze_gradient(self, r, tol):
"""Tests that the automatic gradient of a phase space squeezing is correct."""
def circuit(y):
qml.Displacement(alpha, 0., wires=[0])
qml.Squeezing(y, 0., wires=[0])
return qml.expval(qml.X(0))
dev = qml.device('default.gaussian', wires=1)
circuit = to_autograd(CVQNode(circuit, dev))
grad_fn = autograd.grad(circuit)
autograd_val = grad_fn(r)
# qfunc evaluates to -exp(-r) * hbar * Re(alpha)
manualgrad_val = -np.exp(-r) * hbar * alpha
assert autograd_val == pytest.approx(manualgrad_val, abs=tol)
def test_transform_observable_incorrect_heisenberg_size():
"""The number of dimensions of a CV observable Heisenberg representation does
not match the ev_order attribute."""
class P(CVObservable):
"""Dummy CV observable with incorrect ev_order"""
num_wires = 1
num_params = 0
par_domain = None
ev_order = 2
@staticmethod
def _heisenberg_rep(p):
return np.array([0, 1, 0])
dev = qml.device("default.gaussian", wires=1)
def circuit(x):
qml.Displacement(x, 0.1, wires=0)
return qml.expval(P(0))
node = CVQNode(circuit, dev)
with pytest.raises(QuantumFunctionError, match="Mismatch between the polynomial order"):
node.jacobian([0.5])
def test_number_state_gradient(self, r, tol):
"""Tests that the automatic gradient of a squeezed state with number state expectation is correct."""
def circuit(y):
qml.Squeezing(y, 0., wires=[0])
return qml.expval(
qml.FockStateProjector(np.array([2, 0]), wires=[0, 1]))
dev = qml.device('default.gaussian', wires=2)
circuit = to_autograd(CVQNode(circuit, dev))
grad_fn = autograd.grad(circuit)
# (d/dr) |<2|S(r)>|^2 = 0.5 tanh(r)^3 (2 csch(r)^2 - 1) sech(r)
autograd_val = grad_fn(r)
manualgrad_val = 0.5 * np.tanh(r)**3 * (2 / (np.sinh(r)**2) -
1) / np.cosh(r)
assert autograd_val == pytest.approx(manualgrad_val, abs=tol)