def test_single_argument_step(self, cost_fn, mocker, monkeypatch):
"""Test that a simple QNode with a single argument correctly performs an optimization step,
and that the single-shot gradients generated have the correct shape"""
opt = qml.ShotAdaptiveOptimizer(min_shots=10)
spy_single_shot_expval = mocker.spy(opt,
"_single_shot_expval_gradients")
spy_single_shot_qnodes = mocker.spy(opt,
"_single_shot_qnode_gradients")
spy_grad = mocker.spy(opt, "compute_grad")
x_init = 0.5
new_x = opt.step(cost_fn, x_init)
assert isinstance(new_x, float)
assert new_x != x_init
spy_grad.assert_called_once()
if isinstance(cost_fn, qml.ExpvalCost):
spy_single_shot_expval.assert_called_once()
single_shot_grads = opt._single_shot_expval_gradients(
cost_fn, [x_init], {})
else:
spy_single_shot_qnodes.assert_called_once()
single_shot_grads = opt._single_shot_qnode_gradients(
cost_fn, [x_init], {})
# assert single shot gradients are computed correctly
assert len(single_shot_grads) == 1
assert single_shot_grads[0].shape == (10, )
# monkeypatch the optimizer to use the same single shot gradients
# as previously
monkeypatch.setattr(opt, "_single_shot_qnode_gradients",
lambda *args, **kwargs: single_shot_grads)
monkeypatch.setattr(opt, "_single_shot_expval_gradients",
lambda *args, **kwargs: single_shot_grads)
# reset the shot budget
opt.s = [np.array(10)]
# check that the gradient and variance are computed correctly
grad, grad_variance = opt.compute_grad(cost_fn, [x_init], {})
assert len(grad) == 1
assert len(grad_variance) == 1
assert np.allclose(grad, np.mean(single_shot_grads))
assert np.allclose(grad_variance, np.var(single_shot_grads, ddof=1))
# check that the gradient and variance are computed correctly
# with a different shot budget
opt.s = [np.array(5)]
grad, grad_variance = opt.compute_grad(cost_fn, [x_init], {})
assert len(grad) == 1
assert len(grad_variance) == 1
assert np.allclose(grad, np.mean(single_shot_grads[0][:5]))
assert np.allclose(grad_variance,
np.var(single_shot_grads[0][:5], ddof=1))
def test_multiple_argument_step(self, mocker, monkeypatch):
"""Test that a simple QNode with multiple scalar arguments correctly performs an optimization step,
and that the single-shot gradients generated have the correct shape"""
dev = qml.device("default.qubit", wires=1, shots=100)
@qml.qnode(dev)
def circuit(x, y):
qml.RX(x, wires=0)
qml.RY(y, wires=0)
return qml.expval(qml.PauliZ(0))
opt = qml.ShotAdaptiveOptimizer(min_shots=10)
spy_single_shot = mocker.spy(opt, "_single_shot_qnode_gradients")
spy_grad = mocker.spy(opt, "compute_grad")
args = [0.1, 0.2]
new_x = opt.step(circuit, *args)
assert isinstance(new_x, list)
assert len(new_x) == 2
spy_single_shot.assert_called_once()
spy_grad.assert_called_once()
# assert single shot gradients are computed correctly
single_shot_grads = opt._single_shot_qnode_gradients(circuit, args, {})
assert len(single_shot_grads) == 2
assert single_shot_grads[0].shape == (10, )
# monkeypatch the optimizer to use the same single shot gradients
# as previously
monkeypatch.setattr(opt, "_single_shot_qnode_gradients",
lambda *args, **kwargs: single_shot_grads)
# reset the shot budget
opt.s = [np.array(10), np.array(10)]
# check that the gradient and variance are computed correctly
grad, grad_variance = opt.compute_grad(circuit, args, {})
assert len(grad) == 2
assert len(grad_variance) == 2
assert np.allclose(grad, np.mean(single_shot_grads, axis=1))
assert np.allclose(grad_variance,
np.var(single_shot_grads, ddof=1, axis=1))
# check that the gradient and variance are computed correctly
# with a different shot budget
opt.s = [np.array(5), np.array(7)]
grad, grad_variance = opt.compute_grad(circuit, args, {})
assert len(grad) == 2
assert len(grad_variance) == 2
for p, s in zip(range(2), opt.s):
assert np.allclose(grad[p], np.mean(single_shot_grads[p][:s]))
assert np.allclose(grad_variance[p],
np.var(single_shot_grads[p][:s], ddof=1))
def test_sample_values_hermitian(self, tol):
"""Tests if the samples of a Hermitian observable returned by sample have
the correct values
"""
dev = plf.WavefunctionDevice(wires=1, shots=1_000_000)
theta = 0.543
A = np.array([[1, 2j], [-2j, 0]])
with qml.tape.QuantumTape() as tape:
qml.RX(theta, wires=[0])
O = qml.sample(qml.Hermitian(A, wires=[0]))
# test correct variance for <Z> of a rotated state
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
s1 = dev.sample(O.obs)
# s1 should only contain the eigenvalues of
# the hermitian matrix
eigvals = np.linalg.eigvalsh(A)
assert np.allclose(sorted(list(set(s1))), sorted(eigvals), atol=tol, rtol=0)
# the analytic mean is 2*sin(theta)+0.5*cos(theta)+0.5
assert np.allclose(
np.mean(s1), 2 * np.sin(theta) + 0.5 * np.cos(theta) + 0.5, atol=0.1, rtol=0
)
# the analytic variance is 0.25*(sin(theta)-4*cos(theta))^2
assert np.allclose(
np.var(s1), 0.25 * (np.sin(theta) - 4 * np.cos(theta)) ** 2, atol=0.1, rtol=0
)
def test_sample_values_hermitian(self, qvm, tol):
"""Tests if the samples of a Hermitian observable returned by sample have
the correct values
"""
theta = 0.543
shots = 1000_000
A = np.array([[1, 2j], [-2j, 0]])
dev = plf.QVMDevice(device="1q-qvm", shots=shots)
dev.apply('RX', wires=[0], par=[theta])
dev._obs_queue = [qml.Hermitian(A, wires=[0], do_queue=False)]
dev.pre_measure()
s1 = dev.sample('Hermitian', [0], [A])
# s1 should only contain the eigenvalues of
# the hermitian matrix
eigvals = np.linalg.eigvalsh(A)
assert np.allclose(sorted(list(set(s1))),
sorted(eigvals),
atol=tol,
rtol=0)
# the analytic mean is 2*sin(theta)+0.5*cos(theta)+0.5
assert np.allclose(np.mean(s1),
2 * np.sin(theta) + 0.5 * np.cos(theta) + 0.5,
atol=0.1,
rtol=0)
# the analytic variance is 0.25*(sin(theta)-4*cos(theta))^2
assert np.allclose(np.var(s1),
0.25 * (np.sin(theta) - 4 * np.cos(theta))**2,
atol=0.1,
rtol=0)
def test_sample_values_hermitian(self, device, tol):
"""Tests if the samples of a Hermitian observable returned by sample have
the correct values
"""
n_wires = 1
dev = device(n_wires)
if dev.shots is None:
pytest.skip("Device is in analytic mode, cannot test sampling.")
if "Hermitian" not in dev.observables:
pytest.skip("Skipped because device does not support the Hermitian observable.")
A_ = np.array([[1, 2j], [-2j, 0]])
theta = 0.543
@qml.qnode(dev)
def circuit():
qml.RX(theta, wires=[0])
return qml.sample(qml.Hermitian(A_, wires=0))
res = circuit().flatten()
# res should only contain the eigenvalues of
# the hermitian matrix
eigvals = np.linalg.eigvalsh(A_)
assert np.allclose(sorted(list(set(res.tolist()))), sorted(eigvals), atol=tol(dev.shots))
# the analytic mean is 2*sin(theta)+0.5*cos(theta)+0.5
assert np.allclose(
np.mean(res), 2 * np.sin(theta) + 0.5 * np.cos(theta) + 0.5, atol=tol(False)
)
# the analytic variance is 0.25*(sin(theta)-4*cos(theta))^2
assert np.allclose(
np.var(res), 0.25 * (np.sin(theta) - 4 * np.cos(theta)) ** 2, atol=tol(False)
)
def test_sample_values_hermitian(self, qvm, tol):
"""Tests if the samples of a Hermitian observable returned by sample have
the correct values
"""
theta = 0.543
shots = 1_000_000
A = np.array([[1, 2j], [-2j, 0]])
dev = plf.QVMDevice(device="1q-qvm", shots=shots)
O1 = qml.sample(qml.Hermitian(A, wires=[0]))
circuit_graph = CircuitGraph([qml.RX(theta, wires=[0])] + [O1], {}, dev.wires)
dev.apply(circuit_graph.operations, rotations=circuit_graph.diagonalizing_gates)
dev._samples = dev.generate_samples()
s1 = dev.sample(O1)
# s1 should only contain the eigenvalues of
# the hermitian matrix
eigvals = np.linalg.eigvalsh(A)
assert np.allclose(sorted(list(set(s1))), sorted(eigvals), atol=tol, rtol=0)
# the analytic mean is 2*sin(theta)+0.5*cos(theta)+0.5
assert np.allclose(
np.mean(s1), 2 * np.sin(theta) + 0.5 * np.cos(theta) + 0.5, atol=0.1, rtol=0
)
# the analytic variance is 0.25*(sin(theta)-4*cos(theta))^2
assert np.allclose(
np.var(s1), 0.25 * (np.sin(theta) - 4 * np.cos(theta)) ** 2, atol=0.1, rtol=0
)
def test_sample_values_projector(self, device, tol):
"""Tests if the samples of a Projector observable returned by sample have
the correct values
"""
n_wires = 1
dev = device(n_wires)
if dev.shots is None:
pytest.skip("Device is in analytic mode, cannot test sampling.")
if "Projector" not in dev.observables:
pytest.skip(
"Skipped because device does not support the Projector observable."
)
theta = 0.543
@qml.qnode(dev)
def circuit(basis_state):
qml.RX(theta, wires=[0])
return qml.sample(qml.Projector(basis_state, wires=0))
res = circuit([0]).flatten()
# res should only contain 0 or 1, the eigenvalues of the projector
assert np.allclose(sorted(list(set(res.tolist()))), [0, 1],
atol=tol(dev.shots))
assert np.allclose(np.mean(res), np.cos(theta / 2)**2, atol=tol(False))
assert np.allclose(np.var(res),
np.cos(theta / 2)**2 - (np.cos(theta / 2)**2)**2,
atol=tol(False))
res = circuit([1]).flatten()
# res should only contain 0 or 1, the eigenvalues of the projector
assert np.allclose(sorted(list(set(res.tolist()))), [0, 1],
atol=tol(dev.shots))
assert np.allclose(np.mean(res), np.sin(theta / 2)**2, atol=tol(False))
assert np.allclose(np.var(res),
np.sin(theta / 2)**2 - (np.sin(theta / 2)**2)**2,
atol=tol(False))
def compute_grad(
self, objective_fn, args, kwargs
): # pylint: disable=signature-differs,arguments-differ
r"""Compute gradient of the objective function, as well as the variance of the gradient,
at the given point.
Args:
objective_fn (function): the objective function for optimization
args: arguments to the objective function
kwargs: keyword arguments to the objective function
Returns:
tuple[array[float], array[float]]: a tuple of NumPy arrays containing the gradient
:math:`\nabla f(x^{(t)})` and the variance of the gradient
"""
if isinstance(objective_fn, qml.ExpvalCost):
grads = self._single_shot_expval_gradients(objective_fn, args, kwargs)
elif isinstance(objective_fn, qml.QNode) or hasattr(objective_fn, "device"):
grads = self._single_shot_qnode_gradients(objective_fn, args, kwargs)
else:
raise ValueError(
"The objective function must either be encoded as a single QNode or "
"an ExpvalCost object for the Shot adaptive optimizer. "
)
# grads will have dimension [max(self.s), *params.shape]
# For each parameter, we want to truncate the number of shots to self.s[idx],
# and take the mean and the variance.
gradients = []
gradient_variances = []
for i, grad in enumerate(grads):
p_ind = np.ndindex(*grad.shape[1:])
g = np.zeros_like(grad[0])
s = np.zeros_like(grad[0])
for idx in p_ind:
grad_slice = grad[(slice(0, self.s[i][idx]),) + idx]
g[idx] = np.mean(grad_slice)
s[idx] = np.var(grad_slice, ddof=1)
gradients.append(g)
gradient_variances.append(s)
return gradients, gradient_variances
def test_pauliz_hadamard(self, device, tol, skip_if):
"""Test that a tensor product involving PauliZ and PauliY and hadamard works correctly"""
n_wires = 3
dev = device(n_wires)
if dev.shots is None:
pytest.skip("Device is in analytic mode, cannot test sampling.")
skip_if(dev, {"supports_tensor_observables": False})
theta = 0.432
phi = 0.123
varphi = -0.543
@qml.qnode(dev)
def circuit():
qml.RX(theta, wires=[0])
qml.RX(phi, wires=[1])
qml.RX(varphi, wires=[2])
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[1, 2])
return qml.sample(
qml.PauliZ(wires=[0]) @ qml.Hadamard(wires=[1]) @ qml.PauliY(wires=[2])
)
res = circuit()
# s1 should only contain 1 and -1
assert np.allclose(res ** 2, 1, atol=tol(False))
mean = np.mean(res)
expected = -(np.cos(varphi) * np.sin(phi) + np.sin(varphi) * np.cos(theta)) / np.sqrt(2)
assert np.allclose(mean, expected, atol=tol(False))
var = np.var(res)
expected = (
3
+ np.cos(2 * phi) * np.cos(varphi) ** 2
- np.cos(2 * theta) * np.sin(varphi) ** 2
- 2 * np.cos(theta) * np.sin(phi) * np.sin(2 * varphi)
) / 4
assert np.allclose(var, expected, atol=tol(False))
grad_vals = []
for i in range(num_samples):
print(f"num_qubits {num_qubits}, step {i}")
dev = qml.device("default.qubit", wires=num_qubits)
ansatz = mera_circuit(num_qubits, periodic, fix_layers)
cost_fn = qml.ExpvalCost(ansatz, H, dev)
grad = qml.grad(cost_fn)
num_params_per_gate = 15
num_gates = get_num_mera_gates(num_qubits, periodic, fix_layers)
num_params = num_params_per_gate * num_gates
params = np.pi * (np.random.rand(num_params) - 1.0)
gradient = np.array(grad(params)[0])
grad_vals.append(gradient)
variances.append(np.mean(np.var(grad_vals, axis=0)))
print(variances)
#variances = np.array(np.mean(variances, axis=1))
qubits = np.array(qubits)
# Fit the semilog plot to a straight line
p = np.polyfit(qubits, np.log(variances), 1)
# Plot the straight line fit to the semilog
plt.semilogy(qubits, variances, "o")
plt.semilogy(qubits,
np.exp(p[0] * qubits + p[1]),
"o-.",
label="Slope {:3.2f}".format(p[0]))
plt.xlabel(r"N Qubits")
shots = 10000
dev = qml.device("default.gaussian", wires=1, shots=shots, analytic=False)
# circuit is a simple displacement of the ground state and returns a sample of size shots
@qml.qnode(dev)
def variational_circuit(x=None):
qml.Displacement(x, 0.0, wires=0)
return qml.sample(qml.X(0))
output = variational_circuit(x=input)
# calculate expectation value using the Berry-Essen theorem
ev1 = np.mean(output)
var = np.var(output)
ev = np.random.normal(ev1, np.sqrt(var / shots))
# plot
min_ = min(output)
max_ = max(output)
bins = np.linspace(min_, max_, 100)
fig = plt.figure()
plt.hist(output, bins)
plt.plot([ev, ev], [0, 350], 'r-')
plt.yticks()
plt.xlabel("$x$", size=22)
plt.ylabel("f", rotation='horizontal', labelpad=15, size=22)
plt.tick_params(axis="both", which="major", labelsize=22)
plt.tick_params(axis="both", which="minor", labelsize=22)
plt.legend(['expectation value', 'data'], prop={'size': 12}, loc='upper right')
# for more accurate results.
qcircuit = qml.QNode(rand_circuit, dev)
grad = qml.grad(qcircuit, argnum=0)
num_samples = 200
grad_vals = []
for i in range(num_samples):
params = np.random.uniform(0, 2 * np.pi, size=num_qubits)
grad_vals.append(
grad(params, random_gate_sequence=gate_sequence,
num_qubits=num_qubits))
print("Variance of the gradient for {} samples: {}".format(
num_samples, np.var(grad_vals)))
###########################################################
# Evaluate the gradient for more qubits
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# We can repeat the above analysis with increasing number
# of qubits.
def generate_random_circuit(num_qubits):
"""
Generates a random quantum circuit based on (McClean et. al., 2019).
Args:
num_qubits (int): the number of qubits in the circuit
"""
def test_hermitian(self, device, tol, skip_if):
"""Test that a tensor product involving qml.Hermitian works correctly"""
n_wires = 3
dev = device(n_wires)
if dev.shots is None:
pytest.skip("Device is in analytic mode, cannot test sampling.")
if "Hermitian" not in dev.observables:
pytest.skip(
"Skipped because device does not support the Hermitian observable."
)
skip_if(dev, {"supports_tensor_observables": False})
theta = 0.432
phi = 0.123
varphi = -0.543
A_ = 0.1 * np.array([
[-6, 2 + 1j, -3, -5 + 2j],
[2 - 1j, 0, 2 - 1j, -5 + 4j],
[-3, 2 + 1j, 0, -4 + 3j],
[-5 - 2j, -5 - 4j, -4 - 3j, -6],
])
@qml.qnode(dev)
def circuit():
qml.RX(theta, wires=[0])
qml.RX(phi, wires=[1])
qml.RX(varphi, wires=[2])
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[1, 2])
return qml.sample(
qml.PauliZ(wires=[0]) @ qml.Hermitian(A_, wires=[1, 2]))
res = circuit()
# res should only contain the eigenvalues of
# the hermitian matrix tensor product Z
Z = np.diag([1, -1])
eigvals = np.linalg.eigvalsh(np.kron(Z, A_))
assert np.allclose(sorted(np.unique(res)),
sorted(eigvals),
atol=tol(False))
mean = np.mean(res)
expected = (0.1 * 0.5 *
(-6 * np.cos(theta) *
(np.cos(varphi) + 1) - 2 * np.sin(varphi) *
(np.cos(theta) + np.sin(phi) - 2 * np.cos(phi)) +
3 * np.cos(varphi) * np.sin(phi) + np.sin(phi)))
assert np.allclose(mean, expected, atol=tol(False))
var = np.var(res)
expected = (
0.01 *
(1057 - np.cos(2 * phi) + 12 *
(27 + np.cos(2 * phi)) * np.cos(varphi) -
2 * np.cos(2 * varphi) * np.sin(phi) *
(16 * np.cos(phi) + 21 * np.sin(phi)) + 16 * np.sin(2 * phi) - 8 *
(-17 + np.cos(2 * phi) + 2 * np.sin(2 * phi)) * np.sin(varphi) -
8 * np.cos(2 * theta) *
(3 + 3 * np.cos(varphi) + np.sin(varphi))**2 - 24 * np.cos(phi) *
(np.cos(phi) + 2 * np.sin(phi)) * np.sin(2 * varphi) -
8 * np.cos(theta) *
(4 * np.cos(phi) *
(4 + 8 * np.cos(varphi) + np.cos(2 * varphi) -
(1 + 6 * np.cos(varphi)) * np.sin(varphi)) + np.sin(phi) *
(15 + 8 * np.cos(varphi) - 11 * np.cos(2 * varphi) +
42 * np.sin(varphi) + 3 * np.sin(2 * varphi)))) / 16)
assert np.allclose(var, expected, atol=tol(False))
# increased for more accurate results. We only consider the
# gradient of the output with respect to the last parameter in the
# circuit. Hence we choose to save ``gradient[-1]`` only.
grad_vals = []
num_samples = 200
for i in range(num_samples):
gate_sequence = {i: np.random.choice(gate_set) for i in range(num_qubits)}
qcircuit = qml.QNode(rand_circuit, dev)
grad = qml.grad(qcircuit, argnum=0)
params = np.random.uniform(0, 2 * np.pi, size=num_qubits)
gradient = grad(params, random_gate_sequence=gate_sequence, num_qubits=num_qubits)
grad_vals.append(gradient[-1])
print("Variance of the gradients for {} random circuits: {}".format(num_samples, np.var(grad_vals)))
print("Mean of the gradients for {} random circuits: {}".format(num_samples, np.mean(grad_vals)))
##############################################################################
# Evaluate the gradient for more qubits
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# We can repeat the above analysis with increasing number of qubits.
qubits = [2, 3, 4, 5, 6]
variances = []
for num_qubits in qubits:
grad_vals = []
grad_vals = []
num_samples = 200
for i in range(num_samples):
gate_sequence = {i: np.random.choice(gate_set) for i in range(num_qubits)}
qcircuit = qml.QNode(rand_circuit, dev)
grad = qml.grad(qcircuit, argnum=0)
params = np.random.uniform(0, 2 * np.pi, size=num_qubits)
gradient = grad(params,
random_gate_sequence=gate_sequence,
num_qubits=num_qubits)
grad_vals.append(gradient[-1])
print("Variance of the gradients for {} random circuits: {}".format(
num_samples, np.var(grad_vals)))
print("Mean of the gradients for {} random circuits: {}".format(
num_samples, np.mean(grad_vals)))
##############################################################################
# Evaluate the gradient for more qubits
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# We can repeat the above analysis with increasing number of qubits.
qubits = [2, 3, 4, 5, 6]
variances = []
for num_qubits in qubits:
grad_vals = []
for i in range(num_samples):
dev = qml.device("default.qubit", wires=num_qubits)
def test_single_array_argument_step(self, cost_fn, mocker, monkeypatch):
"""Test that a simple QNode with a single array argument correctly performs an optimization step,
and that the single-shot gradients generated have the correct shape"""
opt = qml.ShotAdaptiveOptimizer(min_shots=10)
spy_single_shot_expval = mocker.spy(opt, "_single_shot_expval_gradients")
spy_single_shot_qnodes = mocker.spy(opt, "_single_shot_qnode_gradients")
spy_grad = mocker.spy(opt, "compute_grad")
x_init = np.array([[1., 2., 3.], [4., 5., 6.]])
new_x = opt.step(cost_fn, x_init)
assert isinstance(new_x, np.ndarray)
assert not np.allclose(new_x, x_init)
if isinstance(cost_fn, qml.ExpvalCost):
spy_single_shot_expval.assert_called_once()
single_shot_grads = opt._single_shot_expval_gradients(cost_fn, [x_init], {})
else:
spy_single_shot_qnodes.assert_called_once()
single_shot_grads = opt._single_shot_qnode_gradients(cost_fn, [x_init], {})
spy_grad.assert_called_once()
# assert single shot gradients are computed correctly
assert len(single_shot_grads) == 1
assert single_shot_grads[0].shape == (10, 2, 3)
# monkeypatch the optimizer to use the same single shot gradients
# as previously
monkeypatch.setattr(opt, "_single_shot_qnode_gradients", lambda *args, **kwargs: single_shot_grads)
monkeypatch.setattr(opt, "_single_shot_expval_gradients", lambda *args, **kwargs: single_shot_grads)
# reset the shot budget
opt.s = [10 * np.ones([2, 3], dtype=np.int64)]
# check that the gradient and variance are computed correctly
grad, grad_variance = opt.compute_grad(cost_fn, [x_init], {})
assert len(grad) == 1
assert len(grad_variance) == 1
assert grad[0].shape == x_init.shape
assert grad_variance[0].shape == x_init.shape
assert np.allclose(grad, np.mean(single_shot_grads, axis=1))
assert np.allclose(grad_variance, np.var(single_shot_grads, ddof=1, axis=1))
# check that the gradient and variance are computed correctly
# with a different shot budget
opt.s[0] = opt.s[0] // 2 # all array elements have a shot budget of 5
opt.s[0][0, 0] = 8 # set the shot budget of the zeroth element to 8
grad, grad_variance = opt.compute_grad(cost_fn, [x_init], {})
assert len(grad) == 1
assert len(grad_variance) == 1
# check zeroth element
assert np.allclose(grad[0][0, 0], np.mean(single_shot_grads[0][:8, 0, 0]))
assert np.allclose(grad_variance[0][0, 0], np.var(single_shot_grads[0][:8, 0, 0], ddof=1))
# check other elements
assert np.allclose(grad[0][0, 1], np.mean(single_shot_grads[0][:5, 0, 1]))
assert np.allclose(grad_variance[0][0, 1], np.var(single_shot_grads[0][:5, 0, 1], ddof=1))
def test_multiple_array_argument_step(self, mocker, monkeypatch):
"""Test that a simple QNode with multiple array arguments correctly performs an optimization step,
and that the single-shot gradients generated have the correct shape"""
dev = qml.device("default.qubit", wires=1, shots=100)
@qml.qnode(dev)
def circuit(x, y):
qml.RX(x[0, 0], wires=0)
qml.RY(x[0, 1], wires=0)
qml.RZ(x[0, 2], wires=0)
qml.RX(x[1, 0], wires=0)
qml.RY(x[1, 1], wires=0)
qml.RZ(x[1, 2], wires=0)
qml.RX(y[0], wires=0)
qml.RY(y[1], wires=0)
qml.RZ(y[2], wires=0)
return qml.expval(qml.PauliZ(0))
opt = qml.ShotAdaptiveOptimizer(min_shots=10)
spy_single_shot = mocker.spy(opt, "_single_shot_qnode_gradients")
spy_grad = mocker.spy(opt, "compute_grad")
args = [np.array([[1., 2., 3.], [4., 5., 6.]]), np.array([1., 2., 3.])]
new_x = opt.step(circuit, *args)
assert isinstance(new_x, list)
assert len(new_x) == 2
spy_single_shot.assert_called_once()
spy_grad.assert_called_once()
# assert single shot gradients are computed correctly
single_shot_grads = opt._single_shot_qnode_gradients(circuit, args, {})
assert len(single_shot_grads) == 2
assert single_shot_grads[0].shape == (10, 2, 3)
assert single_shot_grads[1].shape == (10, 3)
# monkeypatch the optimizer to use the same single shot gradients
# as previously
monkeypatch.setattr(opt, "_single_shot_qnode_gradients", lambda *args, **kwargs: single_shot_grads)
# reset the shot budget
opt.s = [10 * np.ones([2, 3], dtype=np.int64), 10 * np.ones([3], dtype=np.int64)]
# check that the gradient and variance are computed correctly
grad, grad_variance = opt.compute_grad(circuit, args, {})
assert len(grad) == 2
assert len(grad_variance) == 2
for i in range(2):
assert grad[i].shape == args[i].shape
assert grad_variance[i].shape == args[i].shape
assert np.allclose(grad[0], np.mean(single_shot_grads[0], axis=0))
assert np.allclose(grad_variance[0], np.var(single_shot_grads[0], ddof=1, axis=0))
assert np.allclose(grad[1], np.mean(single_shot_grads[1], axis=0))
assert np.allclose(grad_variance[1], np.var(single_shot_grads[1], ddof=1, axis=0))
# check that the gradient and variance are computed correctly
# with a different shot budget
opt.s[0] = opt.s[0] // 2 # all array elements have a shot budget of 5
opt.s[0][0, 0] = 8 # set the shot budget of the zeroth element to 8
opt.s[1] = opt.s[1] // 5 # all array elements have a shot budget of 2
opt.s[1][0] = 7 # set the shot budget of the zeroth element to 7
grad, grad_variance = opt.compute_grad(circuit, args, {})
assert len(grad) == 2
assert len(grad_variance) == 2
# check zeroth element of arg 0
assert np.allclose(grad[0][0, 0], np.mean(single_shot_grads[0][:8, 0, 0]))
assert np.allclose(grad_variance[0][0, 0], np.var(single_shot_grads[0][:8, 0, 0], ddof=1))
# check other elements of arg 0
assert np.allclose(grad[0][0, 1], np.mean(single_shot_grads[0][:5, 0, 1]))
assert np.allclose(grad_variance[0][0, 1], np.var(single_shot_grads[0][:5, 0, 1], ddof=1))
# check zeroth element of arg 1
assert np.allclose(grad[1][0], np.mean(single_shot_grads[1][:7, 0]))
assert np.allclose(grad_variance[1][0], np.var(single_shot_grads[1][:7, 0], ddof=1))
# check other elements of arg 1
assert np.allclose(grad[1][1], np.mean(single_shot_grads[1][:2, 1]))
assert np.allclose(grad_variance[1][1], np.var(single_shot_grads[1][:2, 1], ddof=1))
def test_projector(self, device, tol, skip_if):
"""Test that a tensor product involving qml.Projector works correctly"""
n_wires = 3
dev = device(n_wires)
if dev.shots is None:
pytest.skip("Device is in analytic mode, cannot test sampling.")
if "Projector" not in dev.observables:
pytest.skip(
"Skipped because device does not support the Projector observable."
)
skip_if(dev, {"supports_tensor_observables": False})
theta = 1.432
phi = 1.123
varphi = -0.543
@qml.qnode(dev)
def circuit(basis_state):
qml.RX(theta, wires=[0])
qml.RX(phi, wires=[1])
qml.RX(varphi, wires=[2])
qml.CNOT(wires=[0, 1])
qml.CNOT(wires=[1, 2])
return qml.sample(
qml.PauliZ(wires=[0]) @ qml.Projector(basis_state,
wires=[1, 2]))
res = circuit([0, 0])
# res should only contain the eigenvalues of the projector matrix tensor product Z, i.e. {-1, 0, 1}
assert np.allclose(sorted(np.unique(res)), [-1, 0, 1], atol=tol(False))
mean = np.mean(res)
expected = (np.cos(varphi / 2) * np.cos(phi / 2) * np.cos(
theta / 2))**2 - (np.cos(varphi / 2) * np.sin(phi / 2) *
np.sin(theta / 2))**2
assert np.allclose(mean, expected, atol=tol(False))
var = np.var(res)
expected = (
(np.cos(varphi / 2) * np.cos(phi / 2) * np.cos(theta / 2))**2 +
(np.cos(varphi / 2) * np.sin(phi / 2) * np.sin(theta / 2))**2 -
((np.cos(varphi / 2) * np.cos(phi / 2) * np.cos(theta / 2))**2 -
(np.cos(varphi / 2) * np.sin(phi / 2) * np.sin(theta / 2))**2)**2)
assert np.allclose(var, expected, atol=tol(False))
res = circuit([0, 1])
assert np.allclose(sorted(np.unique(res)), [-1, 0, 1], atol=tol(False))
mean = np.mean(res)
expected = (np.sin(varphi / 2) * np.cos(phi / 2) * np.cos(
theta / 2))**2 - (np.sin(varphi / 2) * np.sin(phi / 2) *
np.sin(theta / 2))**2
assert np.allclose(mean, expected, atol=tol(False))
var = np.var(res)
expected = (
(np.sin(varphi / 2) * np.cos(phi / 2) * np.cos(theta / 2))**2 +
(np.sin(varphi / 2) * np.sin(phi / 2) * np.sin(theta / 2))**2 -
((np.sin(varphi / 2) * np.cos(phi / 2) * np.cos(theta / 2))**2 -
(np.sin(varphi / 2) * np.sin(phi / 2) * np.sin(theta / 2))**2)**2)
assert np.allclose(var, expected, atol=tol(False))
res = circuit([1, 0])
assert np.allclose(sorted(np.unique(res)), [-1, 0, 1], atol=tol(False))
mean = np.mean(res)
expected = (np.sin(varphi / 2) * np.sin(phi / 2) * np.cos(
theta / 2))**2 - (np.sin(varphi / 2) * np.cos(phi / 2) *
np.sin(theta / 2))**2
assert np.allclose(mean, expected, atol=tol(False))
var = np.var(res)
expected = (
(np.sin(varphi / 2) * np.sin(phi / 2) * np.cos(theta / 2))**2 +
(np.sin(varphi / 2) * np.cos(phi / 2) * np.sin(theta / 2))**2 -
((np.sin(varphi / 2) * np.sin(phi / 2) * np.cos(theta / 2))**2 -
(np.sin(varphi / 2) * np.cos(phi / 2) * np.sin(theta / 2))**2)**2)
assert np.allclose(var, expected, atol=tol(False))
res = circuit([1, 1])
assert np.allclose(sorted(np.unique(res)), [-1, 0, 1], atol=tol(False))
mean = np.mean(res)
expected = (np.cos(varphi / 2) * np.sin(phi / 2) * np.cos(
theta / 2))**2 - (np.cos(varphi / 2) * np.cos(phi / 2) *
np.sin(theta / 2))**2
assert np.allclose(mean, expected, atol=tol(False))
var = np.var(res)
expected = (
(np.cos(varphi / 2) * np.sin(phi / 2) * np.cos(theta / 2))**2 +
(np.cos(varphi / 2) * np.cos(phi / 2) * np.sin(theta / 2))**2 -
((np.cos(varphi / 2) * np.sin(phi / 2) * np.cos(theta / 2))**2 -
(np.cos(varphi / 2) * np.cos(phi / 2) * np.sin(theta / 2))**2)**2)
assert np.allclose(var, expected, atol=tol(False))