def test_variance_squeezed_numberstate(self):
"""test correct variance for number state expectation |<n|S(r)>|^2
on a squeezed state
"""
self.logTestName()
dev = qml.device('default.gaussian', wires=1, hbar=hbar)
n = 1
r = 0.4523
dev.apply('SqueezedState', wires=[0], par=[r, 0])
var = dev.var('NumberState', [0], [np.array([2 * n])])
mean = np.abs(
np.sqrt(fac(2 * n)) / (2**n * fac(n)) * (-np.tanh(r))**n /
np.sqrt(np.cosh(r)))**2
self.assertAlmostEqual(var, mean * (1 - mean), delta=self.tol)
def assertAllAlmostEqual(self, first, second, delta, msg=None):
"""
Like assertAlmostEqual, but works with arrays. All the corresponding elements have to be almost equal.
"""
if isinstance(first, tuple):
# check each element of the tuple separately (needed for when the tuple elements are themselves batches)
if np.all([
np.all(first[idx] == second[idx])
for idx, _ in enumerate(first)
]):
return
if np.all([
np.all(np.abs(first[idx] - second[idx])) <= delta
for idx, _ in enumerate(first)
]):
return
else:
if np.all(first == second):
return
if np.all(np.abs(first - second) <= delta):
return
standardMsg = '{} != {} within {} delta'.format(first, second, delta)
msg = self._formatMessage(msg, standardMsg)
raise self.failureException(msg)
def check_learning_rate(self, coeffs):
r"""Verifies that the learning rate is less than 2 over the Lipschitz constant,
where the Lipschitz constant is given by :math:`\sum |c_i|` for Hamiltonian
coefficients :math:`c_i`.
Args:
coeffs (Sequence[float]): the coefficients of the terms in the Hamiltonian
Raises:
ValueError: if the learning rate is large than :math:`2/\sum |c_i|`
"""
self.lipschitz = np.sum(np.abs(coeffs))
if self._stepsize > 2 / self.lipschitz:
raise ValueError(
f"The learning rate must be less than {2 / self.lipschitz}")
def optimize_circuit(params):
"""Minimize the variational circuit and return its minimum value.
The code you write for this challenge should be completely contained within this function
between the # QHACK # comment markers. You should create a device and convert the
variational_circuit function into an executable QNode. Next, you should minimize the variational
circuit using gradient-based optimization to update the input params. Return the optimized value
of the QNode as a single floating-point number.
Args:
params (np.ndarray): Input parameters to be optimized, of dimension 30
Returns:
float: the value of the optimized QNode
"""
optimal_value = 0.0
# QHACK #
# Initialize the device
dev = qml.device("default.qubit", wires=2)
# Instantiate the QNode
circuit = qml.QNode(variational_circuit, dev)
# Minimize the circuit
opt = qml.AdagradOptimizer(stepsize=0.4)
max_iterations = 500
conv_tol = 1e-6
for n in range(max_iterations):
params, prev_optimal_value = opt.step_and_cost(circuit, params)
optimal_value = circuit(params)
conv = np.abs(optimal_value - prev_optimal_value)
# if n % 20 == 0:
# print('Iteration = {:}, Energy = {:.8f} Ha'.format(n, optimal_value))
if conv <= conv_tol:
break
# QHACK #
# Return the value of the minimized QNode
return optimal_value
def flip_matrix(K):
r"""Remove negative eigenvalues from the given kernel matrix by taking the absolute value.
This method keeps the eigenvectors of the matrix intact.
Args:
K (array[float]): Kernel matrix, assumed to be symmetric.
Returns:
array[float]: Kernel matrix with flipped negative eigenvalues.
Reference:
This method is introduced in `arXiv:2103.16774 <https://arxiv.org/abs/2103.16774>`_.
**Example:**
Consider a symmetric matrix with both positive and negative eigenvalues:
.. code-block :: pycon
>>> K = np.array([[0, 1, 0], [1, 0, 0], [0, 0, 2]])
>>> np.linalg.eigvalsh(K)
array([-1., 1., 2.])
We then can invert the sign of all negative eigenvalues of the matrix, obtaining
non-negative eigenvalues only:
.. code-block :: pycon
>>> K_flipped = qml.kernels.flip_matrix(K)
>>> np.linalg.eigvalsh(K_flipped)
array([1., 1., 2.])
If the input matrix does not have negative eigenvalues, ``flip_matrix``
does not have any effect.
"""
w, v = np.linalg.eigh(K)
if w[0] < 0:
# Transform spectrum: absolute value
w_abs = np.abs(w)
return (v * w_abs) @ np.transpose(v)
return K
def test_finite_diff_squeezed(self, tol):
"""Test that the jacobian of the probability for a squeezed states is
approximated well with finite differences"""
cutoff = 5
dev = qml.device("strawberryfields.fock", wires=1, cutoff_dim=cutoff)
@qml.qnode(dev)
def circuit(r, phi):
qml.Squeezing(r, phi, wires=0)
return qml.probs(wires=[0])
r = 0.4
phi = -0.12
n = np.arange(cutoff)
# construct tape
circuit.construct([r, phi], {})
# differentiate with respect to parameter a
circuit.qtape.trainable_params = {0}
tapes, fn = qml.gradients.finite_diff(circuit.qtape)
res_F = fn(dev.batch_execute(tapes)).flatten()
assert res_F.shape == (cutoff,)
expected_gradient = (
np.abs(np.tanh(r)) ** n
* (1 + 2 * n - np.cosh(2 * r))
* fac(n)
/ (2 ** (n + 1) * np.cosh(r) ** 2 * np.sinh(r) * fac(n / 2) ** 2)
)
expected_gradient[n % 2 != 0] = 0
assert np.allclose(res_F, expected_gradient, atol=tol, rtol=0)
# re-construct tape to reset trainable_params
circuit.construct([r, phi], {})
# differentiate with respect to parameter phi
circuit.qtape.trainable_params = {1}
tapes, fn = qml.gradients.finite_diff(circuit.qtape)
res_F = fn(dev.batch_execute(tapes)).flatten()
expected_gradient = 0
assert np.allclose(res_F, expected_gradient, atol=tol, rtol=0)
def hinge_loss(labels, predictions, type='L2'):
"""
Args:
labels:
predictions:
type: (Default value = 'L2')
Returns:
"""
loss = 0
for l, p in zip(labels, predictions):
if type == 'L1':
loss = loss + np.abs(l - p) # L1 loss
elif type == 'L2':
loss = loss + (l - p)**2 # L2 loss
loss = loss / labels.shape[0]
return loss
def encode_data(self, features):
"""Encodes data according to encoding method."""
wires = range(self.num_q)
# amplitude encoding mode
if self.encoding == "amplitude":
qml.templates.embeddings.AmplitudeEmbedding(features,
wires=wires,
normalize=True)
# angle encoding mode
elif self.encoding == "angle":
qml.templates.embeddings.AngleEmbedding(features,
wires=wires)
elif self.encoding == "mottonen":
norm = np.sum(np.abs(features) ** 2)
features = features / math.sqrt(norm)
qml.templates.state_preparations.MottonenStatePreparation(
features, wires=wires)
def term(params, sign_term, sign_i, i, sign_j, j):
qml.BasisState(np.array([0, 0, 0, 0, 0, 0]), wires=range(6))
variational_circuit_wire_list(params)
shift = np.zeros_like(params)
shift[i] = sign_i * one
shift[j] = sign_j * one
variational_circuit_wire_list(params + shift, wire_list=[3, 4, 5])
# return qml.DiagonalQubitUnitary([1] * 6, wires=[0, 1, 2]), qml.DiagonalQubitUnitary([1] * 6, wires=[3, 4, 5])
# return [
# [qml.expval(qml.PauliX(wire)) for wire in [0, 1, 2]],
# [qml.expval(qml.PauliX(wire)) for wire in [3, 4, 5]],
# ]
return sign_term * np.abs(
qml.dot(
[qml.expval(qml.PauliX(wire)) for wire in [0, 1, 2]],
[qml.expval(qml.PauliX(wire)) for wire in [3, 4, 5]],
))**2
def test_second_order_observable(self, diff_method, kwargs, tol):
"""Test variance of a second order CV expectation value"""
dev = qml.device("default.gaussian", wires=1)
n = 0.12
a = 0.765
@qnode(dev, interface="jax", diff_method=diff_method, **kwargs)
def circuit(n, a):
qml.ThermalState(n, wires=0)
qml.Displacement(a, 0, wires=0)
return qml.var(qml.NumberOperator(0))
res = circuit(n, a)
expected = n ** 2 + n + np.abs(a) ** 2 * (1 + 2 * n)
assert np.allclose(res, expected, atol=tol, rtol=0)
# circuit jacobians
res = jax.grad(circuit, argnums=[0, 1])(n, a)
expected = np.array([2 * a ** 2 + 2 * n + 1, 2 * a * (2 * n + 1)])
assert np.allclose(res, expected, atol=tol, rtol=0)
def test_second_order_cv(self, tol):
"""Test variance of a second order CV expectation value"""
dev = qml.device("strawberryfields.gaussian", wires=1)
@qml.qnode(dev)
def circuit(n, a):
qml.ThermalState(n, wires=0)
qml.Displacement(a, 0, wires=0)
return qml.var(qml.NumberOperator(0))
n = 0.12
a = 0.765
var = circuit(n, a)
expected = n**2 + n + np.abs(a)**2 * (1 + 2 * n)
assert np.allclose(var, expected, atol=tol, rtol=0)
# circuit jacobians
gradF = circuit.jacobian([n, a], method="F")
expected = np.array([2 * a**2 + 2 * n + 1, 2 * a * (2 * n + 1)])
assert np.allclose(gradF, expected, atol=tol, rtol=0)
def test_simulator_qvm_default_agree(tol, qvm, compiler):
"""Test that forest.wavefunction, forest.qvm, and default.qubit agree
on the calculation of quantum gradients."""
w = 2
dev1 = qml.device("default.qubit", wires=w)
dev2 = qml.device("forest.wavefunction", wires=w)
dev3 = qml.device("forest.qvm", device="9q-square-qvm", shots=5000)
in_state = np.zeros([w], requires_grad=False)
in_state[0] = 1
in_state[1] = 1
def func(x, y):
"""Reference QNode"""
qml.BasisState(in_state, wires=list(range(w)))
qml.RY(x, wires=0)
qml.RX(y, wires=1)
qml.CNOT(wires=[0, 1])
return qml.expval(qml.PauliZ(1))
func1 = qml.QNode(func, dev1)
func2 = qml.QNode(func, dev2)
func3 = qml.QNode(func, dev3)
params = [
np.array(0.2, requires_grad=True),
np.array(0.453, requires_grad=True)
]
# check all evaluate to the same value
# NOTE: we increase the tolerance when using the QVM
assert np.all(np.abs(func1(*params) - func2(*params)) <= tol)
assert np.all(np.abs(func1(*params) - func3(*params)) <= 0.1)
assert np.all(np.abs(func2(*params) - func3(*params)) <= 0.1)
df1 = qml.grad(func1)
df2 = qml.grad(func2)
df3 = qml.grad(func3)
# check all gradients evaluate to the same value
# NOTE: we increase the tolerance when using the QVM
assert np.all(
np.abs(np.array(df1(*params)) - np.array(df2(*params))) <= tol)
assert np.all(
np.abs(np.array(df1(*params)) - np.array(df3(*params))) <= 0.1)
assert np.all(
np.abs(np.array(df2(*params)) - np.array(df3(*params))) <= 0.1)
def test_learning_error(self):
"""Test that an exception is raised if the learning rate is beyond the
lipschitz bound"""
coeffs = [0.3, 0.1]
H = qml.Hamiltonian(coeffs, [qml.PauliX(0), qml.PauliZ(0)])
dev = qml.device("default.qubit", wires=1, shots=100)
expval_cost = qml.ExpvalCost(lambda x, **kwargs: qml.RX(x, wires=0), H, dev)
opt = qml.ShotAdaptiveOptimizer(min_shots=10, stepsize=100.)
# lipschitz constant is given by sum(|coeffs|)
lipschitz = np.sum(np.abs(coeffs))
assert opt._stepsize > 2 / lipschitz
with pytest.raises(ValueError, match=f"The learning rate must be less than {2 / lipschitz}"):
opt.step(expval_cost, 0.5)
# for a single QNode, the lipschitz constant is simply 1
opt = qml.ShotAdaptiveOptimizer(min_shots=10, stepsize=100.)
with pytest.raises(ValueError, match=f"The learning rate must be less than {2 / 1}"):
opt.step(expval_cost.qnodes[0], 0.5)
def test_second_order_cv(self, tol):
"""Test variance of a second order CV expectation value"""
dev = qml.device("strawberryfields.fock", wires=1, cutoff_dim=15)
@qml.qnode(dev)
def circuit(n, a):
qml.ThermalState(n, wires=0)
qml.Displacement(a, 0, wires=0)
return qml.var(qml.NumberOperator(0))
n = np.array(0.12, requires_grad=True)
a = np.array(0.105, requires_grad=True)
var = circuit(n, a)
expected = n**2 + n + np.abs(a) ** 2 * (1 + 2 * n)
assert np.allclose(var, expected, atol=tol, rtol=0)
# circuit jacobians
tapes, fn = qml.gradients.finite_diff(circuit.qtape)
gradF = fn(dev.batch_execute(tapes))
expected = np.array([2 * a**2 + 2 * n + 1, 2 * a * (2 * n + 1)])
assert np.allclose(gradF, expected, atol=tol, rtol=0)
def test_parametrized_transform_qnode(self, mocker):
"""Test that a parametrized transform can be applied
to a QNode"""
a = 0.1
b = 0.4
x = 0.543
dev = qml.device("default.qubit", wires=2)
@qml.qnode(dev)
def circuit(x):
qml.Hadamard(wires=0)
qml.RX(x, wires=0)
return qml.expval(qml.PauliX(0))
transform_fn = self.my_transform(circuit, a, b)
spy = mocker.spy(self.my_transform, "construct")
res = transform_fn(x)
spy.assert_called()
tapes, fn = spy.spy_return
assert len(tapes[0].operations) == 2
assert tapes[0].operations[0].name == "Hadamard"
assert tapes[0].operations[1].name == "RY"
assert tapes[0].operations[1].parameters == [a * np.abs(x)]
assert len(tapes[1].operations) == 2
assert tapes[1].operations[0].name == "Hadamard"
assert tapes[1].operations[1].name == "RZ"
assert tapes[1].operations[1].parameters == [b * np.sin(x)]
expected = fn(dev.batch_execute(tapes))
assert res == expected
def test_second_order_cv(self, tol):
"""Test variance of a second order CV expectation value"""
dev = qml.device("default.gaussian", wires=1)
n = 0.12
a = 0.765
with qml.tape.JacobianTape() as tape:
qml.ThermalState(n, wires=0)
qml.Displacement(a, 0, wires=0)
qml.var(qml.NumberOperator(0))
tape.trainable_params = {0, 1}
res = tape.execute(dev)
expected = n**2 + n + np.abs(a)**2 * (1 + 2 * n)
assert np.allclose(res, expected, atol=tol, rtol=0)
# circuit jacobians
tapes, fn = qml.gradients.finite_diff(tape)
grad_F = fn(dev.batch_execute(tapes))
expected = np.array([[2 * a**2 + 2 * n + 1, 2 * a * (2 * n + 1)]])
assert np.allclose(grad_F, expected, atol=tol, rtol=0)
def test_parametrized_transform_tape_decorator(self):
"""Test that a parametrized transform can be applied
to a tape"""
a = 0.1
b = 0.4
x = 0.543
with qml.tape.QuantumTape() as tape:
qml.Hadamard(wires=0)
qml.RX(x, wires=0)
qml.expval(qml.PauliX(0))
tapes, fn = self.my_transform(a, b)(tape)
assert len(tapes[0].operations) == 2
assert tapes[0].operations[0].name == "Hadamard"
assert tapes[0].operations[1].name == "RY"
assert tapes[0].operations[1].parameters == [a * np.abs(x)]
assert len(tapes[1].operations) == 2
assert tapes[1].operations[0].name == "Hadamard"
assert tapes[1].operations[1].name == "RZ"
assert tapes[1].operations[1].parameters == [b * np.sin(x)]
def squared_difference(x, y):
"""Classical node to compute the squared
difference between two inputs"""
return np.abs(x - y)**2
def circuit():
if hasattr(qml, operation):
operation_class = getattr(qml, operation)
else:
operation_class = getattr(pennylane_qiskit,
operation)
if hasattr(qml.expval, observable):
observable_class = getattr(qml.expval, observable)
else:
observable_class = getattr(pennylane_qiskit.expval,
observable)
if operation_class.num_wires > self.num_subsystems:
raise IgnoreOperationException(
'Skipping in automatic test because the operation '
+ operation +
" acts on more than the default number of wires "
+ str(self.num_subsystems) +
". Maybe you want to increase that?")
if observable_class.num_wires > self.num_subsystems:
raise IgnoreOperationException(
'Skipping in automatic test because the observable '
+ observable +
" acts on more than the default number of wires "
+ str(self.num_subsystems) +
". Maybe you want to increase that?")
if operation_class.par_domain == 'N':
operation_pars = rnd_int_pool[:operation_class.
num_params]
elif operation_class.par_domain == 'R':
operation_pars = np.abs(
rnd_float_pool[:operation_class.num_params]
) #todo: some operations/expectations fail when parameters are negative (e.g. thermal state) but par_domain is not fine grained enough to capture this
elif operation_class.par_domain == 'A':
if str(operation) == "QubitUnitary":
operation_pars = [np.array([[1, 0], [0, -1]])]
elif str(operation) == "QubitStateVector":
operation_pars = [np.array(random_ket)]
elif str(operation) == "BasisState":
operation_pars = [
random_zero_one_pool[:self.num_subsystems]
]
operation_class.num_wires = self.num_subsystems
else:
raise IgnoreOperationException(
'Skipping in automatic test because I don\'t know how to generate parameters for the operation '
+ operation)
else:
operation_pars = {}
if observable_class.par_domain == 'N':
observable_pars = rnd_int_pool[:observable_class.
num_params]
if observable_class.par_domain == 'R':
observable_pars = np.abs(
rnd_float_pool[:observable_class.num_params]
) #todo: some operations/expectations fail when parameters are negative (e.g. thermal state) but par_domain is not fine grained enough to capture this
elif observable_class.par_domain == 'A':
if str(observable) == "Hermitian":
observable_pars = [
np.array([[1, 1j], [-1j, 0]])
]
else:
raise IgnoreOperationException(
'Skipping in automatic test because I don\'t know how to generate parameters for the observable '
+ observable)
else:
observable_pars = {}
# apply to the first wires
operation_wires = list(
range(operation_class.num_wires
)) if operation_class.num_wires > 1 else 0
observable_wires = list(
range(observable_class.num_wires)
) if observable_class.num_wires > 1 else 0
operation_class(*operation_pars, operation_wires)
return observable_class(*observable_pars,
observable_wires)
def cost_fn(params):
cost = 0
for k in range(3):
cost += np.abs(circuit(params, A=Paulis[k]) - bloch_v[k])
return cost
print(params)
##############################################################################
# We carry out the optimization over a maximum of 200 steps, aiming to reach a convergence
# tolerance (difference in cost function for subsequent optimization steps) of :math:`\sim 10^{
# -6}`.
max_iterations = 200
conv_tol = 1e-06
for n in range(max_iterations):
params, prev_energy = opt.step_and_cost(cost_fn, params)
energy = cost_fn(params)
conv = np.abs(energy - prev_energy)
if n % 20 == 0:
print('Iteration = {:}, Energy = {:.8f} Ha'.format(n, energy))
if conv <= conv_tol:
break
print()
print('Final convergence parameter = {:.8f} Ha'.format(conv))
print('Final value of the ground-state energy = {:.8f} Ha'.format(energy))
print('Accuracy with respect to the FCI energy: {:.8f} Ha ({:.8f} kcal/mol)'.format(
np.abs(energy - (-1.136189454088)), np.abs(energy - (-1.136189454088))*627.503
)
)
print()
def train_circuit(circuit, parameter_shape, X_train, Y_train, batch_size,
learning_rate, **kwargs):
"""
train a circuit classifier
Args:
circuit (qml.QNode): A circuit that you want to train
parameter_shape: A tuple describing the shape of the parameters. The first entry is the number of qubits,
the second one is the number of layers in the circuit architecture.
X_train (np.ndarray): An array of floats of size (M, n) to be used as training data.
Y_train (np.ndarray): An array of size (M,) which are the categorical labels
associated to the training data.
batch_size (int): Batch size for the circuit training.
learning_rate (float): The learning rate/step size of the optimizer.
kwargs: Hyperparameters for the training (passed as keyword arguments). There are the following hyperparameters:
nsteps (int) : Number of training steps.
optim (pennylane.optimize instance): Optimizer used during the training of the circuit.
Pass as qml.OptimizerName.
Tmax (list): Maximum point T as defined in https://arxiv.org/abs/2010.08512. (Definition 8)
The first element is the maximum number of parameters among all architectures,
the second is the maximum inference time among all architectures in terms of computing time,
the third one is the maximum inference time among all architectures in terms of the number of CNOTS
in the circuit
rate_type (string): Determines the type of error rate in the W-coefficient.
If rate_type == 'accuracy', the inference time of the circuit
is equal to the time it takes to evaluate the accuracy of the trained circuit with
respect to a validation batch three times the size of the training batch size and
the error rate is equal to 1-accuracy (w.r.t. to a validation batch).
If rate_type == 'accuracy', the inference time of the circuit is equal to the time
it takes to train the circuit (for nsteps training steps) and compute the cost at
each step and the error rate is equal to the cost after nsteps training steps.
Returns:
(W_,weights): W-coefficient, trained weights
"""
#print('batch_size',batch_size)
# fix the seed while debugging
#np.random.seed(1337)
def ohe_cost_fcn(params, circuit, ang_array, actual):
'''
use MAE to start
'''
predictions = (np.stack([circuit(params, x)
for x in ang_array]) + 1) * 0.5
return mse(actual, predictions)
def wn_cost_fcn(params, circuit, ang_array, actual):
'''
use MAE to start
'''
w = params[:, -1]
theta = params[:, :-1]
#print(w.shape,w,theta.shape,theta)
predictions = np.asarray([
2. * (1.0 / (1.0 + exp(np.dot(-w, circuit(theta, features=x))))) -
1. for x in ang_array
])
return mse(actual, predictions)
if kwargs['readout_layer'] == 'one_hot':
var = np.zeros(parameter_shape)
elif kwargs['readout_layer'] == "weighted_neuron":
var = np.hstack(
(np.zeros(parameter_shape), np.random.random(
(kwargs['nqubits'], 1)) - 0.5))
rate_type = kwargs['rate_type']
inf_time = kwargs['inf_time']
optim = kwargs['optim']
numcnots = kwargs['numcnots']
Tmax = kwargs[
'Tmax'] #Tmax[0] is maximum parameter size, Tmax[1] maximum inftime (timeit),Tmax[2] maximum number of entangling gates
num_train = len(Y_train)
validation_size = int(0.1 * num_train)
opt = optim(
stepsize=learning_rate
) #all optimizers in autograd module take in argument stepsize, so this works for all
start = time.time()
for _ in range(kwargs['nsteps']):
batch_index = np.random.randint(0, num_train, (batch_size, ))
X_train_batch = np.asarray(X_train[batch_index])
Y_train_batch = np.asarray(Y_train[batch_index])
if kwargs['readout_layer'] == 'one_hot':
var, cost = opt.step_and_cost(
lambda v: ohe_cost_fcn(v, circuit, X_train_batch, Y_train_batch
), var)
elif kwargs['readout_layer'] == 'weighted_neuron':
var, cost = opt.step_and_cost(
lambda v: wn_cost_fcn(v, circuit, X_train_batch, Y_train_batch
), var)
end = time.time()
cost_time = (end - start)
if kwargs['rate_type'] == 'accuracy':
validation_batch = np.random.randint(0, num_train, (validation_size, ))
X_validation_batch = np.asarray(X_train[validation_batch])
Y_validation_batch = np.asarray(Y_train[validation_batch])
start = time.time() # add in timeit function from Wbranch
if kwargs['readout_layer'] == 'one_hot':
predictions = np.stack(
[circuit(var, x) for x in X_validation_batch])
elif kwargs['readout_layer'] == 'weighted_neuron':
n = kwargs.get('nqubits')
w = var[:, -1]
theta = var[:, :-1]
predictions = [
int(
np.round(
2. *
(1.0 /
(1.0 + exp(np.dot(-w, circuit(theta, features=x))))) -
1., 1)) for x in X_validation_batch
]
end = time.time()
inftime = (end - start) / len(X_validation_batch)
if kwargs['readout_layer'] == 'one_hot':
err_rate = (
1.0 - ohe_accuracy(Y_validation_batch, predictions)
) + 10**-7 #add small epsilon to prevent divide by 0 errors
#print('error rate:',err_rate)
#print('weights: ',var)
elif kwargs['readout_layer'] == 'weighted_neuron':
err_rate = (
1.0 - wn_accuracy(Y_validation_batch, predictions)
) + 10**-7 #add small epsilon to prevent divide by 0 errors
#print('error rate:',err_rate)
#print('weights: ',var)
elif kwargs['rate_type'] == 'batch_cost':
err_rate = (
cost) + 10**-7 #add small epsilon to prevent divide by 0 errors
#print('error rate:',err_rate)
#print('weights: ',var)
inftime = cost_time
# QHACK #
if kwargs['inf_time'] == 'timeit':
W_ = np.abs((Tmax[0] - len(var)) / (Tmax[0])) * np.abs(
(Tmax[1] - inftime) / (Tmax[1])) * (1. / err_rate)
elif kwargs['inf_time'] == 'numcnots':
nc_ = numcnots
W_ = np.abs((Tmax[0] - len(var)) / (Tmax[0])) * np.abs(
(Tmax[2] - nc_) / (Tmax[2])) * (1. / err_rate)
return W_, var
params = init_params
gd_param_history = [params]
gd_cost_history = []
for n in range(max_iterations):
# Take step
params, prev_energy = opt.step_and_cost(cost_fn, params)
gd_param_history.append(params)
gd_cost_history.append(prev_energy)
energy = cost_fn(params)
# Calculate difference between new and old energies
conv = np.abs(energy - prev_energy)
if n % 20 == 0:
print(
"Iteration = {:}, Energy = {:.8f} Ha, Convergence parameter = {"
":.8f} Ha".format(n, energy, conv)
)
if conv <= conv_tol:
break
print()
print("Final value of the energy = {:.8f} Ha".format(energy))
print("Number of iterations = ", n)
##############################################################################
def natural_gradient(params):
"""Calculate the natural gradient of the qnode() cost function.
The code you write for this challenge should be completely contained within this function
between the # QHACK # comment markers.
You should evaluate the metric tensor and the gradient of the QNode, and then combine these
together using the natural gradient definition. The natural gradient should be returned as a
NumPy array.
The metric tensor should be evaluated using the equation provided in the problem text. Hint:
you will need to define a new QNode that returns the quantum state before measurement.
Args:
params (np.ndarray): Input parameters, of dimension 6
Returns:
np.ndarray: The natural gradient evaluated at the input parameters, of dimension 6
"""
# QHACK #
def get_state(params):
""" Get the state before a measurement """
qnode(params)
return dev.state
# Calculate the unshifted state (its conjugate transpose)
state_unshifted = np.conjugate(get_state(params)).T
def shift_vector(i):
vector = np.zeros(6)
vector[i] = 1
return vector
metric_tensor = np.zeros((6, 6))
for i in range(6):
for j in range(i + 1):
state_shifted_1 = get_state(params +
(shift_vector(i) + shift_vector(j)) *
np.pi / 2)
state_shifted_2 = get_state(params +
(shift_vector(i) - shift_vector(j)) *
np.pi / 2)
state_shifted_3 = get_state(params +
(-shift_vector(i) + shift_vector(j)) *
np.pi / 2)
state_shifted_4 = get_state(params -
(shift_vector(i) + shift_vector(j)) *
np.pi / 2)
metric_tensor[
i,
j] = (-np.abs(np.dot(state_unshifted, state_shifted_1))**2 +
np.abs(np.dot(state_unshifted, state_shifted_2))**2 +
np.abs(np.dot(state_unshifted, state_shifted_3))**2 -
np.abs(np.dot(state_unshifted, state_shifted_4))**2) / 8
if i != j:
metric_tensor[j, i] = metric_tensor[i, j]
grad = qml.grad(qnode)
gradient = grad(params)[0]
metric_tensor_inv = np.linalg.inv(metric_tensor)
natural_grad = np.dot(metric_tensor_inv, gradient)
# QHACK #
return natural_grad
class AutogradBox(qml.math.TensorBox):
"""Implements the :class:`~.TensorBox` API for ``pennylane.numpy`` tensors.
For more details, please refer to the :class:`~.TensorBox` documentation.
"""
abs = wrap_output(lambda self: np.abs(self.data))
angle = wrap_output(lambda self: np.angle(self.data))
arcsin = wrap_output(lambda self: np.arcsin(self.data))
cast = wrap_output(lambda self, dtype: np.tensor(self.data, dtype=dtype))
diag = staticmethod(wrap_output(lambda values, k=0: np.diag(values, k=k)))
expand_dims = wrap_output(
lambda self, axis: np.expand_dims(self.data, axis=axis))
ones_like = wrap_output(lambda self: np.ones_like(self.data))
reshape = wrap_output(lambda self, shape: np.reshape(self.data, shape))
sqrt = wrap_output(lambda self: np.sqrt(self.data))
sum = wrap_output(lambda self, axis=None, keepdims=False: np.sum(
self.data, axis=axis, keepdims=keepdims))
T = wrap_output(lambda self: self.data.T)
squeeze = wrap_output(lambda self: self.data.squeeze())
@staticmethod
def astensor(tensor):
return np.tensor(tensor)
@staticmethod
@wrap_output
def concatenate(values, axis=0):
return np.concatenate(AutogradBox.unbox_list(values), axis=axis)
@staticmethod
@wrap_output
def dot(x, y):
x, y = AutogradBox.unbox_list([x, y])
if x.ndim == 0 and y.ndim == 0:
return x * y
if x.ndim == 2 and y.ndim == 2:
return x @ y
return np.dot(x, y)
@property
def interface(self):
return "autograd"
def numpy(self):
if hasattr(self.data, "_value"):
# Catches the edge case where the data is an Autograd arraybox,
# which only occurs during backpropagation.
return self.data._value
return self.data.numpy()
@property
def requires_grad(self):
return self.data.requires_grad
@wrap_output
def scatter_element_add(self, index, value):
size = self.data.size
flat_index = np.ravel_multi_index(index, self.shape)
t = [0] * size
t[flat_index] = value
self.data = self.data + np.array(t).reshape(self.shape)
return self.data
@property
def shape(self):
return self.data.shape
@staticmethod
@wrap_output
def stack(values, axis=0):
return np.stack(AutogradBox.unbox_list(values), axis=axis)
@wrap_output
def take(self, indices, axis=None):
indices = self.astensor(indices)
if axis is None:
return self.data.flatten()[indices]
fancy_indices = [slice(None)] * axis + [indices]
return self.data[tuple(fancy_indices)]
@staticmethod
@wrap_output
def where(condition, x, y):
return np.where(condition, *AutogradBox.unbox_list([x, y]))
print(params)
##############################################################################
# We carry out the optimization over a maximum of 200 steps, aiming to reach a convergence
# tolerance (difference in cost function for subsequent optimization steps) of :math:`\sim 10^{
# -6}`.
max_iterations = 200
conv_tol = 1e-06
prev_energy = cost_fn(params)
for n in range(max_iterations):
params = opt.step(cost_fn, params)
energy = cost_fn(params)
conv = np.abs(energy - prev_energy)
if n % 20 == 0:
print('Iteration = {:}, Energy = {:.8f} Ha'.format(n, energy))
if conv <= conv_tol:
break
prev_energy = energy
print()
print('Final convergence parameter = {:.8f} Ha'.format(conv))
print('Final value of the ground-state energy = {:.8f} Ha'.format(energy))
print('Accuracy with respect to the FCI energy: {:.8f} Ha ({:.8f} kcal/mol)'.
format(np.abs(energy - (-1.136189454088)),
np.abs(energy - (-1.136189454088)) * 627.503))
params = np.random.normal(0, np.pi, len(singles) + len(doubles))
print(params)
##############################################################################
# We carry out the optimization over a maximum of 100 steps, aiming to reach a convergence
# tolerance of :math:`\sim 10^{-6}`. Furthermore, we track the value of
# the total spin :math:`S` of the prepared state as it is optimized through
# the iterative procedure.
max_iterations = 100
conv_tol = 1e-06
prev_energy = cost_fn(params)
for n in range(max_iterations):
params = opt.step(cost_fn, params)
energy = cost_fn(params)
conv = np.abs(energy - prev_energy)
spin = total_spin(params)
if n % 4 == 0:
print("Iteration = {:}, E = {:.8f} Ha, S = {:.4f}".format(
n, energy, spin))
if conv <= conv_tol:
break
prev_energy = energy
print()
print("Final convergence parameter = {:.8f} Ha".format(conv))
print("Final value of the ground-state energy = {:.8f} Ha".format(energy))
def cost(a):
"""A function of the device quantum state, as a function
of input QNode parameters."""
circuit(a)
res = np.abs(dev.state)**2
return res[1] - res[0]
def expZ(state):
return np.abs(state[0])**2 - np.abs(state[1])**2
params = init_params
gd_param_history = [params]
gd_cost_history = []
for n in range(max_iterations):
# Take step
params, prev_energy = opt.step_and_cost(cost_fn, params)
gd_param_history.append(params)
gd_cost_history.append(prev_energy)
energy = cost_fn(params)
# Calculate difference between new and old energies
conv = np.abs(energy - prev_energy)
if n % 20 == 0:
print(
"Iteration = {:}, Energy = {:.8f} Ha, Convergence parameter = {"
":.8f} Ha".format(n, energy, conv))
if conv <= conv_tol:
break
print()
print("Final value of the energy = {:.8f} Ha".format(energy))
print("Number of iterations = ", n)
##############################################################################
# We then repeat the process for the optimizer employing quantum natural gradients: