def run_vqe(H, ansatz, params=None):
from pennylane.optimize import NesterovMomentumOptimizer, AdamOptimizer
num_qubits = len(H.wires)
num_layers = 4
if params is None:
params = qml.init.strong_ent_layers_uniform(num_layers, num_qubits, 3)
cost_fn = qml.ExpvalCost(ansatz, H, dev)
stepsize = 0.1
opt = NesterovMomentumOptimizer(stepsize)
max_iterations = 300
conv_tol = 1e-8
energy = 0
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)
stepsize *= 0.99
opt.update_stepsize(stepsize)
if DEBUG and n % 20 == 0:
print('Iteration = {:}, Energy = {:.8f} Ha'.format(n, energy))
if conv <= conv_tol:
break
return energy, params
def optimize(feats_train, feats_val, Y_train, Y_val, features, Y):
num_qubits = 2
num_layers = 6
var_init = (0.01 * np.random.randn(num_layers, num_qubits, 3), 0.0)
opt = NesterovMomentumOptimizer(0.01)
batch_size = 5
# train the variational classifier
var = var_init
for it in range(60):
# Update the weights by one optimizer step
batch_index = np.random.randint(0, num_train, (batch_size, ))
feats_train_batch = feats_train[batch_index]
Y_train_batch = Y_train[batch_index]
var = opt.step(lambda v: cost(v, feats_train_batch, Y_train_batch),
var)
# Compute predictions on train and validation set
predictions_train = [
np.sign(variational_classifier(var, angles=f)) for f in feats_train
]
predictions_val = [
np.sign(variational_classifier(var, angles=f)) for f in feats_val
]
# Compute accuracy on train and validation set
acc_train = accuracy(Y_train, predictions_train)
acc_val = accuracy(Y_val, predictions_val)
print(
"Iter: {:5d} | Cost: {:0.7f} | Acc train: {:0.7f} | Acc validation: {:0.7f} "
"".format(it + 1, cost(var, features, Y), acc_train, acc_val))
return var
def setUp(self):
self.sgd_opt = GradientDescentOptimizer(stepsize)
self.mom_opt = MomentumOptimizer(stepsize, momentum=gamma)
self.nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
self.adag_opt = AdagradOptimizer(stepsize)
self.rms_opt = RMSPropOptimizer(stepsize, decay=gamma)
self.adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
self.fnames = ['test_function_1', 'test_function_2', 'test_function_3']
self.univariate_funcs = [
np.sin, lambda x: np.exp(x / 10.), lambda x: x**2
]
self.grad_uni_fns = [
np.cos, lambda x: np.exp(x / 10.) / 10., lambda x: 2 * x
]
self.multivariate_funcs = [
lambda x: np.sin(x[0]) + np.cos(x[1]),
lambda x: np.exp(x[0] / 3) * np.tanh(x[1]),
lambda x: np.sum([x_**2 for x_ in x])
]
self.grad_multi_funcs = [
lambda x: np.array([np.cos(x[0]), -np.sin(x[1])]),
lambda x: np.array([
np.exp(x[0] / 3) / 3 * np.tanh(x[1]),
np.exp(x[0] / 3) * (1 - np.tanh(x[1])**2)
]), lambda x: np.array([2 * x_ for x_ in x])
]
self.mvar_mdim_funcs = [
lambda x: np.sin(x[0, 0]) + np.cos(x[1, 0]) - np.sin(x[0, 1]) + x[
1, 1], lambda x: np.exp(x[0, 0] / 3) * np.tanh(x[0, 1]),
lambda x: np.sum([x_[0]**2 for x_ in x])
]
self.grad_mvar_mdim_funcs = [
lambda x: np.array([[np.cos(x[0, 0]), -np.cos(x[0, 1])],
[-np.sin(x[1, 0]), 1.]]),
lambda x: np.array([[
np.exp(x[0, 0] / 3) / 3 * np.tanh(x[0, 1]),
np.exp(x[0, 0] / 3) * (1 - np.tanh(x[0, 1])**2)
], [0., 0.]]), lambda x: np.array([[2 * x_[0], 0.] for x_ in x])
]
self.class_fun = class_fun
self.quant_fun = quant_fun
self.hybrid_fun = hybrid_fun
self.hybrid_fun_nested = hybrid_fun_nested
self.hybrid_fun_flat = hybrid_fun_flat
self.hybrid_fun_mdarr = hybrid_fun_mdarr
self.hybrid_fun_mdlist = hybrid_fun_mdlist
self.mixed_list = [(0.2, 0.3), np.array([0.4, 0.2, 0.4]), 0.1]
self.mixed_tuple = (np.array([0.2, 0.3]), [0.4, 0.2, 0.4], 0.1)
self.nested_list = [[[0.2], 0.3], [0.1, [0.4]], -0.1]
self.flat_list = [0.2, 0.3, 0.1, 0.4, -0.1]
self.multid_array = np.array([[0.1, 0.2], [-0.1, -0.4]])
self.multid_list = [[0.1, 0.2], [-0.1, -0.4]]
def train_classifier(x_train, y_train, x_test, y_test, shots=50):
from pennylane.optimize import NesterovMomentumOptimizer, AdamOptimizer
old_shots = dev.shots
dev.shots = shots
num_train = len(x_train)
num_layers = 4
var_init = (qml.init.strong_ent_layers_uniform(num_layers, n_qubits,
3), 0.0)
stepsize = 0.1
opt = NesterovMomentumOptimizer(stepsize)
batch_size = 5
maxit = 20
# train the variational classifier
var = var_init
for it in range(maxit):
# Update the weights by one optimizer step
batch_index = np.random.randint(0, num_train, (batch_size, ))
x_train_batch = x_train[batch_index]
y_train_batch = y_train[batch_index]
var = opt.step(lambda v: cost(v, x_train_batch, y_train_batch),
var)
# stepsize *= 0.95
# opt.update_stepsize(stepsize)
# Compute predictions on train and validation set
predictions_train = [
np.sign(variational_classifier(var, f)) for f in x_train
]
acc_train = accuracy(y_train, predictions_train)
if DEBUG:
predictions_val = [
np.sign(variational_classifier(var, f)) for f in x_test
]
acc_val = accuracy(y_test, predictions_val)
print(
"Iter: {:5d} | Cost: {:0.7f} | Acc train: {:0.7f} | Acc validation: {:0.7f} "
"".format(it + 1, cost(var, x_train, y_train), acc_train,
acc_val))
if acc_train > 0.95:
break
dev.shots = old_shots
return var
def run_vqe_excited2(H, ansatz, gs_params, fes_params, params=None):
from pennylane.optimize import NesterovMomentumOptimizer, AdamOptimizer
num_qubits = len(H.wires)
num_layers = 4
if params is None:
params = qml.init.strong_ent_layers_uniform(num_layers, num_qubits, 3)
@qml.qnode(dev)
def overlap(params, wires):
variational_ansatz(gs_params, wires)
qml.inv(qml.template(variational_ansatz)(params, wires))
return qml.probs([0, 1, 2])
@qml.qnode(dev)
def overlap2(params, wires):
variational_ansatz(fes_params, wires)
qml.inv(qml.template(variational_ansatz)(params, wires))
return qml.probs([0, 1, 2])
def cost_fn(params, **kwargs):
h_cost = qml.ExpvalCost(ansatz, H, dev)
h = h_cost(params, **kwargs)
o = overlap(params, wires=H.wires)
o2 = overlap2(params, wires=H.wires)
return h + 1.5 * o[0] + o2[0]
stepsize = 0.3
opt = NesterovMomentumOptimizer(stepsize)
max_iterations = 300
conv_tol = 1e-8
energy = 0
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)
stepsize *= 0.99
opt.update_stepsize(stepsize)
if DEBUG and n % 20 == 0:
print('Iteration = {:}, Energy = {:.8f} Ha'.format(n, energy))
if conv <= conv_tol:
break
return energy, params
class A:
sgd_opt = GradientDescentOptimizer(stepsize)
mom_opt = MomentumOptimizer(stepsize, momentum=gamma)
nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
adag_opt = AdagradOptimizer(stepsize)
rms_opt = RMSPropOptimizer(stepsize, decay=gamma)
adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
def test_step_and_cost_autograd_nesterov_multid_array(self):
"""Test that the correct cost is returned via the step_and_cost method for the
Nesterov momentum optimizer"""
stepsize, gamma = 0.1, 0.5
nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
multid_array = np.array([[0.1, 0.2], [-0.1, -0.4]])
@qml.qnode(qml.device("default.qubit", wires=1))
def quant_fun_mdarr(var):
qml.RX(var[0, 1], wires=[0])
qml.RY(var[1, 0], wires=[0])
qml.RY(var[1, 1], wires=[0])
return qml.expval(qml.PauliZ(0))
_, res = nesmom_opt.step_and_cost(quant_fun_mdarr, multid_array)
expected = quant_fun_mdarr(multid_array)
assert np.all(res == expected)
def test_nesterovmomentum_optimizer_univar(self, x_start, tol):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for univariate functions."""
stepsize, gamma = 0.1, 0.5
nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
univariate_funcs = [np.sin, lambda x: np.exp(x / 10.0), lambda x: x ** 2]
grad_uni_fns = [
lambda x: (np.cos(x),),
lambda x: (np.exp(x / 10.0) / 10.0,),
lambda x: (2 * x,),
]
for gradf, f in zip(grad_uni_fns, univariate_funcs):
nesmom_opt.reset()
x_onestep = nesmom_opt.step(f, x_start)
x_onestep_target = x_start - gradf(x_start)[0] * stepsize
assert np.allclose(x_onestep, x_onestep_target, atol=tol)
x_twosteps = nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_start)[0]
shifted_grad_term = gradf(x_onestep - stepsize * momentum_term)[0]
x_twosteps_target = x_onestep - (shifted_grad_term + momentum_term) * stepsize
assert np.allclose(x_twosteps, x_twosteps_target, atol=tol)
def test_step_and_cost_autograd_nesterov_multiple_inputs(self):
"""Test that the correct cost is returned via the step_and_cost method for the
Nesterov momentum optimizer"""
stepsize, gamma = 0.1, 0.5
nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
@qml.qnode(qml.device("default.qubit", wires=1))
def quant_fun(*variables):
qml.RX(variables[0][1], wires=[0])
qml.RY(variables[1][2], wires=[0])
qml.RY(variables[2], wires=[0])
return qml.expval(qml.PauliZ(0))
inputs = [
np.array((0.2, 0.3), requires_grad=True),
np.array([0.4, 0.2, 0.4], requires_grad=True),
np.array(0.1, requires_grad=True),
]
_, res = nesmom_opt.step_and_cost(quant_fun, *inputs)
expected = quant_fun(*inputs)
assert np.all(res == expected)
def train_and_test(X_train, Y_train, X_test, Y_test):
opt = NesterovMomentumOptimizer(0.01)
batch_size = 5
# train the variational classifier
var = var_init
test_accuracies = []
train_accuracies = []
costs = []
for it in range(num_iterations):
# Update the weights by one optimizer step
batch_index = np.random.randint(0, num_train, (batch_size, ))
X_train_batch = X_train[batch_index]
Y_train_batch = Y_train[batch_index]
var = opt.step(lambda v: cost(v, X_train_batch, Y_train_batch), var)
# Compute predictions on train and validation set
predictions_train = [np.sign(variational_classifier(var, f)) for f in X_train]
predictions_test = [np.sign(variational_classifier(var, f)) for f in X_test]
# Compute accuracy on train and validation set
acc_train = accuracy(Y_train, predictions_train)
acc_test = accuracy(Y_test, predictions_test)
# Compute cost on all samples
c = cost(var, X, Y)
costs.append(c)
test_accuracies.append(acc_test)
train_accuracies.append(acc_train)
print("Iter: {:5d} | Cost: {:0.7f} | Acc train: {:0.7f} | Acc validation: {:0.7f} "
"".format(it+1, c, acc_train, acc_test))
return train_accuracies, test_accuracies, costs, var
def opt(opt_name):
stepsize, gamma, delta = 0.1, 0.5, 0.8
if opt_name == "gd":
return GradientDescentOptimizer(stepsize)
if opt_name == "nest":
return NesterovMomentumOptimizer(stepsize, momentum=gamma)
if opt_name == "moment":
return MomentumOptimizer(stepsize, momentum=gamma)
if opt_name == "ada":
return AdagradOptimizer(stepsize)
if opt_name == "rms":
return RMSPropOptimizer(stepsize, decay=gamma)
if opt_name == "adam":
return AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
def test_nesterovmomentum_optimizer_multivar(self, tol):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for multivariate functions."""
stepsize, gamma = 0.1, 0.5
nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
multivariate_funcs = [
lambda x: np.sin(x[0]) + np.cos(x[1]),
lambda x: np.exp(x[0] / 3) * np.tanh(x[1]),
lambda x: np.sum([x_ ** 2 for x_ in x]),
]
grad_multi_funcs = [
lambda x: (np.array([np.cos(x[0]), -np.sin(x[1])]),),
lambda x: (
np.array(
[
np.exp(x[0] / 3) / 3 * np.tanh(x[1]),
np.exp(x[0] / 3) * (1 - np.tanh(x[1]) ** 2),
]
),
),
lambda x: (np.array([2 * x_ for x_ in x]),),
]
x_vals = np.linspace(-10, 10, 16, endpoint=False)
for gradf, f in zip(grad_multi_funcs, multivariate_funcs):
for jdx in range(len(x_vals[:-1])):
nesmom_opt.reset()
x_vec = x_vals[jdx : jdx + 2]
x_onestep = nesmom_opt.step(f, x_vec)
x_onestep_target = x_vec - gradf(x_vec)[0] * stepsize
assert np.allclose(x_onestep, x_onestep_target, atol=tol)
x_twosteps = nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_vec)[0]
shifted_grad_term = gradf(x_onestep - stepsize * momentum_term)[0]
x_twosteps_target = x_onestep - (shifted_grad_term + momentum_term) * stepsize
assert np.allclose(x_twosteps, x_twosteps_target, atol=tol)
# load parity data
data = np.loadtxt("data/parity.txt")
X = data[:, :-1]
Y = data[:, -1]
Y = Y * 2 - np.ones(len(Y)) # shift label from {0, 1} to {-1, 1}
# initialize weight layers
np.random.seed(0)
num_qubits = 4
num_layers = 2
var_init = (0.01 * np.random.randn(num_layers, num_qubits, 3), 0.0)
# create optimizer
opt = NesterovMomentumOptimizer(0.5)
batch_size = 5
# train the variational classifier
var = var_init
for it in range(25):
# Update the weights by one optimizer step
batch_index = np.random.randint(0, len(X), (batch_size, ))
X_batch = X[batch_index]
Y_batch = Y[batch_index]
var = opt.step(lambda v: cost(v, X_batch, Y_batch), var)
# Compute accuracy
predictions = [np.sign(variational_classifier(var, x=x)) for x in X]
acc = accuracy(Y, predictions)
eta2 = 0.1
opt.update_stepsize(eta2)
assert opt._stepsize == eta2
def reset(opt):
if getattr(opt, "reset", None):
opt.reset()
@pytest.mark.parametrize(
"opt, opt_name",
[
(GradientDescentOptimizer(stepsize), "gd"),
(MomentumOptimizer(stepsize, momentum=gamma), "moment"),
(NesterovMomentumOptimizer(stepsize, momentum=gamma), "nest"),
(AdagradOptimizer(stepsize), "ada"),
(RMSPropOptimizer(stepsize, decay=gamma), "rms"),
(AdamOptimizer(stepsize, beta1=gamma, beta2=delta), "adam"),
(RotosolveOptimizer(), "roto"),
],
)
class TestOverOpts:
"""Tests keywords, multiple arguements, and non-training arguments in relevent optimizers"""
def test_kwargs(self, mocker, opt, opt_name, tol):
"""Test that the keywords get passed and alter the function"""
class func_wrapper:
@staticmethod
def func(x, c=1.0):
return (x - c)**2
##############################################################################
# We initialize the variables randomly (but fix a seed for
# reproducability). The first variable in the list is used as a bias,
# while the rest is fed into the gates of the variational circuit.
np.random.seed(0)
num_qubits = 4
num_layers = 2
var_init = (0.01 * np.random.randn(num_layers, num_qubits, 3), 0.0)
print(var_init)
##############################################################################
# Next we create an optimizer and choose a batch size…
opt = NesterovMomentumOptimizer(0.5)
batch_size = 5
##############################################################################
# …and train the optimizer. We track the accuracy - the share of correctly
# classified data samples. For this we compute the outputs of the
# variational classifier and turn them into predictions in
# :math:`\{-1,1\}` by taking the sign of the output.
var = var_init
for it in range(25):
# Update the weights by one optimizer step
batch_index = np.random.randint(0, len(X), (batch_size, ))
X_batch = X[batch_index]
Y_batch = Y[batch_index]
class BasicTest(BaseTest):
"""Basic optimizer tests.
"""
def setUp(self):
self.sgd_opt = GradientDescentOptimizer(stepsize)
self.mom_opt = MomentumOptimizer(stepsize, momentum=gamma)
self.nesmom_opt = NesterovMomentumOptimizer(stepsize, momentum=gamma)
self.adag_opt = AdagradOptimizer(stepsize)
self.rms_opt = RMSPropOptimizer(stepsize, decay=gamma)
self.adam_opt = AdamOptimizer(stepsize, beta1=gamma, beta2=delta)
self.fnames = ['test_function_1', 'test_function_2', 'test_function_3']
self.univariate_funcs = [
np.sin, lambda x: np.exp(x / 10.), lambda x: x**2
]
self.grad_uni_fns = [
np.cos, lambda x: np.exp(x / 10.) / 10., lambda x: 2 * x
]
self.multivariate_funcs = [
lambda x: np.sin(x[0]) + np.cos(x[1]),
lambda x: np.exp(x[0] / 3) * np.tanh(x[1]),
lambda x: np.sum([x_**2 for x_ in x])
]
self.grad_multi_funcs = [
lambda x: np.array([np.cos(x[0]), -np.sin(x[1])]),
lambda x: np.array([
np.exp(x[0] / 3) / 3 * np.tanh(x[1]),
np.exp(x[0] / 3) * (1 - np.tanh(x[1])**2)
]), lambda x: np.array([2 * x_ for x_ in x])
]
self.mvar_mdim_funcs = [
lambda x: np.sin(x[0, 0]) + np.cos(x[1, 0]) - np.sin(x[0, 1]) + x[
1, 1], lambda x: np.exp(x[0, 0] / 3) * np.tanh(x[0, 1]),
lambda x: np.sum([x_[0]**2 for x_ in x])
]
self.grad_mvar_mdim_funcs = [
lambda x: np.array([[np.cos(x[0, 0]), -np.cos(x[0, 1])],
[-np.sin(x[1, 0]), 1.]]),
lambda x: np.array([[
np.exp(x[0, 0] / 3) / 3 * np.tanh(x[0, 1]),
np.exp(x[0, 0] / 3) * (1 - np.tanh(x[0, 1])**2)
], [0., 0.]]), lambda x: np.array([[2 * x_[0], 0.] for x_ in x])
]
self.class_fun = class_fun
self.quant_fun = quant_fun
self.hybrid_fun = hybrid_fun
self.hybrid_fun_nested = hybrid_fun_nested
self.hybrid_fun_flat = hybrid_fun_flat
self.hybrid_fun_mdarr = hybrid_fun_mdarr
self.hybrid_fun_mdlist = hybrid_fun_mdlist
self.mixed_list = [(0.2, 0.3), np.array([0.4, 0.2, 0.4]), 0.1]
self.mixed_tuple = (np.array([0.2, 0.3]), [0.4, 0.2, 0.4], 0.1)
self.nested_list = [[[0.2], 0.3], [0.1, [0.4]], -0.1]
self.flat_list = [0.2, 0.3, 0.1, 0.4, -0.1]
self.multid_array = np.array([[0.1, 0.2], [-0.1, -0.4]])
self.multid_list = [[0.1, 0.2], [-0.1, -0.4]]
def test_mixed_inputs_for_hybrid_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for hybrid optimization tasks."""
self.logTestName()
hybrid_list = self.sgd_opt.step(self.hybrid_fun, self.mixed_list)
hybrid_tuple = self.sgd_opt.step(self.hybrid_fun, self.mixed_tuple)
self.assertAllAlmostEqual(hybrid_list[0],
hybrid_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(hybrid_list[1],
hybrid_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(hybrid_list[2],
hybrid_tuple[2],
delta=self.tol)
def test_mixed_inputs_for_classical_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for purely classical optimization tasks."""
self.logTestName()
class_list = self.sgd_opt.step(self.class_fun, self.mixed_list)
class_tuple = self.sgd_opt.step(self.class_fun, self.mixed_tuple)
self.assertAllAlmostEqual(class_list[0],
class_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(class_list[1],
class_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(class_list[2],
class_tuple[2],
delta=self.tol)
def test_mixed_inputs_for_quantum_optimization(self):
"""Tests that gradient descent optimizer treats parameters of mixed types the same
for purely quantum optimization tasks."""
self.logTestName()
quant_list = self.sgd_opt.step(self.quant_fun, self.mixed_list)
quant_tuple = self.sgd_opt.step(self.quant_fun, self.mixed_tuple)
self.assertAllAlmostEqual(quant_list[0],
quant_tuple[0],
delta=self.tol)
self.assertAllAlmostEqual(quant_list[1],
quant_tuple[1],
delta=self.tol)
self.assertAllAlmostEqual(quant_list[2],
quant_tuple[2],
delta=self.tol)
def test_nested_and_flat_returns_same_update(self):
"""Tests that gradient descent optimizer has the same output for
nested and flat lists."""
self.logTestName()
nested = self.sgd_opt.step(self.hybrid_fun_nested, self.nested_list)
flat = self.sgd_opt.step(self.hybrid_fun_flat, self.flat_list)
self.assertAllAlmostEqual(flat, list(_flatten(nested)), delta=self.tol)
def test_array_and_list_return_same_update(self):
"""Tests that gradient descent optimizer has the same output for
lists and arrays."""
self.logTestName()
array = self.sgd_opt.step(self.hybrid_fun_mdarr, self.multid_array)
list = self.sgd_opt.step(self.hybrid_fun_mdlist, self.multid_list)
self.assertAllAlmostEqual(array, list, delta=self.tol)
def test_gradient_descent_optimizer_univar(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
x_new = self.sgd_opt.step(f, x_start)
x_correct = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_new, x_correct, delta=self.tol)
def test_gradient_descent_optimizer_multivar(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
x_vec = x_vals[jdx:jdx + 2]
x_new = self.sgd_opt.step(f, x_vec)
x_correct = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_new, x_correct, delta=self.tol)
def test_gradient_descent_optimizer_multivar_multidim(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
for multi-variate functions and with higher dimensional inputs."""
self.logTestName()
for gradf, f, name in zip(self.grad_mvar_mdim_funcs,
self.mvar_mdim_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-3])):
x_vec = x_vals[jdx:jdx + 4]
x_vec_multidim = np.reshape(x_vec, (2, 2))
x_new = self.sgd_opt.step(f, x_vec_multidim)
x_correct = x_vec_multidim - gradf(
x_vec_multidim) * stepsize
x_new_flat = x_new.flatten()
x_correct_flat = x_correct.flatten()
self.assertAllAlmostEqual(x_new_flat,
x_correct_flat,
delta=self.tol)
def test_gradient_descent_optimizer_usergrad(self):
"""Tests that basic stochastic gradient descent takes gradient-descent steps correctly
using user-provided gradients."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns[::-1],
self.univariate_funcs, self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
x_new = self.sgd_opt.step(f, x_start, grad_fn=gradf)
x_correct = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_new, x_correct, delta=self.tol)
def test_momentum_optimizer_univar(self):
"""Tests that momentum optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.mom_opt.reset()
x_onestep = self.mom_opt.step(f, x_start)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.mom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_start)
x_twosteps_target = x_onestep - (gradf(x_onestep) +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_momentum_optimizer_multivar(self):
"""Tests that momentum optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.mom_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.mom_opt.step(f, x_vec)
x_onestep_target = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.mom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_vec)
x_twosteps_target = x_onestep - (gradf(x_onestep) +
momentum_term) * stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_univar(self):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.nesmom_opt.reset()
x_onestep = self.nesmom_opt.step(f, x_start)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_start)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_multivar(self):
"""Tests that nesterov momentum optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.nesmom_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.nesmom_opt.step(f, x_vec)
x_onestep_target = x_vec - gradf(x_vec) * stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f, x_onestep)
momentum_term = gamma * gradf(x_vec)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_nesterovmomentum_optimizer_usergrad(self):
"""Tests that nesterov momentum optimizer takes gradient-descent steps correctly
using user-provided gradients."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns[::-1],
self.univariate_funcs, self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.nesmom_opt.reset()
x_onestep = self.nesmom_opt.step(f, x_start, grad_fn=gradf)
x_onestep_target = x_start - gradf(x_start) * stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.nesmom_opt.step(f,
x_onestep,
grad_fn=gradf)
momentum_term = gamma * gradf(x_start)
shifted_grad_term = gradf(x_onestep -
stepsize * momentum_term)
x_twosteps_target = x_onestep - (shifted_grad_term +
momentum_term) * stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adagrad_optimizer_univar(self):
"""Tests that adagrad optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.adag_opt.reset()
x_onestep = self.adag_opt.step(f, x_start)
past_grads = gradf(x_start) * gradf(x_start)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_start - gradf(
x_start) * adapt_stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adag_opt.step(f, x_onestep)
past_grads = gradf(x_start) * gradf(x_start) + gradf(
x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adagrad_optimizer_multivar(self):
"""Tests that adagrad optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.adag_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.adag_opt.step(f, x_vec)
past_grads = gradf(x_vec) * gradf(x_vec)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_vec - gradf(x_vec) * adapt_stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adag_opt.step(f, x_onestep)
past_grads = gradf(x_vec) * gradf(x_vec) + gradf(
x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_rmsprop_optimizer_univar(self):
"""Tests that rmsprop optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.rms_opt.reset()
x_onestep = self.rms_opt.step(f, x_start)
past_grads = (1 - gamma) * gradf(x_start) * gradf(x_start)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_start - gradf(
x_start) * adapt_stepsize
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.rms_opt.step(f, x_onestep)
past_grads = (1 - gamma) * gamma * gradf(x_start)*gradf(x_start) \
+ (1 - gamma) * gradf(x_onestep)*gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_rmsprop_optimizer_multivar(self):
"""Tests that rmsprop optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.rms_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.rms_opt.step(f, x_vec)
past_grads = (1 - gamma) * gradf(x_vec) * gradf(x_vec)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_onestep_target = x_vec - gradf(x_vec) * adapt_stepsize
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.rms_opt.step(f, x_onestep)
past_grads = (1 - gamma) * gamma * gradf(x_vec) * gradf(x_vec) \
+ (1 - gamma) * gradf(x_onestep) * gradf(x_onestep)
adapt_stepsize = stepsize / np.sqrt(past_grads + 1e-8)
x_twosteps_target = x_onestep - gradf(
x_onestep) * adapt_stepsize
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adam_optimizer_univar(self):
"""Tests that adam optimizer takes one and two steps correctly
for uni-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_uni_fns, self.univariate_funcs,
self.fnames):
with self.subTest(i=name):
for x_start in x_vals:
self.adam_opt.reset()
x_onestep = self.adam_opt.step(f, x_start)
adapted_stepsize = stepsize * np.sqrt(1 - delta) / (1 -
gamma)
firstmoment = gradf(x_start)
secondmoment = gradf(x_start) * gradf(x_start)
x_onestep_target = x_start - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adam_opt.step(f, x_onestep)
adapted_stepsize = stepsize * np.sqrt(1 - delta**2) / (
1 - gamma**2)
firstmoment = (gamma * gradf(x_start) +
(1 - gamma) * gradf(x_onestep))
secondmoment = (
delta * gradf(x_start) * gradf(x_start) +
(1 - delta) * gradf(x_onestep) * gradf(x_onestep))
x_twosteps_target = x_onestep - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def test_adam_optimizer_multivar(self):
"""Tests that adam optimizer takes one and two steps correctly
for multi-variate functions."""
self.logTestName()
for gradf, f, name in zip(self.grad_multi_funcs,
self.multivariate_funcs, self.fnames):
with self.subTest(i=name):
for jdx in range(len(x_vals[:-1])):
self.adam_opt.reset()
x_vec = x_vals[jdx:jdx + 2]
x_onestep = self.adam_opt.step(f, x_vec)
adapted_stepsize = stepsize * np.sqrt(1 - delta) / (1 -
gamma)
firstmoment = gradf(x_vec)
secondmoment = gradf(x_vec) * gradf(x_vec)
x_onestep_target = x_vec - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAllAlmostEqual(x_onestep,
x_onestep_target,
delta=self.tol)
x_twosteps = self.adam_opt.step(f, x_onestep)
adapted_stepsize = stepsize * np.sqrt(1 - delta**2) / (
1 - gamma**2)
firstmoment = (gamma * gradf(x_vec) +
(1 - gamma) * gradf(x_onestep))
secondmoment = (
delta * gradf(x_vec) * gradf(x_vec) +
(1 - delta) * gradf(x_onestep) * gradf(x_onestep))
x_twosteps_target = x_onestep - adapted_stepsize * firstmoment / (
np.sqrt(secondmoment) + 1e-8)
self.assertAllAlmostEqual(x_twosteps,
x_twosteps_target,
delta=self.tol)
def get_opt():
opt = NesterovMomentumOptimizer(0.5)
batch_size = 5
return (opt, batch_size)
batch_size = 5
# calculate number of batches
batches = len(X_train) // batch_size
# select number of epochs
n_epochs = 5
# draw random quantum node weights
theta = strong_ent_layers_uniform(n_layers, n_qubits, seed=15)
# train the variational classifier
# start of main learning loop
# build the optimizer object
pennylane_opt = NesterovMomentumOptimizer()
log = []
# split training data into batches
X_batches = np.array_split(np.arange(len(X_train)), batches)
for it, batch_index in enumerate(chain(*(n_epochs * [X_batches]))):
# Update the weights by one optimizer step
batch_cost = \
lambda t: cost(t, X_train[batch_index], e_train[batch_index])
theta = pennylane_opt.step(batch_cost, theta)
log.append({"theta": theta})
# end of learning loop
# convert scores to classes
scores = np.array([circuit(theta, x=x) for x in X_test])
y_pred = sgn(scores)