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Conector Torch y QNNs Híbridas

This tutorial introduces Qiskit’s TorchConnector class, and demonstrates how the TorchConnector allows for a natural integration of any NeuralNetwork from Qiskit Machine Learning into a PyTorch workflow. TorchConnector takes a Qiskit NeuralNetwork and makes it available as a PyTorch Module. The resulting module can be seamlessly incorporated into PyTorch classical architectures and trained jointly without additional considerations, enabling the development and testing of novel hybrid quantum-classical machine learning architectures.

Contenido:

Parte 1: Clasificación y Regresión Simples

The first part of this tutorial shows how quantum neural networks can be trained using PyTorch’s automatic differentiation engine (torch.autograd, link) for simple classification and regression tasks.

1. Clasificación

   1. Clasificación con PyTorch y EstimatorQNN

   2. Clasificación con PyTorch y SamplerQNN

2. Regresión

   1. Regresión con PyTorch y SamplerQNN

Parte 2: Clasificación MNIST, QNNs Híbridas

La segunda parte de este tutorial ilustra cómo incrustar una NeuralNetwork (Cuántica) en un flujo de trabajo PyTorch de destino (en este caso, una arquitectura CNN típica) para clasificar los datos MNIST de una manera híbrida cuántica-clásica.

---

# Necessary imports

import numpy as np
import matplotlib.pyplot as plt

from torch import Tensor
from torch.nn import Linear, CrossEntropyLoss, MSELoss
from torch.optim import LBFGS

from qiskit import QuantumCircuit
from qiskit.utils import algorithm_globals
from qiskit.circuit import Parameter
from qiskit.circuit.library import RealAmplitudes, ZZFeatureMap
from qiskit_machine_learning.neural_networks import SamplerQNN, EstimatorQNN
from qiskit_machine_learning.connectors import TorchConnector

# Set seed for random generators
algorithm_globals.random_seed = 42

Parte 1: Clasificación y Regresión Simples

1. Clasificación

First, we show how TorchConnector allows to train a Quantum NeuralNetwork to solve a classification tasks using PyTorch’s automatic differentiation engine. In order to illustrate this, we will perform binary classification on a randomly generated dataset.

# Generate random dataset

# Select dataset dimension (num_inputs) and size (num_samples)
num_inputs = 2
num_samples = 20

# Generate random input coordinates (X) and binary labels (y)
X = 2 * algorithm_globals.random.random([num_samples, num_inputs]) - 1
y01 = 1 * (np.sum(X, axis=1) >= 0)  # in { 0,  1}, y01 will be used for SamplerQNN example
y = 2 * y01 - 1  # in {-1, +1}, y will be used for EstimatorQNN example

# Convert to torch Tensors
X_ = Tensor(X)
y01_ = Tensor(y01).reshape(len(y)).long()
y_ = Tensor(y).reshape(len(y), 1)

# Plot dataset
for x, y_target in zip(X, y):
    if y_target == 1:
        plt.plot(x[0], x[1], "bo")
    else:
        plt.plot(x[0], x[1], "go")
plt.plot([-1, 1], [1, -1], "--", color="black")
plt.show()

A. Clasificación con PyTorch y EstimatorQNN

Vincular un EstimatorQNN a PyTorch es relativamente sencillo. Aquí ilustramos esto usando el EstimatorQNN construido a partir de un mapa de características y un ansatz.

# Set up a circuit
feature_map = ZZFeatureMap(num_inputs)
ansatz = RealAmplitudes(num_inputs)
qc = QuantumCircuit(num_inputs)
qc.compose(feature_map, inplace=True)
qc.compose(ansatz, inplace=True)
qc.draw("mpl")

# Setup QNN
qnn1 = EstimatorQNN(
    circuit=qc, input_params=feature_map.parameters, weight_params=ansatz.parameters
)

# Set up PyTorch module
# Note: If we don't explicitly declare the initial weights
# they are chosen uniformly at random from [-1, 1].
initial_weights = 0.1 * (2 * algorithm_globals.random.random(qnn1.num_weights) - 1)
model1 = TorchConnector(qnn1, initial_weights=initial_weights)
print("Initial weights: ", initial_weights)

Initial weights:  [-0.01256962  0.06653564  0.04005302 -0.03752667  0.06645196  0.06095287
 -0.02250432 -0.04233438]

# Test with a single input
model1(X_[0, :])

tensor([-0.3285], grad_fn=<_TorchNNFunctionBackward>)

Optimizador

The choice of optimizer for training any machine learning model can be crucial in determining the success of our training’s outcome. When using TorchConnector, we get access to all of the optimizer algorithms defined in the [torch.optim] package (link). Some of the most famous algorithms used in popular machine learning architectures include Adam, SGD, or Adagrad. However, for this tutorial we will be using the L-BFGS algorithm (torch.optim.LBFGS), one of the most well know second-order optimization algorithms for numerical optimization.

Función de Pérdida

As for the loss function, we can also take advantage of PyTorch’s pre-defined modules from torch.nn, such as the Cross-Entropy or Mean Squared Error losses.

💡 Clarification : In classical machine learning, the general rule of thumb is to apply a Cross-Entropy loss to classification tasks, and MSE loss to regression tasks. However, this recommendation is given under the assumption that the output of the classification network is a class probability value in the \([0, 1]\) range (usually this is achieved through a Softmax layer). Because the following example for EstimatorQNN does not include such layer, and we don’t apply any mapping to the output (the following section shows an example of application of parity mapping with SamplerQNNs), the QNN’s output can take any value in the range \([-1, 1]\). In case you were wondering, this is the reason why this particular example uses MSELoss for classification despite it not being the norm (but we encourage you to experiment with different loss functions and see how they can impact training results).

# Define optimizer and loss
optimizer = LBFGS(model1.parameters())
f_loss = MSELoss(reduction="sum")

# Start training
model1.train()  # set model to training mode


# Note from (https://pytorch.org/docs/stable/optim.html):
# Some optimization algorithms such as LBFGS need to
# reevaluate the function multiple times, so you have to
# pass in a closure that allows them to recompute your model.
# The closure should clear the gradients, compute the loss,
# and return it.
def closure():
    optimizer.zero_grad()  # Initialize/clear gradients
    loss = f_loss(model1(X_), y_)  # Evaluate loss function
    loss.backward()  # Backward pass
    print(loss.item())  # Print loss
    return loss


# Run optimizer step4
optimizer.step(closure)

25.535646438598633
22.696760177612305
20.039228439331055
19.687908172607422
19.267208099365234
19.025373458862305
18.154708862304688
17.337854385375977
19.082578659057617
17.073287963867188
16.21839141845703
14.992582321166992
14.929339408874512
14.914533615112305
14.907636642456055
14.902364730834961
14.902134895324707
14.90211009979248
14.902111053466797

tensor(25.5356, grad_fn=<MseLossBackward0>)

# Evaluate model and compute accuracy
y_predict = []
for x, y_target in zip(X, y):
    output = model1(Tensor(x))
    y_predict += [np.sign(output.detach().numpy())[0]]

print("Accuracy:", sum(y_predict == y) / len(y))

# Plot results
# red == wrongly classified
for x, y_target, y_p in zip(X, y, y_predict):
    if y_target == 1:
        plt.plot(x[0], x[1], "bo")
    else:
        plt.plot(x[0], x[1], "go")
    if y_target != y_p:
        plt.scatter(x[0], x[1], s=200, facecolors="none", edgecolors="r", linewidths=2)
plt.plot([-1, 1], [1, -1], "--", color="black")
plt.show()

Accuracy: 0.8

Los círculos rojos indican puntos de datos clasificados incorrectamente.

B. Clasificación con PyTorch y SamplerQNN

Vincular una SamplerQNN``a PyTorch requiere un poco más de atención que con ``EstimatorQNN. Sin la configuración correcta, la propagación hacia atrás (backpropagation) no es posible.

In particular, we must make sure that we are returning a dense array of probabilities in the network’s forward pass (sparse=False). This parameter is set up to False by default, so we just have to make sure that it has not been changed.

⚠️ Atención: Si definimos una función de interpretación personalizada (en el ejemplo: parity), debemos recordar proporcionar explícitamente la forma de salida deseada (en el ejemplo: 2). Para obtener más información sobre la configuración inicial de parámetros para SamplerQNN, consulta la documentación oficial de qiskit.

# Define feature map and ansatz
feature_map = ZZFeatureMap(num_inputs)
ansatz = RealAmplitudes(num_inputs, entanglement="linear", reps=1)

# Define quantum circuit of num_qubits = input dim
# Append feature map and ansatz
qc = QuantumCircuit(num_inputs)
qc.compose(feature_map, inplace=True)
qc.compose(ansatz, inplace=True)

# Define SamplerQNN and initial setup
parity = lambda x: "{:b}".format(x).count("1") % 2  # optional interpret function
output_shape = 2  # parity = 0, 1
qnn2 = SamplerQNN(
    circuit=qc,
    input_params=feature_map.parameters,
    weight_params=ansatz.parameters,
    interpret=parity,
    output_shape=output_shape,
)

# Set up PyTorch module
# Reminder: If we don't explicitly declare the initial weights
# they are chosen uniformly at random from [-1, 1].
initial_weights = 0.1 * (2 * algorithm_globals.random.random(qnn2.num_weights) - 1)
print("Initial weights: ", initial_weights)
model2 = TorchConnector(qnn2, initial_weights)

Initial weights:  [ 0.0364991  -0.0720495  -0.06001836 -0.09852755]

Para obtener un recordatorio sobre el optimizador y las opciones de funciones de pérdida, puedes volver a esta sección.

# Define model, optimizer, and loss
optimizer = LBFGS(model2.parameters())
f_loss = CrossEntropyLoss()  # Our output will be in the [0,1] range

# Start training
model2.train()

# Define LBFGS closure method (explained in previous section)
def closure():
    optimizer.zero_grad(set_to_none=True)  # Initialize gradient
    loss = f_loss(model2(X_), y01_)  # Calculate loss
    loss.backward()  # Backward pass

    print(loss.item())  # Print loss
    return loss


# Run optimizer (LBFGS requires closure)
optimizer.step(closure);

0.6925069093704224
0.6881508231163025
0.6516683101654053
0.6485998034477234
0.6394743919372559
0.7057444453239441
0.669085681438446
0.766187310218811
0.7188469171524048
0.7919709086418152
0.7598814964294434
0.7028256058692932
0.7486447095870972
0.6890242695808411
0.7760348916053772
0.7892935276031494
0.7556288242340088
0.7058126330375671
0.7203161716461182
0.7030722498893738

# Evaluate model and compute accuracy
y_predict = []
for x in X:
    output = model2(Tensor(x))
    y_predict += [np.argmax(output.detach().numpy())]

print("Accuracy:", sum(y_predict == y01) / len(y01))

# plot results
# red == wrongly classified
for x, y_target, y_ in zip(X, y01, y_predict):
    if y_target == 1:
        plt.plot(x[0], x[1], "bo")
    else:
        plt.plot(x[0], x[1], "go")
    if y_target != y_:
        plt.scatter(x[0], x[1], s=200, facecolors="none", edgecolors="r", linewidths=2)
plt.plot([-1, 1], [1, -1], "--", color="black")
plt.show()

Accuracy: 0.5

Los círculos rojos indican puntos de datos clasificados incorrectamente.

2. Regresión

Usamos un modelo basado en la EstimatorQNN para ilustrar también cómo realizar una tarea de regresión. El conjunto de datos elegido en este caso se genera aleatoriamente siguiendo una onda sinusoidal.

# Generate random dataset

num_samples = 20
eps = 0.2
lb, ub = -np.pi, np.pi
f = lambda x: np.sin(x)

X = (ub - lb) * algorithm_globals.random.random([num_samples, 1]) + lb
y = f(X) + eps * (2 * algorithm_globals.random.random([num_samples, 1]) - 1)
plt.plot(np.linspace(lb, ub), f(np.linspace(lb, ub)), "r--")
plt.plot(X, y, "bo")
plt.show()

A. Regresión con PyTorch y EstimatorQNN

The network definition and training loop will be analogous to those of the classification task using EstimatorQNN. In this case, we define our own feature map and ansatz, but let’s do it a little different.

# Construct simple feature map
param_x = Parameter("x")
feature_map = QuantumCircuit(1, name="fm")
feature_map.ry(param_x, 0)

# Construct simple feature map
param_y = Parameter("y")
ansatz = QuantumCircuit(1, name="vf")
ansatz.ry(param_y, 0)

qc = QuantumCircuit(1)
qc.compose(feature_map, inplace=True)
qc.compose(ansatz, inplace=True)

# Construct QNN
qnn3 = EstimatorQNN(circuit=qc, input_params=[param_x], weight_params=[param_y])

# Set up PyTorch module
# Reminder: If we don't explicitly declare the initial weights
# they are chosen uniformly at random from [-1, 1].
initial_weights = 0.1 * (2 * algorithm_globals.random.random(qnn3.num_weights) - 1)
model3 = TorchConnector(qnn3, initial_weights)

Para obtener un recordatorio sobre el optimizador y las opciones de funciones de pérdida, puedes volver a esta sección.

# Define optimizer and loss function
optimizer = LBFGS(model3.parameters())
f_loss = MSELoss(reduction="sum")

# Start training
model3.train()  # set model to training mode

# Define objective function
def closure():
    optimizer.zero_grad(set_to_none=True)  # Initialize gradient
    loss = f_loss(model3(Tensor(X)), Tensor(y))  # Compute batch loss
    loss.backward()  # Backward pass
    print(loss.item())  # Print loss
    return loss


# Run optimizer
optimizer.step(closure)

14.947757720947266
2.948650360107422
8.952412605285645
0.37905153632164
0.24995625019073486
0.2483610212802887
0.24835753440856934

tensor(14.9478, grad_fn=<MseLossBackward0>)

# Plot target function
plt.plot(np.linspace(lb, ub), f(np.linspace(lb, ub)), "r--")

# Plot data
plt.plot(X, y, "bo")

# Plot fitted line
y_ = []
for x in np.linspace(lb, ub):
    output = model3(Tensor([x]))
    y_ += [output.detach().numpy()[0]]
plt.plot(np.linspace(lb, ub), y_, "g-")
plt.show()

---

Parte 2: Clasificación MNIST, QNNs Híbridas

En esta segunda parte, mostramos cómo aprovechar una red neuronal híbrida cuántica-clásica utilizando TorchConnector, para realizar una tarea de clasificación de imágenes más compleja en el conjunto de datos de dígitos manuscritos del MNIST.

Para obtener una explicación más detallada (pre-TorchConnector) sobre las redes neuronales híbridas cuánticas-clásicas, puedes consultar la sección correspondiente en el Libro de texto de Qiskit.

# Additional torch-related imports
import torch
from torch import cat, no_grad, manual_seed
from torch.utils.data import DataLoader
from torchvision import datasets, transforms
import torch.optim as optim
from torch.nn import (
    Module,
    Conv2d,
    Linear,
    Dropout2d,
    NLLLoss,
    MaxPool2d,
    Flatten,
    Sequential,
    ReLU,
)
import torch.nn.functional as F

Paso 1: Definición de cargadores de datos para entrenamiento y prueba

Aprovechamos la API de torchvision para cargar directamente un subconjunto del conjunto de datos MNIST y definir los DataLoaders de torch (enlace) para entrenar y probar.

# Train Dataset
# -------------

# Set train shuffle seed (for reproducibility)
manual_seed(42)

batch_size = 1
n_samples = 100  # We will concentrate on the first 100 samples

# Use pre-defined torchvision function to load MNIST train data
X_train = datasets.MNIST(
    root="./data", train=True, download=True, transform=transforms.Compose([transforms.ToTensor()])
)

# Filter out labels (originally 0-9), leaving only labels 0 and 1
idx = np.append(
    np.where(X_train.targets == 0)[0][:n_samples], np.where(X_train.targets == 1)[0][:n_samples]
)
X_train.data = X_train.data[idx]
X_train.targets = X_train.targets[idx]

# Define torch dataloader with filtered data
train_loader = DataLoader(X_train, batch_size=batch_size, shuffle=True)

Si realizamos una visualización rápida, podemos ver que el conjunto de datos de entrenamiento consta de imágenes de 0s y 1s escritos a mano.

n_samples_show = 6

data_iter = iter(train_loader)
fig, axes = plt.subplots(nrows=1, ncols=n_samples_show, figsize=(10, 3))

while n_samples_show > 0:
    images, targets = data_iter.__next__()

    axes[n_samples_show - 1].imshow(images[0, 0].numpy().squeeze(), cmap="gray")
    axes[n_samples_show - 1].set_xticks([])
    axes[n_samples_show - 1].set_yticks([])
    axes[n_samples_show - 1].set_title("Labeled: {}".format(targets[0].item()))

    n_samples_show -= 1

# Test Dataset
# -------------

# Set test shuffle seed (for reproducibility)
# manual_seed(5)

n_samples = 50

# Use pre-defined torchvision function to load MNIST test data
X_test = datasets.MNIST(
    root="./data", train=False, download=True, transform=transforms.Compose([transforms.ToTensor()])
)

# Filter out labels (originally 0-9), leaving only labels 0 and 1
idx = np.append(
    np.where(X_test.targets == 0)[0][:n_samples], np.where(X_test.targets == 1)[0][:n_samples]
)
X_test.data = X_test.data[idx]
X_test.targets = X_test.targets[idx]

# Define torch dataloader with filtered data
test_loader = DataLoader(X_test, batch_size=batch_size, shuffle=True)

Paso 2: Definición del Modelo Híbrido y de la QNN

Este segundo paso muestra el poder del TorchConnector. Después de definir nuestra capa de red neuronal cuántica (en este caso, una EstimatorQNN), podemos incrustarla en una capa en nuestro Module de torch, al inicializar un conector torch como TorchConnector(qnn).

⚠️ Atención: Para tener un gradiente de propagación hacia atrás (backpropagation) adecuado en modelos híbridos, DEBEMOS establecer el parámetro inicial input_gradients en TRUE durante la inicialización de la qnn.

# Define and create QNN
def create_qnn():
    feature_map = ZZFeatureMap(2)
    ansatz = RealAmplitudes(2, reps=1)
    qc = QuantumCircuit(2)
    qc.compose(feature_map, inplace=True)
    qc.compose(ansatz, inplace=True)

    # REMEMBER TO SET input_gradients=True FOR ENABLING HYBRID GRADIENT BACKPROP
    qnn = EstimatorQNN(
        circuit=qc,
        input_params=feature_map.parameters,
        weight_params=ansatz.parameters,
        input_gradients=True,
    )
    return qnn


qnn4 = create_qnn()

# Define torch NN module


class Net(Module):
    def __init__(self, qnn):
        super().__init__()
        self.conv1 = Conv2d(1, 2, kernel_size=5)
        self.conv2 = Conv2d(2, 16, kernel_size=5)
        self.dropout = Dropout2d()
        self.fc1 = Linear(256, 64)
        self.fc2 = Linear(64, 2)  # 2-dimensional input to QNN
        self.qnn = TorchConnector(qnn)  # Apply torch connector, weights chosen
        # uniformly at random from interval [-1,1].
        self.fc3 = Linear(1, 1)  # 1-dimensional output from QNN

    def forward(self, x):
        x = F.relu(self.conv1(x))
        x = F.max_pool2d(x, 2)
        x = F.relu(self.conv2(x))
        x = F.max_pool2d(x, 2)
        x = self.dropout(x)
        x = x.view(x.shape[0], -1)
        x = F.relu(self.fc1(x))
        x = self.fc2(x)
        x = self.qnn(x)  # apply QNN
        x = self.fc3(x)
        return cat((x, 1 - x), -1)


model4 = Net(qnn4)

Paso 3: Entrenamiento

# Define model, optimizer, and loss function
optimizer = optim.Adam(model4.parameters(), lr=0.001)
loss_func = NLLLoss()

# Start training
epochs = 10  # Set number of epochs
loss_list = []  # Store loss history
model4.train()  # Set model to training mode

for epoch in range(epochs):
    total_loss = []
    for batch_idx, (data, target) in enumerate(train_loader):
        optimizer.zero_grad(set_to_none=True)  # Initialize gradient
        output = model4(data)  # Forward pass
        loss = loss_func(output, target)  # Calculate loss
        loss.backward()  # Backward pass
        optimizer.step()  # Optimize weights
        total_loss.append(loss.item())  # Store loss
    loss_list.append(sum(total_loss) / len(total_loss))
    print("Training [{:.0f}%]\tLoss: {:.4f}".format(100.0 * (epoch + 1) / epochs, loss_list[-1]))

Training [10%]  Loss: -1.1630
Training [20%]  Loss: -1.5294
Training [30%]  Loss: -1.7855
Training [40%]  Loss: -1.9863
Training [50%]  Loss: -2.2257
Training [60%]  Loss: -2.4513
Training [70%]  Loss: -2.6758
Training [80%]  Loss: -2.8832
Training [90%]  Loss: -3.1006
Training [100%] Loss: -3.3061

# Plot loss convergence
plt.plot(loss_list)
plt.title("Hybrid NN Training Convergence")
plt.xlabel("Training Iterations")
plt.ylabel("Neg. Log Likelihood Loss")
plt.show()

Now we’ll save the trained model, just to show how a hybrid model can be saved and re-used later for inference. To save and load hybrid models, when using the TorchConnector, follow the PyTorch recommendations of saving and loading the models.

torch.save(model4.state_dict(), "model4.pt")

Paso 4: Evaluación

Partimos de recrear el modelo y cargar el estado desde el archivo previamente guardado. Creaste una capa QNN usando otro simulador o un hardware real. Por lo tanto, puedes entrenar un modelo en hardware real disponible en la nube y luego, para la inferencia, usar un simulador o viceversa. En aras de la simplicidad, creamos una nueva red neuronal cuántica de la misma manera que arriba.

qnn5 = create_qnn()
model5 = Net(qnn5)
model5.load_state_dict(torch.load("model4.pt"))

<All keys matched successfully>

model5.eval()  # set model to evaluation mode
with no_grad():

    correct = 0
    for batch_idx, (data, target) in enumerate(test_loader):
        output = model5(data)
        if len(output.shape) == 1:
            output = output.reshape(1, *output.shape)

        pred = output.argmax(dim=1, keepdim=True)
        correct += pred.eq(target.view_as(pred)).sum().item()

        loss = loss_func(output, target)
        total_loss.append(loss.item())

    print(
        "Performance on test data:\n\tLoss: {:.4f}\n\tAccuracy: {:.1f}%".format(
            sum(total_loss) / len(total_loss), correct / len(test_loader) / batch_size * 100
        )
    )

Performance on test data:
        Loss: -3.3585
        Accuracy: 100.0%

# Plot predicted labels

n_samples_show = 6
count = 0
fig, axes = plt.subplots(nrows=1, ncols=n_samples_show, figsize=(10, 3))

model5.eval()
with no_grad():
    for batch_idx, (data, target) in enumerate(test_loader):
        if count == n_samples_show:
            break
        output = model5(data[0:1])
        if len(output.shape) == 1:
            output = output.reshape(1, *output.shape)

        pred = output.argmax(dim=1, keepdim=True)

        axes[count].imshow(data[0].numpy().squeeze(), cmap="gray")

        axes[count].set_xticks([])
        axes[count].set_yticks([])
        axes[count].set_title("Predicted {}".format(pred.item()))

        count += 1

🎉🎉🎉🎉 Ahora puedes experimentar con tus propios conjuntos de datos y arquitecturas híbridas utilizando Qiskit Machine Learning. ¡Buena suerte!

import qiskit.tools.jupyter

%qiskit_version_table
%qiskit_copyright

Version Information

Qiskit Software	Version
qiskit-terra	0.22.0
qiskit-aer	0.11.1
qiskit-ignis	0.7.0
qiskit	0.33.0
qiskit-machine-learning	0.5.0
System information
Python version	3.7.9
Python compiler	MSC v.1916 64 bit (AMD64)
Python build	default, Aug 31 2020 17:10:11
OS	Windows
CPUs	4
Memory (Gb)	31.837730407714844
Thu Nov 03 09:57:38 2022 GMT Standard Time

This code is a part of Qiskit

© Copyright IBM 2017, 2022.

This code is licensed under the Apache License, Version 2.0. You may
obtain a copy of this license in the LICENSE.txt file in the root directory
of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.

Any modifications or derivative works of this code must retain this
copyright notice, and modified files need to carry a notice indicating
that they have been altered from the originals.