IBM Qiskit量子机器学习速成（三）

Torch连接器和混合量子神经网络

本章内容介绍如何将QNN作为一般的Torch神经层嵌入Torch框架的经典神经网络。首先我们会学习如何嵌入EstimatorQNN，最后我们会使用这一技术实现手写数字的识别。

一般步骤

首先创建特征映射电路(feature map)和假设(ansatz)分别作为输入层和权重层

# 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)

事实上这一过程完全可以被qiskit_machine_learning.circuit.library里的QNNCircuit简化

feature_map = ZZFeatureMap(num_inputs)
ansatz = RealAmplitudes(num_inputs)
qc =  QNNCircuit(feature_map, ansatz)

下一步，创建量子神经网络，此处以EstimatorQNN为例.

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

接下来，使用qiskit_machine_learning.connector中的TorchConnector完成连接工作

# 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(qnn.num_weights) - 1)

model = TorchConnector(qnn, initial_weights=initial_weights)

注意如果我们不设置初始权重，TorchConnector会自动加入默认权重。

此时我们已经可以向模型内部传入数据了，而传入的数据必须是PyTorch的Tensor

model(dataTensor[0, :])

为了优化我们的模型，我们需要引入优化器与损失函数。

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

# Start training
model.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(model(X_), y_)  # Evaluate loss function
    loss.backward()  # Backward pass
    print(loss.item())  # Print loss
    return loss


# Run optimizer step4
optimizer.step(closure)

手写数字识别实战

本节内容将使用EstimatorQNN实现MNIST数据集的分类与识别。

首先导入本节需要的所有库

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.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
# 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

下一步，导入MNIST数据集（这种导入方式是PyTorch中司空见惯且极为方便的）。其中，我们先创建了训练集，随后创建了测试数据集。

# 训练数据集
# -------------

# 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)

# 测试数据集
# -------------

# 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)

万事俱备后，我们可以开始创建量子神经网络了

# 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


qnn = create_qnn()

以上只是量子神经网络，为了嵌入到经典神经网络中，我们需要PyTorch框架的帮助。

# 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)


model = Net(qnn)

尤其留意QNN是如何作为神经网络的一层被嵌入到经典神经网络的！

万事俱备后，我们只需要训练模型即可。

# 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
model.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 = model(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]))

如果我们想保存当前的模型，可以使用PyTorch中常见的方法。

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

当我们想根据数据文件恢复模型时，可以使用

qnn2 = create_qnn()
model2 = Net(qnn2)
model2.load_state_dict(torch.load("model.pt"))

接下来可以检验一下恢复出的模型的效果

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
        )
    )

最后，打印模型的预测结果

# 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