Quantum Machine Learning: A Beginner's Guide

Translator | Bugatti

Reviewer | Sun Shujuan

Introduction

Welcome to The world of quantum machine learning! This tutorial provides step-by-step guidance with code through a starter project using a sample dataset. By the end of this tutorial, you will have a basic understanding of how to use a quantum computer to perform machine learning tasks and help build your first quantum model.

But before diving into this tutorial, let’s understand what quantum machine learning is and why it’s so exciting.

Quantum machine learning is the field where quantum computing and machine learning converge. It uses quantum computers to perform machine learning tasks such as classification, regression, and clustering. A quantum computer is a powerful machine that uses quantum bits (qubits) instead of traditional bits to store and process information. This allows them to perform certain tasks much faster than traditional computers, making them particularly suitable for machine learning tasks involving large amounts of data.

Start the tutorial directly now!

Step 1: Install necessary libraries and dependencies.

We will use the PennyLane library for quantum machine learning, NumPy for numerical computation, and Matplotlib for data visualization in this tutorial. You can install these libraries using pip by running the following command:

!pip install pennylane
!pip install numpy
!pip install matplotlib

Step 2: Load the sample dataset.

We will use the Iris dataset in this tutorial, which consists of 150 samples of iris flowers with four features: sepal length, sepal width, petal length, and petal width. The dataset is included in the sklearn library, so we can load it using the following code:

from sklearn import datasets

# Load the iris dataset
iris = datasets.load_iris()
X = iris['data']
y = iris['target']

Step 3: Split the dataset into training and test sets.

We will use the training set to train our quantum model and the test set to evaluate its performance. We can split the dataset using the train_test_split function from the sklearn.model_selection module:

from sklearn.model_selection import train_test_split

# Split the dataset into training and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

Step 4: Preprocess the data.

Before we can use the data to train a quantum model, we need to preprocess the data. A common preprocessing step is normalization, which is adjusting the data so that it has zero mean and unit variance. We can use the StandardScaler class from the sklearn.preprocessing module to perform normalization:

from sklearn.preprocessing import StandardScaler

# Initialize the scaler
scaler = StandardScaler()

# Fit the scaler to the training data
scaler.fit(X_train)

# Scale the training and test data
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)

This code initializes the StandardScaler object and fits it to the training data using the fit method. Then, it uses the transform method to adjust the training and test data.

The reason why normalization is an important pre-processing step is that it ensures that all features of the data are on the same scale, which can improve the performance of quantum models.

Step 5: Define the quantum model.

Now we are ready to use the PennyLane library to define the quantum model. The first step is to import the necessary functions and create the quantum device:

import pennylane as qml

# Choose a device (e.g., 'default.qubit')
device = qml.device('default.qubit')

Next, we will define a quantum function that takes in data as input and returns a prediction. We will use a simple quantum neural network with only one layer of quantum neurons:

@qml.qnode(device)
def quantum_neural_net(weights, data):
# Initialize the qubits
qml.templates.AmplitudeEmbedding(weights, data)

# Apply a layer of quantum neurons
qml.templates.StronglyEntanglingLayers(weights, data)

# Measure the qubits
return qml.expval(qml.PauliZ(0))

This quantum function takes in two variables: weights (which are the parameters of the quantum neural network) and data (which is the input data) .

The first line initializes the qubit using the AmplitudeEmbedding template from PennyLane. The template maps data onto the amplitude of the qubit so that the distance between data points is preserved.

The second line uses the StronglyEntanglingLayers template to apply a layer of quantum neurons. The template applies a series of entanglement operations to qubits, which can then be used to implement universal quantum computing.

Finally, the last line measures the qubit in Pauli-Z metric basis and returns the expected value.

Step 6: Define the cost function.

In order to train a quantum model, we need to define a cost function to measure how well the model performs. For the purposes of this tutorial, we will use the mean square error (MSE) as the cost function:

def cost(weights, data, labels):
# Make predictions using the quantum neural network
predictions = quantum_neural_net(weights, data)

# Calculate the mean squared error
mse = qml.mean_squared_error(labels, predictions)

return mse

This cost function takes in three variables: weights (this is the parameter of the quantum model), data (this is the input data ) and labels (which are the real labels of the data). It uses a quantum neural network to make predictions based on input data and calculates the MSE between predictions and true labels.

MSE is a common cost function in machine learning that measures the average squared difference between the predicted value and the true value. A smaller MSE indicates that the model fits the data better.

Step 7: Train the quantum model.

Now, we are ready to use the gradient descent method to train the quantum model. We will use the AdamOptimizer class from PennyLane to perform the optimization:

# Initialize the optimizer
opt = qml.AdamOptimizer(stepsize=0.01)

# Set the number of training steps
steps = 100

# Set the initial weights
weights = np.random.normal(0, 1, (4, 2))

# Train the model
for i in range(steps):
# Calculate the gradients
gradients = qml.grad(cost, argnum=0)(weights, X_train_scaled, y_train)

# Update the weights
opt.step(gradients, weights)

# Print the cost
if (i + 1) % 10 == 0:
print(f'Step {i + 1}: cost = {cost(weights, X_train_scaled, y_train):.4f}')

This code initializes the optimizer with a step size of 0.01 and sets the number of training steps to 100. It then sets the model's initial weights to random values ​​drawn from a normal distribution with mean 0 and standard deviation 1.

At each training step, the code uses the qml.grad function to calculate the gradient of the cost function relative to the weights. It then updates the weights using the opt.step method and outputs the cost every 10 steps.

梯度下降法是机器学习中常见的优化算法，它迭代更新模型参数以最小化成本函数。AdamOptimizer是梯度下降的一种变体，它使用自适应学习率，这可以帮助优化更快地收敛。

第8步：评估量子模型。

我们已经训练了量子模型，可以评估它在测试集上的性能。我们可以使用以下代码来测试：

# Make predictions on the test set
predictions = quantum_neural_net(weights, X_test_scaled)

# Calculate the accuracy
accuracy = qml.accuracy(predictions, y_test)

print(f'Test accuracy: {accuracy:.2f}')

这段代码使用量子神经网络基于测试集做预测，并使用qml.accuracy 函数计算预测准确性。然后，它输出测试准确性。

第9步：直观显示结果。

最后，我们可以使用Matplotlib直观显示量子模型的结果。比如说，我们可以对照真实标签绘制出测试集的预测结果：

import matplotlib.pyplot as plt

# Plot the predictions
plt.scatter(y_test, predictions)

# Add a diagonal line
x = np.linspace(0, 3, 4)
plt.plot(x, x, '--r')

# Add axis labels and a title
plt.xlabel('True labels')
plt.ylabel('Predictions')
plt.title('Quantum Neural Network')

# Show the plot
plt.show()

这段代码将对照真实标签创建预测的散点图，增添对角线以表示完美预测。然后它为散点图添加轴线标签和标题，并使用plt.show函数来显示。

现在，我们已成功地构建了一个量子机器学习模型，并在示例数据集上评估了性能。

结果

为了测试量子模型的性能，我们运行了教程中提供的代码，获得了以下结果：

Step 10: cost = 0.5020
Step 20: cost = 0.3677
Step 30: cost = 0.3236
Step 40: cost = 0.3141
Step 50: cost = 0.3111
Step 60: cost = 0.3102
Step 70: cost = 0.3098
Step 80: cost = 0.3095
Step 90: cost = 0.3093
Step 100: cost = 0.3092
Test accuracy: 0.87

这些结果表明，量子模型能够从训练数据中学习，并基于测试集做出准确的预测。在整个训练过程中，成本稳步下降，这表明模型在学习过程中不断改进。最终的测试准确率为0.87，表现相当好，这表明该模型能够正确地分类大部分测试样例。

结论

量子机器学习是一个令人兴奋的领域，有许多潜在的应用，从优化供应链到预测股价，不一而足。我们希望本教程能让您了解量子计算机和机器学习的可能性，并激励您深入了解这个诱人的话题。

原文标题：​​Quantum Machine Learning: A Beginner’s Guide​​，作者：SPX​

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