IBM Qiskit量子机器学习速成（四）

量子核机器学习

一般步骤

量子核机器学习的一般步骤如下

定义量子核

我们使用FidelityQuantumKernel类创建量子核，该类需要传入两个参数：特征映射和忠诚度(fidelity)。如果我们不传入忠诚度，该类会自动创建一个忠诚度。

注意各个类所属的模块！

from qiskit.circuit.library import ZZFeatureMap
from qiskit.primitives import Sampler
from qiskit_algorithms.state_fidelities import ComputeUncompute
from qiskit_machine_learning.kernels import FidelityQuantumKernel

feature_map = ZZFeatureMap(feature_dimension=dimension, reps=2, entanglement="linear")

sampler = Sampler()

fidelity = ComputeUncompute(sampler=sampler)

kernel = FidelityQuantumKernel(fidelity=fidelity, feature_map=feature_map)

利用经典支持向量分类器

量子核在经典支持向量分类器中有两种方式：

将核本身作为可调用函数

注意：经典模式下传入的是kernel.evaluate

from sklearn.svm import SVC

svc = SVC(kernel=kernel.evaluate)

svc.fit(train_features, train_labels)

score_callable_function = svc.score(test_features, test_labels)

print(f"Callable kernel classification test score: {score_callable_function}")

提前计算核矩阵

使用kernel.evaluate函数进行核矩阵的计算

matrix_train = kernel.evaluate(x_vec=train_features)
matrix_test = kernel.evaluate(x_vec=test_features, y_vec=train_features)

利用量子支撑向量分类器

注意：量子模式下传入的是kernel本身

from qiskit_machine_learning.algorithms import QSVC

qsvc = QSVC(quantum_kernel=kernel)

qsvc.fit(train_features, train_labels)

qsvc_score = qsvc.score(test_features, test_labels)

使用量子核的谱聚类方法

定义量子核方法同前，此处只需要从sklearn中导入SpectralClustering类。

from sklearn.cluster import SpectralClustering
from sklearn.metrics import normalized_mutual_info_score

matrix = kernel.evaluate(x_vec=train_features)

spectral = SpectralClustering(2, affinity="precomputed")

cluster_labels = spectral.fit_predict(matrix)

cluster_score = normalized_mutual_info_score(cluster_labels, train_labels)

实战演练

导入数据集

我们接下来使用一组来自qiskit_machine_learning.datasets的人造随机数据

from qiskit_machine_learning.datasets import ad_hoc_data

adhoc_dimension = 2
train_features, train_labels, test_features, test_labels, adhoc_total = ad_hoc_data(
    training_size=20,
    test_size=5,
    n=adhoc_dimension,
    gap=0.3,
    plot_data=False,
    one_hot=False,
    include_sample_total=True,
)

其中gap描述了两类不同数据间的距离。官网提供了以下函数来可视化这一组数据

import matplotlib.pyplot as plt
import numpy as np


def plot_features(ax, features, labels, class_label, marker, face, edge, label):
    # A train plot
    ax.scatter(
        # x coordinate of labels where class is class_label
        features[np.where(labels[:] == class_label), 0],
        # y coordinate of labels where class is class_label
        features[np.where(labels[:] == class_label), 1],
        marker=marker,
        facecolors=face,
        edgecolors=edge,
        label=label,
    )


def plot_dataset(train_features, train_labels, test_features, test_labels, adhoc_total):

    plt.figure(figsize=(5, 5))
    plt.ylim(0, 2 * np.pi)
    plt.xlim(0, 2 * np.pi)
    plt.imshow(
        np.asmatrix(adhoc_total).T,
        interpolation="nearest",
        origin="lower",
        cmap="RdBu",
        extent=[0, 2 * np.pi, 0, 2 * np.pi],
    )

    # A train plot
    plot_features(plt, train_features, train_labels, 0, "s", "w", "b", "A train")

    # B train plot
    plot_features(plt, train_features, train_labels, 1, "o", "w", "r", "B train")

    # A test plot
    plot_features(plt, test_features, test_labels, 0, "s", "b", "w", "A test")

    # B test plot
    plot_features(plt, test_features, test_labels, 1, "o", "r", "w", "B test")

    plt.legend(bbox_to_anchor=(1.05, 1), loc="upper left", borderaxespad=0.0)
    plt.title("Ad hoc dataset")

    plt.show()

运行以下命令查看数据形状

plot_dataset(train_features, train_labels, test_features, test_labels, adhoc_total)

随后，和一般步骤完全相同，先定义量子核。

注意此时还没有导入数据！

from qiskit.circuit.library import ZZFeatureMap
from qiskit.primitives import Sampler
from qiskit_algorithms.state_fidelities import ComputeUncompute
from qiskit_machine_learning.kernels import FidelityQuantumKernel

adhoc_feature_map = ZZFeatureMap(feature_dimension=adhoc_dimension, reps=2, entanglement="linear")

sampler = Sampler()

fidelity = ComputeUncompute(sampler=sampler)

adhoc_kernel = FidelityQuantumKernel(fidelity=fidelity, feature_map=adhoc_feature_map)

接下来我们分别介绍经典支撑向量分类器和量子支撑向量分类器的用法

经典支撑向量分类器

一方面，我们可以直接传入量子核的取值函数

from sklearn.svm import SVC

adhoc_svc = SVC(kernel=adhoc_kernel.evaluate)

adhoc_svc.fit(train_features, train_labels)

adhoc_score_callable_function = adhoc_svc.score(test_features, test_labels)

print(f"Callable kernel classification test score: {adhoc_score_callable_function}")

另一方面，我们还可以根据已知数据提前计算核矩阵

adhoc_matrix_train = adhoc_kernel.evaluate(x_vec=train_features)
adhoc_matrix_test = adhoc_kernel.evaluate(x_vec=test_features, y_vec=train_features)

adhoc_svc = SVC(kernel="precomputed")

adhoc_svc.fit(adhoc_matrix_train, train_labels)

adhoc_score_precomputed_kernel = adhoc_svc.score(adhoc_matrix_test, test_labels)

print(f"Precomputed kernel classification test score: {adhoc_score_precomputed_kernel}")

量子支撑向量分类器

直接传入量子核即可

from qiskit_machine_learning.algorithms import QSVC

qsvc = QSVC(quantum_kernel=adhoc_kernel)

qsvc.fit(train_features, train_labels)

qsvc_score = qsvc.score(test_features, test_labels)

print(f"QSVC classification test score: {qsvc_score}")