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Bu sayfa, docs/tutorials/03_quantum_kernel.ipynb sayfasından oluşturulmuştur.

Kuantum Çekirdek Makine Öğrenimi

Makine öğrenmesinin genel görevi, verilerdeki kalıpları bulmak ve incelemektir. Birçok veri kümesi için, veri noktaları daha yüksek boyutlu bir öznitelik uzayında, bir çekirdek fonksiyonu kullanılarak daha iyi anlaşılır: \(k(\vec{x}_i, \vec{x}_j) = \langle f(\ vec{x}_i), f(\vec{x}_j) \rangle\) burada \(k\) çekirdek fonksiyonudur, \(\vec{x}_i, \vec{x}_j\) \(n\) boyutlu girdiler, \(f\) \(n\)-boyutundan \(m\)-boyut uzayına ve \(\langle a,b \rangle\) arasındaki bir haritadır ve nokta çarpımını gösterir. Sonlu verileri dikkate alırken; bir çekirdek fonksiyonu, bir matris olarak temsil edilebilir: \(K_{ij} = k(\vec{x}_i,\vec{x}_j)\).

Kuantum çekirdek makine öğreniminde, bir kuantum öznitelik haritası \(\phi(\vec{x})\) klasik bir özellik vektörünü \(\vec{x}\) bir kuantum Hilbert uzayına eşlemek için kullanılır, \(| \phi(\vec{x})\rangle \langle \phi(\vec{x})|\), öyle ki \(K_{ij} = \left| \langle \phi^\dagger(\vec{x}_j)| \phi(\vec{x}_i) \rangle \right|^{2}\).Daha fazla ayrıntı için Supervised learning with quantum enhanced feature spaces bölümüne bakın.

Bu defterde, bir kuantum özellik haritası kullanarak bir çekirdek matrisini hesaplamak için qiskit kullanıyoruz, ardından bu çekirdek matrisini ``scikit-learn``de sınıflandırma ve kümeleme algoritmalarında kullanıyoruz.

import matplotlib.pyplot as plt
import numpy as np

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

from qiskit import BasicAer
from qiskit.algorithms.state_fidelities import ComputeUncompute
from qiskit.circuit.library import ZZFeatureMap
from qiskit.primitives import Sampler
from qiskit.utils import algorithm_globals
from qiskit_machine_learning.algorithms import QSVC
from qiskit_machine_learning.kernels import FidelityQuantumKernel
from qiskit_machine_learning.datasets import ad_hoc_data

seed = 12345
algorithm_globals.random_seed = seed

Sınıflandırma

Sınıflandırma örneğimiz için, Supervised learning with quantum enhanced feature spaces ve scikit-learn ile denetimli öğrenme’de açıklandığı gibi ad hoc veri kümesini kullanacağız. support vector machine sınıflandırma (svc) algoritması.

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,
)

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],
)

plt.scatter(
    train_features[np.where(train_labels[:] == 0), 0],
    train_features[np.where(train_labels[:] == 0), 1],
    marker="s",
    facecolors="w",
    edgecolors="b",
    label="A train",
)
plt.scatter(
    train_features[np.where(train_labels[:] == 1), 0],
    train_features[np.where(train_labels[:] == 1), 1],
    marker="o",
    facecolors="w",
    edgecolors="r",
    label="B train",
)
plt.scatter(
    test_features[np.where(test_labels[:] == 0), 0],
    test_features[np.where(test_labels[:] == 0), 1],
    marker="s",
    facecolors="b",
    edgecolors="w",
    label="A test",
)
plt.scatter(
    test_features[np.where(test_labels[:] == 1), 0],
    test_features[np.where(test_labels[:] == 1), 1],
    marker="o",
    facecolors="r",
    edgecolors="w",
    label="B test",
)

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

plt.show()

With our training and testing datasets ready, we set up the FidelityQuantumKernel class to calculate a kernel matrix using the ZZFeatureMap. We use the reference implementation of the Sampler primitive and the ComputeUncompute fidelity that computes overlaps between states. These are the default values and if you don’t pass a Sampler or Fidelity instance, the same objects will be created automatically for you.

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)

The scikit-learn SVC algorithm allows us to define a custom kernel in two ways: by providing the kernel as a callable function or by precomputing the kernel matrix. We can do either of these using the FidelityQuantumKernel class in qiskit.

Takip eden kod, çekirdeği çağrılabilir bir fonksiyon olarak verir:

adhoc_svc = SVC(kernel=adhoc_kernel.evaluate)
adhoc_svc.fit(train_features, train_labels)
adhoc_score = adhoc_svc.score(test_features, test_labels)

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

Callable kernel classification test score: 1.0

Aşağıdaki kod, eğitim ve test çekirdek matrislerini scikit-learn svc algoritmasına sağlamadan evvel önceden hesaplar ve çizer:

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

fig, axs = plt.subplots(1, 2, figsize=(10, 5))
axs[0].imshow(
    np.asmatrix(adhoc_matrix_train), interpolation="nearest", origin="upper", cmap="Blues"
)
axs[0].set_title("Ad hoc training kernel matrix")
axs[1].imshow(np.asmatrix(adhoc_matrix_test), interpolation="nearest", origin="upper", cmap="Reds")
axs[1].set_title("Ad hoc testing kernel matrix")
plt.show()

adhoc_svc = SVC(kernel="precomputed")
adhoc_svc.fit(adhoc_matrix_train, train_labels)
adhoc_score = adhoc_svc.score(adhoc_matrix_test, test_labels)

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

Precomputed kernel classification test score: 1.0

Qiskit Machine Learning also contains the QSVC class that extends the SVC class from scikit-learn, that can be used as follows:

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}")

QSVC classification test score: 1.0

Kümelemek

Kümeleme örneğimiz için, yine Supervised learning with quantum enhanced feature spaces bölümünde açıklandığı gibi ad hoc veri kümesini ve scikit-learn spectral kümeleme algoritmasını kullanacağız.

Veri kümesini iki sınıf arasında daha büyük bir boşlukla yeniden oluşturacağız ve kümeleme denetimsiz bir makine öğrenimi görevi olduğundan, bir test örneğine ihtiyacımız yok.

adhoc_dimension = 2
train_features, train_labels, test_features, test_labels, adhoc_total = ad_hoc_data(
    training_size=25,
    test_size=0,
    n=adhoc_dimension,
    gap=0.6,
    plot_data=False,
    one_hot=False,
    include_sample_total=True,
)

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],
)
plt.scatter(
    train_features[np.where(train_labels[:] == 0), 0],
    train_features[np.where(train_labels[:] == 0), 1],
    marker="s",
    facecolors="w",
    edgecolors="b",
    label="A",
)
plt.scatter(
    train_features[np.where(train_labels[:] == 1), 0],
    train_features[np.where(train_labels[:] == 1), 1],
    marker="o",
    facecolors="w",
    edgecolors="r",
    label="B",
)

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

plt.show()

We again set up the FidelityQuantumKernel class to calculate a kernel matrix using the ZZFeatureMap, and the default values this time.

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

adhoc_kernel = FidelityQuantumKernel(feature_map=adhoc_feature_map)

The scikit-learn spectral clustering algorithm allows us to define a custom kernel in two ways: by providing the kernel as a callable function or by precomputing the kernel matrix. Using the FidelityQuantumKernel class in Qiskit Machine Learning, we can only use the latter.

The following code precomputes and plots the kernel matrices before providing it to the scikit-learn spectral clustering algorithm, and scoring the labels using normalized mutual information, since we a priori know the class labels.

adhoc_matrix = adhoc_kernel.evaluate(x_vec=train_features)

plt.figure(figsize=(5, 5))
plt.imshow(np.asmatrix(adhoc_matrix), interpolation="nearest", origin="upper", cmap="Greens")
plt.title("Ad hoc clustering kernel matrix")
plt.show()

adhoc_spectral = SpectralClustering(2, affinity="precomputed")
cluster_labels = adhoc_spectral.fit_predict(adhoc_matrix)
cluster_score = normalized_mutual_info_score(cluster_labels, train_labels)

print(f"Clustering score: {cluster_score}")

Clustering score: 0.7287008798015754

scikit-learn önceden hesaplanmış bir çekirdek matrisi kullanabilen başka algoritmalara sahiptir, işte birkaçı:

• Agglomerative clustering

• Support vector regression

• Ridge regression

• Gaussian process regression

• Principal component analysis

import qiskit.tools.jupyter

%qiskit_version_table
%qiskit_copyright

Version Information

Qiskit Software	Version
qiskit-terra	0.22.0
qiskit-aer	0.11.0
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
Mon Oct 10 12:01:53 2022 GMT Daylight Time

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