Overview of quantum support vector machines and examples of algorithms and implementations

Overview of quantum support vector machines.

Quantum Support Vector Machines (Q-SVMs) are an extension to quantum computing, as described in ‘Quantum Computing Overview and References/Reference Books’ of classical Support Vector Machines (SVMs). SVMs are powerful algorithms for solving machine learning classification problems, and the power of quantum computing can be harnessed to improve their efficiency.

An overview of Q-SVMs is as follows.

1. review of classical SVMs: SVMs are used to classify data into two classes, taking a feature vector as input and classifying it to an optimal boundary (decision boundary); SVMs select the data points closest to this decision boundary as support vectors, and then classify these support The decision boundary is determined by maximising the distance to these support vectors.

2. quantum computing and Q-SVM: Q-SVM uses qubits and quantum gates to exploit quantum parallelism in the computation of SVMs. Specifically, it works by the following steps.

Construction of a quantum circuit.
1. encoding feature vectors: classical data is encoded into qubits. This requires an encoding method using qubits to represent the feature vector.

2. building quantum circuits: building quantum circuits based on the kernel function of the SVM. Typically, a circuit is constructed using quantum superposition and interference to extract information from the kernel matrix.

Measurement and class classification
3. measurement of quantum bits: the quantum circuit is executed and measurements are made. The measurement results indicate to which class each data point belongs. 4.

4. class classification: based on the measurement results, each data point is classified into the appropriate class. This allows the prediction of which class a new data point belongs to.

Advantages of Q-SVM include the following

• Exploiting quantum parallelism: Q-SVMs can deal with large-scale problems more efficiently than classical SVMs.
• High dimensional data: quantum computers are a particularly effective approach for processing data in high dimensional feature spaces.

Application examples

The following are examples of applications of QSVM.

1. medical field

• Disease diagnosis: the use of QSVM in the analysis of medical data (e.g. genetic information and diagnostic images) can support faster and more accurate disease classification and early diagnosis. This is particularly promising for the analysis of MRI and CT images, when processing large image data sets.
• Drug development: efforts are also underway to build models for predicting drug effects using QSVM to streamline the classification of drug candidates and the selection of appropriate targets.

2. financial sector

• Risk analysis: QSVM is applied to classification problems to predict price fluctuations of stock prices and financial instruments. It is said to enable faster and more accurate risk assessment than conventional methods.
• Fraud detection: using QSVM to analyse transaction data in real time and quickly identify fraudulent transactions.

3. energy sector

• Electricity demand forecasting: efforts are underway to improve the efficiency of the electricity grid by applying QSVM to forecast energy demand and adjust supply. QSVM’s high-speed processing is useful in analysing large time-series data.
• New energy development: QSVM is used to classify material properties and select appropriate energy conversion processes.

4. manufacturing and logistics

• Quality control: QSVM is used to analyse large amounts of sensor data from production processes in real-time to detect defective products and abnormalities.
• Logistics optimisation: used to build models for streamlining delivery routes and parcel classification problems.

5. natural science

• Materials science: apply QSVM to discover new materials and classify their properties. In particular, more precise classification is possible based on simulation data, which quantum computers are particularly good at.
• Weather forecasting: use QSVM as a tool for fast analysis of complex weather data and for forecasting the impact of typhoons and climate change.

6. security sector

• Cryptanalysis: using QSVM to analyse cryptographic communication data and build models to classify unauthorised access.
• Cyber-attack detection: applied to the problem of classifying network traffic to detect suspicious patterns fast and accurately.

implementation example

Quantum support vector machine (QSVM) implementations are usually done using libraries for quantum computing (e.g. Qiskit, PennyLane, TensorFlow Quantum, etc.). In the following, an example implementation of a QSVM using Qiskit, IBM’s quantum computing framework, is presented.

Example implementation of QSVM (using Qiskit)

1. install the necessary libraries

pip install qiskit-machine-learning
pip install matplotlib numpy

2. code example: the following example uses QSVM to classify a simple dataset.

from qiskit import Aer
from qiskit.utils import algorithm_globals
from qiskit_machine_learning.algorithms import QSVM
from qiskit_machine_learning.kernels import QuantumKernel
from qiskit.circuit.library import ZZFeatureMap
from sklearn.datasets import make_classification
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
import numpy as np

# 1. data set preparation
# Generating datasets for classification with sklearn.
X, y = make_classification(n_samples=100, n_features=2, n_classes=2, random_state=42, n_informative=2, n_redundant=0)
y = 2 * y - 1  # SVM requires labels to be -1 and 1
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Data scaling
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

# 2. setting up the quantum kernel
feature_map = ZZFeatureMap(feature_dimension=2, reps=2)  # feature mapping
quantum_kernel = QuantumKernel(feature_map=feature_map, quantum_instance=Aer.get_backend('statevector_simulator'))

# 3. construction of the QSVM model
qsvm = QSVM(quantum_kernel)
qsvm.fit(X_train, y_train)

# 4. model evaluation
score = qsvm.score(X_test, y_test)
print(f"Accuracy of test data: {score:.2f}")

# 5. visualisation
import matplotlib.pyplot as plt

# data plot
plt.scatter(X_train[:, 0], X_train[:, 1], c=y_train, cmap='coolwarm', label="training data")
plt.scatter(X_test[:, 0], X_test[:, 1], c=y_test, cmap='coolwarm', marker='x', label="test data")
plt.title(‘QSVM data distribution.")
plt.legend()
plt.show()

Code description.

1. Prepare dataset: use make_classification to generate dataset for classification. After scaling the data, convert labels to -1 and 1 for SVM.
2. Set up quantum kernel: use ZZFeatureMap to set up the quantum feature mapping. The quantum kernel operates on this basis.
3. Building the QSVM model: define a quantum SVM using QuantumKernel and QSVM and train it on the training data.
4. Evaluation: evaluate the accuracy against test data using the score method.
5. Visualisation: visualise the data distribution and intuitively check the classification results.

Key points

• Use of simulators: In the example above, statevector_simulator is used, but to run on real quantum hardware, change to ibmq_qasm_simulator or a real machine (e.g. ibmq_manila).
• Scaling: QSVM is constrained by the number of qubits, so dimensionality reduction is necessary for large data sets.
• Hyper-parameter tuning: performance can be improved by tuning e.g. the reps (number of repeats) of the feature mapping.

reference book

Reference books related to quantum support vector machines (QSVMs) and quantum machine learning are listed below.

Fundamentals of Quantum Computing.

1. Quantum Computation and Quantum Information

2. An Introduction to Quantum Computing

Quantum Machine Learning.

3. Quantum Machine Learning: What Quantum Computing Means to Data Mining

4. Quantum Machine Learning: An Applied Approach

Practical Guide.

5. Learn Quantum Computing with Python and Qiskit

6. Programming Quantum Computers: Essential Algorithms and Code Samples

Relevant theory and applications.

7. Machine Learning with Quantum Computers

8. Classical and Quantum Computation

Papers.

9. Machine learning methods in quantum computing theory

10.Quantum support vector machine for big data classification