Support Vector Machine (SVM) is considered one of the main classification Machine Learning algorithms. Following the original formulation,an SVM generation has quadratic complexity, leaving room for exploring resolution methods with better performance. One way to enhance its efficiency is by utilizing Quantum Computing algorithms, such as the HHL. This work presents an automation of a Quantum Machine Learning algorithm that uses HHL to generate SVMs fixed at the origin of a two-dimensional hyperplane.
Support Vector Machine (SVM) is considered one of the main classification Machine Learning algorithms. Following the original formulation,an SVM generation has quadratic complexity, leaving room for exploring resolution methods with better performance. One way to enhance its efficiency is by utilizing Quantum Computing algorithms, such as the HHL. This work presents an automation of a Quantum Machine Learning algorithm that uses HHL to generate SVMs fixed at the origin of a two-dimensional hyperplane.
Abstract Least Squares Support Vector Machine (LS-SVM) is a reformulation of the Support Vector Machine(SVM) algorithm that uses a hyperplane to classify elements in a dataset, with the coefficients of the hyperplane being determined by solving a linear system of equations. A quantum algorithm, the Harrow-Hassidim-Lloyd (HHL) algorithm, has the potential to offer exponential advantages over classical algorithms for solving linear systems, although an efficient implementation is yet to be developed. The current era of quantum computing presents a series of technical challenges for implementing and executing circuits, with smaller circuits being less susceptible to noise. In response to this scenario, circuit reduction optimizations have been developed to enhance execution quality. This paper presents the process of using optimized HHL quantum circuits to generate LS-SVMs applied to the classification of pulsar candidates, where the quantum generated SVMs closely matched the performance of their classical counterparts and obtained competitive results against other Quantum Machine Learning methods even when using a real quantum device, with the optimized circuits having a significant execution speedup over the original quantum circuits.
Recent developments in Quantum Computing (QC) have paved the way for an enhancement of computing capabilities. Quantum Machine Learning (QML) aims at developing Machine Learning (ML) models specifically designed for quantum computers. The availability of the first quantum processors enabled further research, in particular the exploration of possible practical applications of QML algorithms. In this work, quantum formulations of the Support Vector Machine (SVM) are presented. Then, their implementation using existing quantum technologies is discussed and Remote Sensing (RS) image classification is considered for evaluation.
The current development of Support Vector Machines (SVM) has reached a bottleneck, with issues such as long training times and weak interpretability when dealing with large-scale, multi-dimensional data. This paper introduces the concept of Quantum Support Vector Machines (QSVM) and achieves efficient solutions through quantum algorithms such as the HHL algorithm. The research designs a computational architecture that combines classical and quantum computing, utilizing the Pauli decomposition of Hermitian matrices to simulate the quantum simulation of Hamiltonian quantities and implementing the quantum simulation of unitary operators. Based on the conclusions, a complete quantum linear solver circuit is designed, achieving exponential growth in computational complexity. Experiments using the Iris dataset demonstrate the excellent classification performance of QSVM, which outperform classical SVM in classification accuracy, computational time complexity, and memory requirements. More efficient quantum mapping algorithms and quantum circuit optimization methods are implemented, providing new ideas and methods for the application of SVM to large-scale datasets.
Due to the similarity of the computational and probabilistic nature of quantum computing and machine learning, the idea arose to optimize the learning process using quantum methods. There are both fundamentally new algorithms, such as HHL, and quantum-improved ones: QPCA, QSVM. In this article, we will look at the QSVM algorithm step by step, starting from the basics described in section 2 and gradually delving into the composition of the algorithm. Thus, after the basics, we will consider the quantum phase estimation, which is part of the HHL algorithm, and then the QSVM algorithm, the component of which is the HHL. We also will consider the QPCA algorithm, which can be applied before the QSVM algorithm to reduce the dimension of the data sample. In this way, we explore the fundamental difference between classical algorithms and their quantum counterparts. We also implement the QSVM method in practice and compare the obtained practical results with theory. As a result, we obtained high quality of accuracy (100 %) compared to the classical SVM (83 %) on a data sample of dimension 72. However, we found out that the learning time on a quantum device is far from ideal (it can reach 5 min for a sample of this size). The study aims to theoretically argue or disprove the hypothesis about the efficiency of quantum computing for machine learning algorithms. The object of research is the programming of quantum computers. The research subject is the study of quantum computing mechanisms for the implementation of machine learning problems. The research result is a software module that allows evaluating the efficiency of the classification task on a quantum computer. It also can be used to compare the results obtained from classical and quantum devices. Research methods: theoretical analysis of the foundations of quantum computing: principles of superposition and entanglement, linear algebra, probability theory over complex numbers; building a model of one qubit and multi-qubit system; research of quantum machine learning algorithms’ work principles and their complexity; empirical comparison of quantum machine learning methods with their classical counterparts.
In this chapter and the next one, we will explore the exciting areas of quantum machine learning and quantum deep learning. Machine learning and deep learning have seen great success in recent years because of the increase in the computational power at our disposal and because of the high-end research in these fields. Quantum machine learning presents an exciting opportunity to increase the computational efficiency of the existing machine learning algorithms as well as presents a way to tackle some of the more computationally intractable problems. In this chapter, we start with the Harrow-Hassidim-Lloyd algorithm, popularly known as HHL, which acts as the matrix inversion routine in the quantum computing domain. Hence, HHL will be the default choice for algorithms such as linear regression and least square support vector machines. Subsequently, we touch upon quantum linear regression and support vector machines in detail in this chapter. We will then move on to implementing quantum routines such as quantum dot product and quantum Euclidean distances since they are integral to several machine learning algorithms such as the k-means clustering and nearest neighbor methods. In this regard, we will implement the k-means clustering method in detail. Also, we will discuss how Grover’s algorithm can be used to optimize quantum objectives by illustrating its usage in the cluster assignment in the k-means algorithm. Principal component analysis is an important machine learning technique, and we will walk through its quantum implementation in great detail as well.
Quantum computing has been proven to excel in factorization issues and unordered search problems due to its capability of quantum parallelism. This unique feature allows exponential speed-up in solving certain problems. However, this advantage does not apply universally, and challenges arise when combining classical and quantum computing to achieve acceleration in computation speed. This paper aims to address these challenges by exploring the current state of quantum machine learning and benchmarking the performance of quantum and classical algorithms in terms of accuracy. Specifically, we conducted experiments with three datasets for binary classification, implementing Support Vector Machine (SVM) and Quantum SVM (QSVM) algorithms. Our findings suggest that the QSVM algorithm outperforms classical SVM on complex datasets, and the performance gap between quantum and classical models increases with dataset complexity, as simple models tend to overfit with complex datasets. While there is still a long way to go in terms of developing quantum hardware with sufficient resources, quantum machine learning holds great potential in areas such as unsupervised learning and generative models. Moving forward, more efforts are needed to explore new quantum learning models that can leverage the power of quantum mechanics to overcome the limitations of classical machine learning.