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CRC Press eBooks

Classical Machine Learning Essentials for Quantum Machine Learning

Hamid D. Ismail

Published Nov 4, 2026• 0 citations
Publisher

Abstract

This chapter reviews the principal concepts and computational structures of classical machine learning that provide the foundation for quantum machine learning (QML). It examines linear models, support vector machines, principal component analysis, neural networks, probabilistic learning, generative modeling, and optimization, with emphasis on the linear algebraic, statistical, and variational principles that reappear in quantum algorithms. Particular attention is given to computational bottlenecks such as matrix inversion, eigenvalue decomposition, kernel evaluation, sampling, and high-dimensional optimization since these are among the areas where quantum methods may offer advantages under suitable assumptions. This chapter also discusses classes of learning problems that are most plausibly positioned to benefit from quantum speedups and highlights the importance of data access models, encoding assumptions, and realistic complexity analysis in assessing the promise of QML.

DOI
10.1201/9781042002818-3

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This chapter reviews the principal concepts and computational structures of classical machine learning that provide the foundation for quantum machine learning (QML). It examines linear models, support vector machines, principal component analysis, neural networks, probabilistic learning, generative modeling, and optimization, with emphasis on the linear algebraic, statistical, and variational principles that reappear in quantum algorithms. Particular attention is given to computational bottlenecks such as matrix inversion, eigenvalue decomposition, kernel evaluation, sampling, and high-dimensional optimization since these are among the areas where quantum methods may offer advantages under suitable assumptions. This chapter also discusses classes of learning problems that are most plausibly positioned to benefit from quantum speedups and highlights the importance of data access models, encoding assumptions, and realistic complexity analysis in assessing the promise of QML.
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Machine Learning (ML) has changed the way computers work by letting them learn from data and make smart choices. However, traditional ML techniques encounter scalability and efficiency constraints as datasets get larger and computational problems become more complicated[1]. These restrictions could be circumvented by the new paradigms that quantum computing offers by using entanglement and superposition [2], [3]. The combination of the Quantum computing with the Machine Learning is called the Quantum Machine Learning(QML), offers efficiency improvements, new algorithmic opportunities, and speedups in certain linear algebraic operations. So, this review dives deeply into quantum-classical algorithms, with a particular emphasis on the approaches like quantum neural network and quantum support vector machines. We examine computational complexity, architectural design, benchmarking findings, and real-world applications (such as optimization, cryptography, and classification). We also discuss important issues including scalability, data encoding, and noise, and we suggest future paths for error prevention and scalable structures.
Quantum Machine Learning (QML) represents a promising frontier of research where the principles of quantum mechanics are combined with machine learning to offer potentially superior performance over classical counterparts. This review article explores the current advancements in QML, specifically focusing on the performance improvement and comparison between standard classical algorithms and their quantum implementations. We initiate with an overview of fundamental quantum algorithms that have found applicability within machine learning contexts, such as quantum principal component analysis and quantum support vector machines. The review then delves into a critical assessment of these quantum approaches, highlighting case studies where quantum implementations have demonstrated computational speedups or improved accuracy. Furthermore, we investigate the inherent challenges and limitations that currently hinder the widespread adoption of QML technologies, including the issues of decoherence, error rates, and quantum resource requirements. In addition, the review provides insights into the current state of quantum hardware and its scalability for machine learning tasks. Throughout, comparisons are made to outline scenarios in which quantum machine learning presents a genuine advantage over classical techniques, supported by performance metrics and benchmark datasets. The article concludes by discussing future directions in QML research, with an emphasis on algorithmic innovation and hardware improvement, to realize the full potential of quantum-enhanced machine learning.
This chapter covers a number of disparate applications of quantum computing in the area of machine learning. We only consider situations where the dataset is classical (rather than quantum). We cover quantum algorithms for big-data problems relying upon high-dimensional linear algebra, such as Gaussian process regression and support vector machines. We discuss the prospect of achieving a quantum speedup with these algorithms, which face certain input/output caveats and must compete against quantum-inspired classical algorithms. We also cover heuristic quantum algorithms for energy-based models, which are generative machine learning models that learn to produce outputs similar to those in a training dataset. Next, we cover a quantum algorithm for the tensor principal component analysis problem, where a quartic speedup may be available, as well as quantum algorithms for topological data analysis, which aim to compute topologically invariant properties of a dataset. We conclude by covering quantum neural networks and quantum kernel methods, where the machine learning model itself is quantum in nature.
The paper "Quantum Machine Learning: Leveraging Quantum Computing for Enhanced Learning Algorithms" explores the integration of quantum computing principles into classical machine learning techniques, aiming to address limitations such as scalability and computational inefficiency. It presents the foundational concepts of quantum computing, including superposition and entanglement, and their application in accelerating machine learning processes. The study emphasizes the potential for quantum algorithms to significantly improve the performance of machine learning tasks by processing large datasets more efficiently and exploring larger hypothesis spaces. Key quantum machine learning algorithms discussed include Quantum Support Vector Machines (QSVM), Quantum Principal Component Analysis (QPCA), and Quantum Neural Networks (QNN), each of which leverages quantum mechanics to overcome the computational barriers faced by classical algorithms. The Quantum Approximate Optimization Algorithm (QAOA) is also highlighted for its ability to optimize machine learning models more effectively. While the theoretical benefits of Quantum Machine Learning (QML) are promising, the practical application of these techniques is currently limited by the constraints of existing quantum hardware. This research contributes to the emerging field of QML by examining its potential advantages and future implications in addressing complex data processing challenges.
The rise of machine learning algorithms in multidisciplinary areas is inevitable. Quantum computers are a significant recent area of development where complex algorithms can be efficiently executed for better performance. Implementing complex algorithms in quantum machines for hardware support systems is escalating due to the emergence of robotics and automated systems in all domains. The acceleration of artificial systems in hardware-based systems requires special approaches, and quantum approaches are more successful in devising accelerated hybrid systems. This chapter mainly deals with the approaches to implementing machine learning algorithms using quantum computing. The chapter was initiated with the question: “Why is quantum computing required to implement machine learning algorithms?” The major hiccup in implementing any machine learning algorithm in classical systems is the complexity of the algorithms. High dimensionality is a curse in implementing machine learning algorithms in classical systems. Quantum computing is a rescuing angel to address the issue of high dimensionality using parallelism. Quantum mechanics is well-versed in generating counterintuitive patterns. The deep learning paradigms identify the data patterns and vice versa by generating similar patterns. Classical machine learning suffers by generating patterns from the quantum of data or information, whereas the quantum mechanism succeeds by implementing the same algorithm using the quantum mechanism. The potential of the quantum mechanism to overcast some of the specific problems by its implementation strategy is called quantum potential, and the strategy used to increase the quantum potential is called the quantum algorithm. The chapter deals with the complexity of quantum computing mechanisms while implementing machine learning algorithms as the prima facie. Following the complexity analysis, usage of feature maps and extraction in the quantum mechanism is discussed for a clear understanding. Quantum embedding techniques are discussed prior to algorithms used to implement machine learning in quantum computers. The remaining sections of the chapter introduces Deutch-Jozsa, HHL, QUBO quantum mechanism-based algorithms and the execution of conventional machine learning algorithms such as principal component analysis (PCA), K-Means, K-Medians, and Support Vector Machines (SVM). Critical emphasis is placed on solving NP-Hard problems using quantum mechanisms for addressing real-time problems. This chapter helps readers to implement quantum approaches for applying machine learning algorithms in large-scale systems. This chapter deals with the main concepts in understanding quantum computing for machine learning systems, and major algorithms and foundations have been discussed for better understanding of quantum computing in machine learning.