This chapter provides a formal, self-contained exposition of quantum-inspired machine learning (QiML), a subfield focusing on applying ideas of quantum mechanics to the development of powerful classical algorithms. Our starting point is setting up a defensible taxonomy to dissociate QiML from actual quantum machine learning, and to describe its historical antecedents in simulated annealing and more recent dequantization of quantum algorithms. The highlights of the chapter pursue four central streams of inspiration systematically, namely: (1) quantum many-body physics is used to turn model and data into simple tensor networks; (2) quantum feature maps lead to randomized kernel methods, quantum inpainting, and quantum groups; (3) quantum numerical linear atomization algorithm (HHL) provides the template to develop fast linear solvers and randomized numerical linear algebra; and (4) quantum approximate optimization algorithm (QAOA) is used to talk about non-convex optimization heuristics. In every region, we sketch the supporting theory, provide concrete algorithms along with quasi-pseudocode and complexity example, and introduce theoretical guarantees. A large experimental section compares these approaches to classical baselines on standard data, as well as providing detailed case studies in resource-constrained ML, large-scale linear models, and combinatorial optimization. The chapter is rounded off by concluding with some practical hints and tips, a critical reflection on the ethical issues, and a discussion of open problems in the field, providing relevant literature to graduate students and practitioners in a well-brought-up and detailed piece of work.
This chapter provides a formal, self-contained exposition of quantum-inspired machine learning (QiML), a subfield focusing on applying ideas of quantum mechanics to the development of powerful classical algorithms. Our starting point is setting up a defensible taxonomy to dissociate QiML from actual quantum machine learning, and to describe its historical antecedents in simulated annealing and more recent dequantization of quantum algorithms. The highlights of the chapter pursue four central streams of inspiration systematically, namely: (1) quantum many-body physics is used to turn model and data into simple tensor networks; (2) quantum feature maps lead to randomized kernel methods, quantum inpainting, and quantum groups; (3) quantum numerical linear atomization algorithm (HHL) provides the template to develop fast linear solvers and randomized numerical linear algebra; and (4) quantum approximate optimization algorithm (QAOA) is used to talk about non-convex optimization heuristics. In every region, we sketch the supporting theory, provide concrete algorithms along with quasi-pseudocode and complexity example, and introduce theoretical guarantees. A large experimental section compares these approaches to classical baselines on standard data, as well as providing detailed case studies in resource-constrained ML, large-scale linear models, and combinatorial optimization. The chapter is rounded off by concluding with some practical hints and tips, a critical reflection on the ethical issues, and a discussion of open problems in the field, providing relevant literature to graduate students and practitioners in a well-brought-up and detailed piece of work.
Quantum-Inspired Machine Learning (QiML) is a subfield of Quantum Machine Learning (QML) that implements quantum mechanical principles using classical computational resources, without requiring quantum hardware. Despite growing interest, QiML is frequently treated as a subset of broader QML surveys, leaving a gap in unified, cross-domain coverage. This survey provides the first dedicated examination of QiML as a standalone field, reviewing literature from 2017 to 2025 across tensor network simulations, dequantized algorithms, and variational quantum circuit simulations. We propose a unified taxonomy spanning these families, survey empirical applications across diverse domains, and assess practical limitations and open problems. Our analysis reveals that algorithmic maturity and practical readiness vary considerably across QiML families, with domain-specific success patterns driven by differing structural assumptions. Fundamental open questions remain around scalability, data embedding, and the relationship between quantum inductive biases and learning efficiency. This survey serves as a reference for researchers seeking a structured understanding of QiML’s current landscape and future directions.
The convergence of machine learning (ML) and quantum computing is quickly becoming a game-changing new frontier in computational science. The most intriguing area of overlap may be quantum optimization, which seeks to reduce the exponentially increasing complexity and computational cost of ML algorithms. As they grow larger and more complicated, traditional optimization methods, particularly in high-dimensional and non-convex space, will inevitably hit performance limits. Quantum optimization is the whole new paradigm that leverages quantum mechanical effects like superposition, entanglement, and tunnelling to explore solution spaces more efficiently. The chapter outlines the theory, practice, and potential of hybrid quantum-classical optimization algorithms for machine learning. The most brilliant research direction in the current NISQ (noisy intermediate-scale quantum) era is mixed systems leveraging classical computing capability augmented by quantum capacity. In such designs, computationally intensive subroutines like optimization for global optima or escape from local minima are left to quantum processors and data preprocessing, iterative refinement, and model testing are performed by classical processors. We start by defining the fundamental principles of quantum computing and acquainting readers with the fundamentals like qubits, quantum gates, and quantum circuits. These are the building blocks for quantum algorithms, which hopefully can be utilized for optimization, for example, the QAOA (quantum approximate optimization algorithm), the VQE (variational quantum Eigensolver), and quantum annealing. They all build to optimize the problems in some way differently: QAOA through parameterized quantum circuits, VQE through approximations of ground states of the Hamiltonians, and quantum annealing through quantum evolution to low-energy solutions. We then form a loop between these quantum algorithms and regular machine learning tasks. Optimization impacts virtually all ML phases, from training neural networks, where one reduces loss functions; feature selection, where one aims to discover the most relevant subset of input variables; and hyperparameter optimization, which often involves expensive search procedures over extremely large combinatorial spaces. Quantum optimization techniques can therefore, in principle, accelerate such procedures through computational complexity reduction and enhancing solutions over challenging landscapes. Realistic simulations and case studies emphasize the degree to which hybrid quantum-classical algorithms have been employed in solving ML problems, that is, QSVMs, quantum-enhanced clustering, and quantum reinforcement learning. Despite their experimental nature, these applications already show encouraging results in terms of improved performance metrics as well as reduction in time-to-solution compared to classical-only solutions. Notwithstanding that, this new field is not bereft of real challenges. Quantum hardware suffers from hard limits on qubit fidelity, decoherence, and scalability in the current times. Furthermore, quantum circuit integration into broad ML pipelines requires novel architectures and software platforms. As a counter to those issues, this chapter surveys recent advances in quantum programming languages, simulators, and hybrid platforms like PennyLane, Qiskit, and TensorFlow Quantum. We conclude by looking to the future possibility that quantum optimization will revolutionize the machine learning landscape. As hardware improves and algorithmic complexity increases, the possibility of quantum-powered learning systems solving hard problems becomes increasingly accessible. From speeding up deep network training to enabling new types of unsupervised learning, quantum optimization holds the potential to recast computational tractability in machine learning. This chapter is an all-encompassing introduction and state-of-the-art work for students, researchers, and practitioners interested in using quantum optimization for practical ML applications. It sets the foundation for understanding how to pursue hybrid approaches (how they may be applied today in the real world and bracing oneself for disruption in the future).
Quantum-inspired algorithms help handle complex optimization and inference challenges in AI and ML. Quantum-like algorithms based on quantum mechanics address challenges classical computer paradigms can't. These algorithms innovate data handling, solution finding, and pattern recognition. Quantum effects like superposition, entanglement, and tunneling influenced them. In particular, they work in parallel to explore large solution spaces and speed up processing for large datasets. Next, quantum-inspired algorithms including quantum annealing, optimization, and neural networks are discussed. Simulated annealing and the quantum approximate optimization algorithm (QAOA) make combinatorial optimization tasks in AI and ML easier. Quantum-inspired evolutionary and swarm intelligence algorithms tackle multi-modal optimization issues quickly. Furthermore, quantum-inspired neural networks (QNNs) have revolutionized deep learning. QNNs use quantum gates and quantum circuits to improve classification, regression, and generative modeling.
This chapter offers a clear and accessible introduction to the field of quantum-inspired neural computing. This area combines ideas from quantum mechanics with traditional neural network models to create new possibilities in machine learning and optimization metaheuristic algorithms. Unlike actual quantum computing, quantum-inspired approaches work on classical computers but borrow key concepts like superposition, entanglement, and probabilistic behaviour to improve how neural networks learn and process information. The study begins by explaining why researchers are interested in using quantum principles in neural networks. It then introduces the basic mathematical ideas behind these concepts, such as quantum states and transformations, and shows how they can be used to design more powerful and flexible learning systems. It focuses on discussing current models, outlining the distinctions between quantum-inspired and true quantum systems, and evaluating the potential benefits and challenges of this approach. In addition, Quantum-inspired neural computing introduces a novel framework that bridges classical artificial intelligence with principles derived from quantum mechanics. By simulating quantum behaviours on classical hardware, it opens new avenues for developing more adaptive and efficient learning models. This emerging approach offers promising advantages in areas such as optimization, parallel processing, and high-dimensional data representation. Finally, despite its potential, the field faces notable limitations and challenges. These include the lack of limited theoretical formalization, and difficulties in scaling models for complex real-world applications. Moreover, distinguishing genuine quantum-inspired advantages from conservative algorithmic improvements remains an current research apprehension.
Quantum Artificial Intelligence (Quantum AI) represents a rapidly developing interdisciplinary field at the intersection of quantum computing and machine learning (ML). It holds the promise of unlocking unprecedented computational capabilities for complex optimization tasks, large-scale data processing, and advanced pattern recognition. In this research, we provide a comprehensive examination of two principal quantum algorithms—the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE)—applied to classical ML challenges. Using a hybrid simulation framework that integrates TensorFlow, scikit-learn, Qiskit, and Cirq, we extensively benchmark quantum-enhanced approaches against conventional methods on both combinatorial optimization and image classification tasks. Our findings indicate that while noise and qubit limitations remain critical barriers, quantum-enhanced models can achieve competitive, and sometimes superior, performance compared to purely classical solutions. We elaborate on the practical implications of these results, discuss hardware and algorithmic constraints, and propose future research directions focusing on error mitigation, scalability, and quantum-native ML models. These insights pave the way for a new computational paradigm, in which quantum resources are harnessed to address previously intractable ML problems.
This chapter investigates the application of quantum computing to optimization, a field traditionally dominated by classical methods but increasingly limited by computational demands in tackling complex, large-scale problems. The discussion focuses on quantum optimization techniques, particularly variational quantum algorithms like the Quantum Approximate Optimization Algorithm (QAOA) and the variational quantum eigensolver (VQE), along with quantum annealing (QA), a process inspired by physical annealing that leverages quantum tunnelling and superposition. The chapter also explores the integration of quantum approaches within machine learning frameworks, where quantum algorithms can potentially accelerate model training and enhance capabilities. Additionally, it presents practical applications and challenges associated with these quantum algorithms, covering their effectiveness on noisy intermediate-scale quantum (NISQ) devices and the evolving landscape of quantum hardware. This chapter concludes with insights into quantum optimization's future potential to address optimization and machine learning challenges that are currently intractable for classical methods, marking a significant shift in computational science.