This chapter introduces the central role of information encoding in quantum machine learning, examining how classical and quantum data can be mapped into quantum states for processing by quantum algorithms. It surveys key encoding strategies—basis, angle, amplitude, and Hamiltonian-based—and discusses their theoretical foundations, resource requirements, and suitability for current quantum hardware. The chapter also explores quantum autoencoders, the nature of quantum data, and practical considerations such as noise, scalability, and reversibility. Together, these topics provide a comprehensive framework for understanding how data is embedded in quantum systems to enable meaningful learning and inference.
This chapter introduces the central role of information encoding in quantum machine learning, examining how classical and quantum data can be mapped into quantum states for processing by quantum algorithms. It surveys key encoding strategies—basis, angle, amplitude, and Hamiltonian-based—and discusses their theoretical foundations, resource requirements, and suitability for current quantum hardware. The chapter also explores quantum autoencoders, the nature of quantum data, and practical considerations such as noise, scalability, and reversibility. Together, these topics provide a comprehensive framework for understanding how data is embedded in quantum systems to enable meaningful learning and inference.
This chapter examines quantum data encoding as a foundational component of quantum machine learning (QML), emphasizing that the way classical data are embedded into quantum states strongly shapes model expressivity, trainability, and practical feasibility. It first develops a general framework in which encoding is viewed as a data-dependent unitary transformation and from a machine-learning perspective as a quantum feature map that defines the geometry of learning in Hilbert space. This chapter then compares the principal encoding strategies: basis encoding, valued for simplicity and interpretability but limited in expressive power; angle encoding, which is hardware-friendly and central to variational models; amplitude encoding, which offers exponential qubit compression but faces significant state-preparation challenges; and hybrid encoding, which combines multiple schemes to balance compression, expressivity, and implementability. A major theme of this chapter is that encoding should be understood as the construction of a quantum feature map whose induced quantum kernel determines similarity, decision boundaries, and generalization behavior. The discussion further highlights the role of encoding in variational quantum algorithms, the relationship between feature-map complexity and potential quantum advantage, and the practical constraints imposed by qubit count, circuit depth, noise, and measurement overhead.
Quantum computing and machine learning (ML) have received significant developments which have set the stage for the next frontier of creative work and usefulness. This paper aims at reviewing various data-encoding techniques in Quantum Machine Learning (QML) while highlighting their significance in transforming classical data into quantum systems. We analyze basis, amplitude, angle, and other high-level encodings in depth to demonstrate how various strategies affect encoding improvements in quantum algorithms. However, they identify major problems with encoding in the framework of QML, including scalability, computational burden, and noise. Future directions for research outline these challenges, aiming to enhance the excellence of encoding techniques in the constantly evolving quantum technology setting. This review shall enable the researcher to gain an enhanced understanding of data encoding in QML, and it also suggests solutions to the current limitations in this area.
The development of quantum computers has been the stimulus that enables the realization of Quantum Machine Learning (QML), an area that integrates the calculational framework of quantum mechanics with the adaptive properties of classical machine learning. This article suggests a broad architecture that allows the connection between classical data pipelines and quantum algorithms, hybrid quantum-classical models emerge as a promising route to scalable and near-term quantum benefit. At the core of this paradigm lies the Classical-Quantum (CQ) paradigm, in which the qubit states of high-dimensional classical data are encoded using sophisticated classical encoding strategies which encode the data in terms of amplitude and angle of rotation, along with superposition mapping. These techniques allow compression of information exponentially into Hilbert space representations, which, together with reduced sample complexity, allows greater feature expressivity. We also examine variational quantum circuits, quantum gates expressed as trainable variables that run with classical optimizers to overcome decoherence, noise, and gate-depth constraints of the existing Noisy Intermediate-Scale Quantum (NISQ) devices. Experimental comparisons with a Quantum Naive Bayes classifier prove that even small quantum circuits can approximate probabilistic inference with competitive accuracy compared to classical benchmarks, and have much better robustness to noisy data distributionsThis model does not only explain the algorithmic and architectural design of QML, it also offers a roadmap to the implementation of quantum kernels, variational algorithms, and hybrid feedback loops into practice, including optimization, computer vision, and medical diagnostics. The results support the idea that hybrid architectures with strong data encoding and adaptive error protection are key to moving QML out of theory to practice.
The encoding of classical data into quantum states constitutes the primary performance bottleneck in Quantum Machine Learning (qml) on Noisy Intermediate-Scale Quantum (nisq) devices. No existing framework jointly characterises resource cost, expressivity, and noise robustness, nor provides actionable selection guidelines for practitioners. This survey addresses that gap through a systematic review of 66 primary works (2017-2026) assembled via a PRISMA-adapted protocol across five academic databases. Four principal contributions are made. First, a three-axis cost-expressivity-robustness taxonomy classifies all major encoding families - basis, angle, dense-angle, amplitude, data re-uploading, and IQP - along independently measurable axes. Second, closed-form depth-fidelity bounds under nisq decoherence channels identify the critical gate-error rate p* ~ 10^-3 below which amplitude encoding is viable. Third, a unified treatment of Fourier expressivity, barren-plateau onset, and quantum kernel concentration as functions of the encoding circuit provides the first joint trainability analysis. Fourth, a five-regime decision framework maps (D, n, p, tau) - feature dimension, qubit budget, error rate, and task type - to a hardware-grounded encoding recommendation. The central finding is that for p >= 10^-3, shallow angle-based encodings consistently outperform amplitude encoding in practice, despite the latter's exponential qubit advantage.
Quantum machine learning combines quantum computing with machine learning to solve complex computational problems more efficiently than classical approaches. This survey provides an introduction to the foundations, algorithms, frameworks, data and applications of quantum machine learning, serving as a resource for researchers and practitioners. We begin by reviewing existing surveys to identify gaps that this work addresses, followed by a detailed discussion of the foundational principles of quantum mechanics and machine learning essential for quantum machine learning. Key algorithms are examined, highlighting their mechanisms, advantages, and applications across various domains. Current frameworks and platforms for implementing quantum machine learning algorithms are explored, emphasizing their unique features and suitability for different contexts. Existing quantum datasets for practical usage are also reported and commented on. This survey also reviews over 135 articles, categorized into theoretical and practical contributions, to identify key advances, limitations, and application areas within quantum machine learning. Critical challenges such as hardware limitations, error rates, and scalability are analyzed to detect the obstacles that must be addressed for practical deployment. By synthesizing these elements into a structured overview, this survey aims at serving as both an introduction and a guide for advancing research and development in this disruptive field.
Encoding classical data into quantum systems is a foundational step in the execution of nearly all quantum algorithms, and a critical bottleneck in realizing practical quantum advantage. This review provides a comprehensive account of the concepts, algorithms, and practical considerations associated with quantum data encoding. We trace the development from its early conceptual foundations to recent advances, considering commonly used access models, such as quantum state preparation, unitary synthesis, QRAM and block encoding. We survey the circuit size, depth, space-time tradeoffs, as well as non-Clifford resources required for fault-tolerant implementation. We also discuss the roles of different access models in quantum algorithms. Special attention is given to structured data, such as sparse data, Boolean functions and data represented by tensor networks. This review bridges theory and applications, serving both as a pedagogical guide for newcomers and as a reference for active researchers. We also highlight the pivotal role of quantum data encoding in quantum computing and provide insights into future directions that will enable quantum advantage.