This chapter presents quantum transfer learning (QTL) as a practical and conceptually grounded framework for integrating quantum computation into modern machine learning. Building on the classical transfer learning paradigm, this chapter shows how pretrained classical models can be reused for large-scale representation learning while variational quantum circuits (VQCs) are deployed as compact downstream adaptation modules. Emphasis is placed on hybrid classical-quantum architectures in which quantum feature extractors operate on low-dimensional embeddings produced by convolutional networks, transformers, or graph neural networks, and their measurement-based outputs are processed by classical heads for prediction. This chapter develops the mathematical and architectural foundations of this approach, explains the role of variational quantum feature maps, and examines why quantum feature extractors may be useful in data-limited and structure-rich settings. Applications to text, image, and molecular data are discussed to illustrate the domain-independent nature of the framework. Practical implementation is addressed through PennyLane and PyTorch integration, highlighting differentiable quantum layers and end-to-end hybrid optimization. A hands-on example using encoded embeddings and VQCs demonstrates methodology, benchmarking, and model evaluation in a realistic supervised-learning setting. This chapter concludes with a critical discussion of limitations, including task dependence, noise, measurement cost, benchmarking challenges, and the continued dominance of large pretrained classical encoders.
This chapter presents quantum transfer learning (QTL) as a practical and conceptually grounded framework for integrating quantum computation into modern machine learning. Building on the classical transfer learning paradigm, this chapter shows how pretrained classical models can be reused for large-scale representation learning while variational quantum circuits (VQCs) are deployed as compact downstream adaptation modules. Emphasis is placed on hybrid classical-quantum architectures in which quantum feature extractors operate on low-dimensional embeddings produced by convolutional networks, transformers, or graph neural networks, and their measurement-based outputs are processed by classical heads for prediction. This chapter develops the mathematical and architectural foundations of this approach, explains the role of variational quantum feature maps, and examines why quantum feature extractors may be useful in data-limited and structure-rich settings. Applications to text, image, and molecular data are discussed to illustrate the domain-independent nature of the framework. Practical implementation is addressed through PennyLane and PyTorch integration, highlighting differentiable quantum layers and end-to-end hybrid optimization. A hands-on example using encoded embeddings and VQCs demonstrates methodology, benchmarking, and model evaluation in a realistic supervised-learning setting. This chapter concludes with a critical discussion of limitations, including task dependence, noise, measurement cost, benchmarking challenges, and the continued dominance of large pretrained classical encoders.
Quantum transfer learning combines pretrained classical deep learning models with quantum circuits to reuse expressive feature representations while limiting the number of trainable parameters. In this work, we introduce a family of compact quantum transfer learning architectures that attach variational quantum classifiers to frozen convolutional backbones for image classification. We instantiate and evaluate several classical-quantum hybrid models implemented in PennyLane and Qiskit, and systematically compare them with a classical transfer-learning baseline across heterogeneous image datasets. To ensure a realistic assessment, we evaluate all approaches under both ideal simulation and noisy emulation using noise models calibrated from IBM quantum hardware specifications, as well as on real IBM quantum hardware. Experimental results show that the proposed quantum transfer learning architectures achieve competitive and, in several cases, superior accuracy while consistently reducing training time and energy consumption relative to the classical baseline. Among the evaluated approaches, PennyLane-based implementations provide the most favorable trade-off between accuracy and computational efficiency, suggesting that hybrid quantum transfer learning can offer practical benefits in realistic NISQ era settings when feature extraction remains classical.
This chapter develops variational quantum models as the dominant framework for near-term quantum machine learning (QML), emphasizing their role as trainable quantum circuits embedded within hybrid quantum-classical optimization loops. Building on earlier chapters on encoding and quantum feature geometry, it formulates parameterized quantum circuits (PQCs) as families of unitary transformations acting on reference states, with model outputs obtained through expectation values of observables. This measurement-based structure makes variational learning inherently stochastic and closely ties model behavior to circuit architecture, observable choice, and optimization strategy. This chapter examines variational quantum circuits (VQCs) as learning models, introduces quantum neural networks (QNNs) as structured variational architectures, and analyzes layered, data-reuploading, recurrent, and hybrid classical-quantum designs. It highlights the central tension between expressivity and trainability, showing how universality and approximation power are counterbalanced by optimization barriers such as barren plateaus. The discussion further develops ansatz design strategies, supervised, fidelity-based, and energy-based losses, regularization under noise, and practical methods for gradient estimation and optimization, including the parameter-shift rule, Simultaneous Perturbation Stochastic Approximation (SPSA), and layer-wise training. Together, these ideas establish variational quantum models as a flexible yet hardware-constrained paradigm whose practical success depends on careful coordination among architecture, measurement, and optimization.
Quantum Transfer Learning (QTL) offers a promising approach for visual quantum machine learning under near-term constraints, where limited qubit counts, shallow circuit depths, and costly hybrid optimization restrict end-to-end quantum training. In this setting, pretrained classical backbones can extract high-level visual features, while compact quantum modules operate as trainable classification heads. However, existing QTL results are difficult to compare because they often differ in datasets, preprocessing, backbone settings, qubit budgets, circuit designs, optimization choices, and reporting protocols. This work presents a controlled benchmarking methodology for evaluating representative QTL methods under a unified transfer-learning pipeline. The benchmark compares DQN-QTL, QPIE-QTL, AE-CQTL, PVCQTL, and ED-QTL under shared preprocessing rules, frozen-backbone settings, training conditions, and reporting metrics. The evaluation focuses on Fashion-MNIST and Hymenoptera Ants vs. Bees as the two main datasets, while CIFAR-10 is used to provide additional configuration-level evidence on a harder natural-image task. Beyond predictive performance, the benchmark analyzes circuit size, trainable parameters, quantum parameters, training time, and architectural sensitivity to qubit count and circuit depth. The results show that no single QTL family dominates across all settings: performance depends on the dataset, encoding strategy, circuit design, and computational cost. These findings highlight the need for resource-aware QTL evaluation and provide guidance for selecting hybrid quantum-classical transfer models under near-term resource constraints.
Abstract Quantum Machine Learning (QML) is a promising field that combines the power of quantum computing with machine learning. Variational quantum circuits, where parameters of circuits are learned classically, have been widely used in many recent applications of QML. This is an instance of a hybrid quantum-classical framework, where both classical and quantum components are present. However, applying these techniques to applications involving massive data is a challenging task. One way to overcome this, is using the concept of classical-quantum transfer learning with the help of dressed quantum circuit, introduced recently, where the underlying neural architecture is pre-trained classically, but at the final steps (decision layer), a quantum circuit is used, followed by quantum measurements and post-processing to classify images with high precision. In this paper, we applied hybrid classical-quantum transfer learning to another task of massive data processing, i.e. Natural Language Processing (NLP). We show how to (binary) classify short texts (e.g., SMS) with classical-quantum transfer learning, which was originally applied to image processing only. Our quantum network was pre-trained by Bidirectional Encoder Representations from the Transformers (BERT) model, and its variational quantum circuit is fine-tuned for text processing. We evaluated the performance of our hybrid neural architecture using the Receiver Operating Characteristic (ROC) curve, which is typically used in the evaluation of classification problems. The results indicate high precision as well as lower loss function. To our knowledge, our work is the first application of quantum transfer learning to the area of NLP. Finally a comparison with a tool that uses learning but in a different way than transfer learning is presented
Quantum machine learning (QML) has emerged as a rapidly developing field at the intersection of quantum computing, artificial intelligence, and data science. As quantum hardware and algorithms continue to advance, there is a growing need for a rigorous and accessible text that explains how quantum principles can be used to design, analyze, and implement machine learning models. This book is intended for graduate students, researchers, and practitioners in computer science, physics, engineering, mathematics, and related disciplines. This book provides a comprehensive introduction to the foundations and modern methods of QML. It begins with the principles of quantum information, Hilbert spaces, quantum circuits, and quantum algorithms relevant to learning tasks. Then, it develops the major paradigms of the field, including quantum data encoding, quantum feature maps and kernels, variational quantum circuits, quantum neural networks, quantum generative models, quantum reinforcement learning, quantum transfer learning, and quantum linear algebra techniques. The text emphasizes both theory and implementation, with programming examples and computational workflows using Qiskit, PennyLane, TensorFlow Quantum, and PyTorch. Additional chapters address tensor network-inspired learning, error mitigation, graphics processing unit (GPU)-accelerated simulation, benchmarking, hybrid quantum-classical architectures, and applications in chemistry, genomics, finance, optimization, and natural language processing. Distinctive in both scope and organization, the book integrates mathematical foundations, algorithmic development, software implementation, and emerging research directions within a single coherent framework, making it suitable both as a graduate-level textbook and as a practical reference for researchers working in QML.
Hybrid quantum-classical learning models increasingly integrate neural networks with variational quantum circuits (VQCs) to exploit complementary inductive biases. However, many existing approaches rely on tightly coupled architectures or task-specific encoders, limiting conceptual clarity, generality, and transferability across learning settings. In this work, we introduce Quantum LEGO Learning, a modular and architecture-agnostic learning framework that treats classical and quantum components as reusable, composable learning blocks with well-defined roles. Within this framework, a pre-trained classical neural network serves as a frozen feature block, while a VQC acts as a trainable adaptive module that operates on structured representations rather than raw inputs. This separation enables efficient learning under constrained quantum resources and provides a principled abstraction for analyzing hybrid models. We develop a block-wise generalization theory that decomposes learning error into approximation and estimation components, explicitly characterizing how the complexity and training status of each block influence overall performance. Our analysis generalizes prior tensor-network-specific results and identifies conditions under which quantum modules provide representational advantages over comparably sized classical heads. Empirically, we validate the framework through systematic block-swap experiments across frozen feature extractors and both quantum and classical adaptive heads. Experiments on quantum dot classification demonstrate stable optimization, reduced sensitivity to qubit count, and robustness to realistic noise.