Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ) devices and usage for solving all types of machine learning problems. Kernel methods rely on the notion of similarity between points in a higher (possibly infinite) dimensional feature space. For machine learning, the notion of similarity assumes that points close in the feature space should be close in the machine learning task space. In this paper, we discuss the use of variational quantum kernels with task-specific quantum metric learning to generate optimal quantum embeddings (a.k.a. quantum feature encodings) that are specific to machine learning tasks. Such task-specific optimal quantum embeddings, implicitly supporting feature selection, are valuable not only to quantum kernel methods in improving the latter's performance, but they can also be valuable to non-kernel QML methods based on parameterized quantum circuits (PQCs) as pretrained embeddings and for transfer learning. This further demonstrates the quantum utility, and quantum advantage (with classically-intractable quantum embeddings), of quantum kernel methods.
Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ) devices and usage for solving all types of machine learning problems. Kernel methods rely on the notion of similarity between points in a higher (possibly infinite) dimensional feature space. For machine learning, the notion of similarity assumes that points close in the feature space should be close in the machine learning task space. In this paper, we discuss the use of variational quantum kernels with task-specific quantum metric learning to generate optimal quantum embeddings (a.k.a. quantum feature encodings) that are specific to machine learning tasks. Such task-specific optimal quantum embeddings, implicitly supporting feature selection, are valuable not only to quantum kernel methods in improving the latter's performance, but they can also be valuable to non-kernel QML methods based on parameterized quantum circuits (PQCs) as pretrained embeddings and for transfer learning. This further demonstrates the quantum utility, and quantum advantage (with classically-intractable quantum embeddings), of quantum kernel methods.
Quantum machine learning (QML) is the use of quantum computing for the computation of machine learning algorithms. With the prevalence and importance of classical data, a hybrid quantum-classical approach to QML is called for. Parameterized Quantum Circuits (PQCs), and particularly Quantum Kernel PQCs, are generally used in the hybrid approach to QML. In this paper we discuss some important aspects of PQCs with quantum kernels including PQCs, quantum kernels, quantum kernels with quantum advantage, and the trainability of quantum kernels. We conclude that quantum kernels with hybrid kernel methods, a.k.a. quantum kernel methods, offer distinct advantages as a hybrid approach to QML. Not only do they apply to Noisy Intermediate-Scale Quantum (NISQ) devices, but they also can be used to solve all types of machine learning problems including regression, classification, clustering, and dimension reduction. Furthermore, beyond quantum utility, quantum advantage can be attained if the quantum kernels, i.e., the quantum feature encodings, are classically intractable.
Quantum kernel methods offer significant theoretical benefits by rendering classically inseparable features separable in quantum space. Yet, the practical application of Quantum Machine Learning (QML), currently constrained by the limitations of Noisy Intermediate-Scale Quantum (NISQ) hardware, necessitates effective strategies to compress and embed large-scale real-world data like images into the constrained capacities of existing quantum devices or simulators. To this end, we propose Quantum Generator Kernels (QGKs), a generator-based approach to quantum kernels, comprising a set of Variational Generator Groups (VGGs) that merge universal generators into a parameterizable operator, ensuring scalable coverage of the available quantum space. Thereby, we address shortcomings of current leading strategies employing hybrid architectures, which might prevent exploiting quantum computing's full potential due to fixed intermediate embedding processes. To optimize the kernel alignment to the target domain, we train a weight vector to parameterize the projection of the VGGs in the current data context. Our empirical results demonstrate superior projection and classification capabilities of the QGK compared to state-of-the-art quantum and classical kernel approaches and show its potential to serve as a versatile framework for various QML applications.
The quantum support vector machines (QSVMs) offer a paradigm change that may leverage quantum mechanical processes to outperform traditional support vector machines (SVMs) in high-dimensional and nonlinear classification tasks. These machines are located at the crossroads of supervised machine learning and quantum computing. The purpose of this chapter is to provide a comprehensive technical analysis of QSVMs, with a particular emphasis on the use of variation quantum circuits for implicit feature space transformations and the development of these circuits within the context of quantum kernel estimation. Through the use of quantum state preparation and interference, we provide a comprehensive explanation of the possible fabrication of quantum kernels that are based on inner product evaluations in exponentially huge Hilbert spaces. When it comes to boosting model expressivity beyond classical limits, the importance that entanglement and quantum feature mapping play is specifically stressed. In addition to this, we investigate algorithmic implementations on noisy intermediate-scale quantum (NISQ) hardware, focusing on problems associated with quantum decoherence, gate fidelity, and loop depth optimization. Several fields, including quantum-enhanced drug discovery, anomaly detection in quantum sensor networks, fault classification in quantum error correction, and portfolio optimization, are now the focus of research that is being conducted in order to develop real-world applications. This chapter comes to a close with an analysis of the existing theoretical limits, resource needs, and future perspectives for the use of QSVMs in machine learning applications in order to achieve a quantum advantage. In order to facilitate the development of scalable quantum machine learning models that are founded on strong mathematical and computational notions, this synthesis is geared at academics and practitioners.
Quantum kernel methods (QKMs) have emerged as a prominent framework for supervised quantum machine learning. Unlike variational quantum algorithms, which rely on gradient-based optimisation and may suffer from issues such as barren plateaus, non-variational QKMs employ fixed quantum feature maps, with model selection performed classically via convex optimisation and cross-validation. This separation of quantum feature embedding from classical training ensures stable optimisation while leveraging quantum circuits to encode data in high-dimensional Hilbert spaces. In this review, we provide a thorough analysis of non-variational supervised QKMs, covering their foundations in classical kernel theory, constructions of fidelity and projected quantum kernels, and methods for their estimation in practice. We examine frameworks for assessing quantum advantage, including generalisation bounds and necessary conditions for separation from classical models, and analyse key challenges such as exponential concentration, dequantisation via tensor-network methods, and the spectral properties of kernel integral operators. We further discuss structured problem classes that may enable advantage, and synthesise insights from comparative and hardware studies. Overall, this review aims to clarify the regimes in which QKMs may offer genuine advantages, and to delineate the conceptual, methodological, and technical obstacles that must be overcome for practical quantum-enhanced learning.
Quantum machine learning (QML) is an emerging interdisciplinary field which incorporates some features of quantum computing with machine learning. Quantum hardware development has sparked research interest for AI scientists because it gives capabilities in high-dimensional data processing and simultaneous operation execution. The investigation within this paper traces the main features of QML by reviewing variational quantum classifiers (VQCs) as well as quantum kernels and hybrid quantum-classical models. VQCs serve as quantum parameterized circuits whose optimization process with classical feedback achieves quantum superiority for classification applications. Quantum kernels expand Hilbert space features to improve traditional kernel methods, thus proving their functionality in quantum feature space. Hybrid approaches unite NISQ hardware with classical systems, which makes QML applicable to real-world applications right now. (Rietsche et al., 2022; Tychola et al., 2023) An analysis explores separate functions and combined effects of these components, which enhance model performance, extend generalization, and boost computational efficiency. The paper discusses necessary knowledge first, along with existing applications, before analyzing them against traditional methods. The paper reviews current QML tools while exploring their operational readiness as well as practical issues and deployment barriers for broader adoption. The paper conducts an in-depth investigation of significant limitations that include hardware noise alongside questions regarding scalability and interpretability. This paper shows how QML will transform machine learning applications through its review of obstacles that must be resolved to achieve its complete potential development. The study presents researchers and practitioners with an extensive comprehension of QML developments and emerging paths for this revolutionary field.
Quantum Machine Learning (QML) is an exciting frontier applying the philosophy of quantum computation to classical machine learning for improved learning performance of complicated tasks. However, QML is greatly challenged by realistic issues like noisy quantum measurements and limited labeled quantum data caused by the high cost and technological limitations. This paper explores the novel transfer-learning mechanisms to tackle these issues, which allow the reuse of the knowledge from related quantum tasks for improving model performance and generalization in resource-limited scenarios. Transfer learning, one of the great and successful concepts of classical machine learning, is to transfer the learned parameters or features from the source domain (or task) to the target domain (or task). We further develop and investigate, in quantum, a methodology where parameterized quantum circuits (PQCs) learnt on a source quantum data set have certain parts partially re-used or fine-tuned for a target task, given limited amount of target data. This strategy also avoids large quantum training runs that are not scalable on state-of-the-art noisy intermediate-scale quantum (NISQ) processors. The suggested methods are layerwise quantum adaptation, quantum kernel reuse and hybrid quantum-classical feature transfer. We investigate the robustness of these mechanisms in presence of noise by simulating quantum circuits using depolarizing and readout noise models. Moreover, we show that pretraining of quantum models on synthetic (or simulated) data sets (which are generated using larger, less noisy systems) can be instrumental in learning on real, small-sized quantum devices. Experiment results in quantum classification tasks demonstrate the effectiveness of transfer learning in boosting the accuracy, accelerating the convergence, and lowering the quantum circuit depth of successfully trained model. It is interesting to mention that transfer using layer-wise models became very resistant to quantum noise, as its performance did not degrade significantly for noisy inputs. These results demonstrate that transfer learning can overcome the scarce quantum data and suppress the harmful impact of measurement noise. This work presents a potential venue for enhancing the applicability of QML in the NISQ era. By transferring knowledge from theoretical quantum learning models to actual quantum hardware constraints, transfer learning allows quantum algorithms to learn faster and generalize better across tasks.