A key problem in the field of quantum computing is understanding whether quantum machine learning (QML) models implemented on noisy intermediate-scale quantum (NISQ) machines can achieve quantum advantages. Recently, Huang et al. [Nat Commun 12, 2631] partially answered this question by the lens of quantum kernel learning. Namely, they exhibited that quantum kernels can learn specific datasets with lower generalization error over the optimal classical kernel methods. However, most of their results are established on the ideal setting and ignore the caveats of near-term quantum machines. To this end, a crucial open question is: does the power of quantum kernels still hold under the NISQ setting? In this study, we fill this knowledge gap by exploiting the power of quantum kernels when the quantum system noise and sample error are considered. Concretely, we first prove that the advantage of quantum kernels is vanished for large size of datasets, few number of measurements, and large system noise. With the aim of preserving the superiority of quantum kernels in the NISQ era, we further devise an effective method via indefinite kernel learning. Numerical simulations accord with our theoretical results. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.
A key problem in the field of quantum computing is understanding whether quantum machine learning (QML) models implemented on noisy intermediate-scale quantum (NISQ) machines can achieve quantum advantages. Recently, Huang et al. [Nat Commun 12, 2631] partially answered this question by the lens of quantum kernel learning. Namely, they exhibited that quantum kernels can learn specific datasets with lower generalization error over the optimal classical kernel methods. However, most of their results are established on the ideal setting and ignore the caveats of near-term quantum machines. To this end, a crucial open question is: does the power of quantum kernels still hold under the NISQ setting? In this study, we fill this knowledge gap by exploiting the power of quantum kernels when the quantum system noise and sample error are considered. Concretely, we first prove that the advantage of quantum kernels is vanished for large size of datasets, few number of measurements, and large system noise. With the aim of preserving the superiority of quantum kernels in the NISQ era, we further devise an effective method via indefinite kernel learning. Numerical simulations accord with our theoretical results. Our work provides theoretical guidance of exploring advanced quantum kernels to attain quantum advantages on NISQ devices.
Quantum kernel methods have been widely recognized as one of the promising quantum machine learning (QML) algorithms that have the potential to achieve quantum advantages. However, their capabilities may be severely degraded by inevitable noises in the current noisy intermediate-scale quantum (NISQ) era. In this article, we theoretically characterize the power of noisy quantum kernels and demonstrate that under depolarizing noise, quantum kernel methods may only have very poor prediction capability, even when the generalization error is small. Specifically, we quantitatively describe the decreasing of the prediction capability of noisy quantum kernels in terms of the rate of quantum noise, the size of training samples, the number of qubits, and the number of layers affected by quantum noises. Our results clearly demonstrate that for a given number of training samples, once the number of layers affected by noise exceeds some threshold, the prediction capability of noisy kernels is very poor. Thus, we provide a crucial warning to employ noisy quantum kernel methods for quantum computation and the theoretical results can also serve as guidelines when developing practical quantum kernel algorithms for achieving quantum advantages.
An interesting approach to using noisy intermediate-scale quantum (NISQ) devices is hybrid classical-quantum machine learning (QML). In these methods, classical processors handle optimisation and large-scale computation, while quantum hardware is devoted to tasks like feature mapping, nonlinear transformations, or kernel evaluation. Practical near-term demonstrations are made possible by this division of labour, which also mitigates existing hardware restrictions. In specialised fields like molecular modelling, materials discovery, and small-sample learning issues, recent advancements in variational quantum circuits, hybrid neural networks, and quantum kernel techniques have produced promising outcomes. However, scalability and wider applicability are still hampered by enduring issues including noise, barren plateaus, and the expense of repeated measurements. Long-term developments will require fault tolerance, logical qubits, and established software infrastructures, whereas near-term success depends on noise-aware algorithm design, repeatable experimental benchmarks, and enhanced error-mitigation strategies. When taken as a whole, these advancements show a viable path to achieving quantum advantage in machine learning. Quanta 2026; 15: 1–12.
Quantum computing has emerged as a transformative paradigm capable of addressing computational challenges beyond the reach of classical systems.In the current era of Noisy Intermediate-Scale Quantum (NISQ) devices, practical quantum hardware is characterized by limited qubit counts, short coherence times, gate errors, and the absence of full error correction.Despite these constraints, significant progress has been made in developing quantum machine learning (QML) techniques tailored to operate on near-term quantum processors.This paper presents a comprehensive review of Quantum Machine Learning in the context of NISQ computing.We first outline the fundamental principles of quantum computing, including qubits, superposition, entanglement, and quantum parallelism, followed by a detailed discussion of the NISQ computing model and its hardware limitations.The review then examines hybrid quantum-classical learning frameworks, variational quantum algorithms, quantum data encoding strategies, and noise mitigation techniques that enable practical implementation on existing platforms.Emerging applications across healthcare, finance, cybersecurity, climate modeling, and materials science are also surveyed to highlight the real-world potential of QML.Furthermore, key challenges such as scalability, trainability issues, and algorithmic robustness are analyzed, along with current research efforts aimed at overcoming these barriers.The paper concludes by identifying promising future directions for advancing QML toward quantum advantage.This review aims to provide researchers and practitioners with a structured understanding of the capabilities, limitations, and opportunities of quantum machine learning in the NISQ era .
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 rapid advancement of quantum computing hardware and software has ushered in a new era for computational science, promising to tackle problems that are intractable for classical computers. Parallelly, machine learning (ML) has revolutionized data analysis and artificial intelligence. The confluence of these two fields, known as Quantum Machine Learning (QML), aims to harness the principles of quantum mechanics-such as superposition, entanglement, and interference-to enhance and redefine classical machine learning algorithms. This survey provides a comprehensive overview of the burgeoning field of QML. We begin by elucidating the fundamental quantum concepts that underpin QML approaches. We then present a detailed taxonomy and analysis of prominent QML algorithms, categorizing them into quantum-enhanced classical models and fully quantum models. Key families of algorithms discussed include Quantum Support Vector Machines (QSVM), Quantum Neural Networks (QNNs), and Quantum Generative Adversarial Networks (QGANs). For each, we explain the theoretical quantum advantage, the circuit implementation, and the current limitations. Furthermore, we delve into the critical challenges facing the practical realization of QML, including the pervasive issue of noise in Noisy Intermediate-Scale Quantum (NISQ) devices, the problem of barren plateaus in training quantum circuits, and the complexities of efficient data encoding (quantum feature maps). We also present a small-scale experimental simulation of a variational quantum classifier on a standardized dataset, demonstrating its principle and comparing its performance with a classical counterpart. Finally, the paper discusses the future trajectory of QML, highlighting the importance of error mitigation, hybrid quantum-classical architectures, and the development of quantum-specific learning inductive biases. We conclude that while fault-tolerant quantum computers remain on the horizon, QML represents a paradigm shift with the potential to deliver profound computational advantages in the coming decades.
The importance of analyzing nontrivial datasets when testing quantum machine learning (QML) models is becoming increasingly prominent in literature, yet a cohesive framework for understanding dataset characteristics remains elusive. In this work, we concentrate on the size of the dataset as an indicator of its complexity and explores the potential for QML models to demonstrate superior data-efficiency compared to classical models, particularly through the lens of quantum kernel methods (QKMs). We provide a method for generating semi-artificial fully classical datasets, on which we show one of the first evidence of the existence of classical datasets where QKMs require less data during training. Additionally, our study introduces a new analytical tool to the QML domain, derived for classical kernel methods, which can be aimed at investigating the classical-quantum gap. Our empirical results reveal that QKMs can achieve low error rates with less training data compared to classical counterparts. Furthermore, our method allows for the generation of datasets with varying properties, facilitating further investigation into the characteristics of real-world datasets that may be particularly advantageous for QKMs. We also show that the predicted performance from the analytical tool we propose - a generalization metric from classical domain - show great alignment empirical evidence, which fills the gap previously existing in the field. We pave a way to a comprehensive exploration of dataset complexities, providing insights into how these complexities influence QML performance relative to traditional methods. This research contributes to a deeper understanding of the generalization benefits of QKM models and potentially a broader family of QML models, setting the stage for future advancements in the field.