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.
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.
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 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 devices in the current Noisy Intermediate-Scale Quantum (NISQ) era are inherently affected by noise, which can degrade the predictive performance of quantum machine learning models. In this work, we introduce a new margin-based robustness measure for Quantum Kernel-Assisted Support Vector Machines (QSVMs), termed the cross-kernel margin. This measure quantifies the stability of a classifier learned under a perturbed kernel relative to the ideal feature space. We derive a posteriori stability bounds for the corresponding cross-kernel inverse squared-margin under kernel perturbations using the Tikhonov-stabilised SVM dual formulation. The local depolarising noise model is then applied to this framework to induce perturbations in the kernel. The resulting bounds are numerically checked using simulations across multiple datasets and further tested using kernel matrices obtained from real quantum hardware and a noisy backend simulator. Furthermore, we empirically compare the degradation of test accuracy under local depolarising noise with the commonly used global depolarising noise model in order to motivate its use in our study. Finally, we present empirical results linking margin-based quantities with the generalisation performance of QSVMs, providing additional motivation for our margin-based robustness analysis.
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.
Kernel methods are the basis of most classical machine learning algorithms such as Gaussian Process (GP) and Support Vector Machine (SVM). Computing kernels using noisy intermediate scale quantum (NISQ) devices has attracted considerable attention due to recent progress in the design of NISQ devices. However noise and errors on current NISQ devices can negatively affect the predicted kernels. In this paper we utilize two quantum kernel machine learning (ML) algorithms to predict the labels of a Breast Cancer dataset on two different NISQ devices: quantum kernel Gaussian Process (qkGP) and quantum kernel Support Vector Machine (qkSVM). We estimate the quantum kernels on the 11 qubit IonQ and the 5 qubit IBMQ Belem quantum devices. Our results demonstrate that the predictive performances of the error mitigated quantum kernel machine learning algorithms improve significantly compared to their non-error mitigated counterparts. On both NISQ devices the predictive performances became comparable to those of noiseless quantum simulators and their classical counterparts
The rapid advancement of Noisy Intermediate-Scale Quantum (NISQ) devices necessitates a systematic evaluation of quantum machine learning (QML) algorithms to determine their feasibility for near-term applications. This study aims to benchmark the Variational Quantum Classifier (VQC)and the Quantum Kernel Support Vector Machine (QSVM) under realistic noise conditions modeled using Qiskit Aer. The primary objective is to investigate the impact of depolarizing and amplitude damping noise on the classification performance of these algorithms. Using the Iris binary classification task, we simulated four noise levels (0, 0.01, 0.05, 0.1) and evaluated accuracy across 1024 measurement shots. Results show that QSVM achieves superior accuracy (70%) under ideal and lownoise conditions, while VQC exhibits higher resilience at moderate noise (50% at 0.05 noise level) due to its adaptive Variational parameters. At higher noise levels (0.1), both models converge to ~35–40% accuracy, indicating significant degradation. These findings provide actionable insights for algorithm selection on NISQ hardware, with VQC favored for moderately noisy devices and QSVM preferable for low-noise or error-mitigated systems. The study concludes by highlighting the need for noise-aware ansatz design and error mitigation techniques to enhance QML performance in NISQ regimes.