# Towards understanding the power of quantum kernels in the NISQ era

arXiv: https://arxiv.org/abs/2103.16774 · HTML: https://mlsanity.com/paper/2103.16774/

## Key facts

- Cited by 43 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 31 Mar 2021.

## Builds on (most cited first, 17 of 17)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Experimental Quantum Generative Adversarial Networks for Image Generation](https://mlsanity.com/paper/2010.06201/) (2020)
- [Practical Coreset Constructions for Machine Learning](https://mlsanity.com/paper/1703.06476/) (2017)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Quantum noise protects quantum classifiers against adversaries](https://mlsanity.com/paper/2003.09416/) (2020)
- [Quantum Generative Models for Small Molecule Drug Discovery](https://mlsanity.com/paper/2101.03438/) (2021)
- [Quantum Perceptron Models](https://mlsanity.com/paper/1602.04799/) (2016)
- [Enabling Multi-programming Mechanism for Quantum Computing in the NISQ Era](https://mlsanity.com/paper/2102.05321/) (2021)
- [Experimental kernel-based quantum machine learning in finite feature space](https://mlsanity.com/paper/1906.04137/) (2019)
- [Sublinear quantum algorithms for training linear and kernel-based classifiers](https://mlsanity.com/paper/1904.02276/) (2019)
- [Quantum Differentially Private Sparse Regression Learning](https://mlsanity.com/paper/2007.11921/) (2020)
- [Protocol for implementing quantum nonparametric learning with trapped ions](https://mlsanity.com/paper/1906.03388/) (2019)

## Built on by (most cited first, 30 of 43)

- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [The Inductive Bias of Quantum Kernels](https://mlsanity.com/paper/2106.03747/) (2021)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [Training Quantum Embedding Kernels on Near-Term Quantum Computers](https://mlsanity.com/paper/2105.02276/) (2021)
- [Recent advances for quantum classifiers](https://mlsanity.com/paper/2108.13421/) (2021)
- [Bandwidth Enables Generalization in Quantum Kernel Models](https://mlsanity.com/paper/2206.06686/) (2022)
- [A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerance](https://mlsanity.com/paper/2401.11351/) (2024)
- [QKSAN: A Quantum Kernel Self-Attention Network](https://mlsanity.com/paper/2308.13422/) (2023)
- [The dilemma of quantum neural networks](https://mlsanity.com/paper/2106.04975/) (2021)
- [Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classification](https://mlsanity.com/paper/2301.01597/) (2022)
- [Quantum kernels for real-world predictions based on electronic health records](https://mlsanity.com/paper/2112.06211/) (2021)
- [Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applications](https://mlsanity.com/paper/2307.00908/) (2023)
- [Quantum Neural Network Classifiers: A Tutorial](https://mlsanity.com/paper/2206.02806/) (2022)
- ['Eliv'agar: Efficient Quantum Circuit Search for Classification](https://mlsanity.com/paper/2401.09393/) (2024)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Fock State-enhanced Expressivity of Quantum Machine Learning Models](https://mlsanity.com/paper/2107.05224/) (2021)
- [Quantum Advantage Seeker with Kernels (QuASK): a software framework to speed up the research in quantum machine learning](https://mlsanity.com/paper/2206.15284/) (2022)
- [Quantum Gaussian Process Regression for Bayesian Optimization](https://mlsanity.com/paper/2304.12923/) (2023)
- [Quantum Machine Learning for Finance](https://mlsanity.com/paper/2109.04298/) (2021)
- [A kernel-based quantum random forest for improved classification](https://mlsanity.com/paper/2210.02355/) (2022)
- [Neural auto-designer for enhanced quantum kernels](https://mlsanity.com/paper/2401.11098/) (2024)
- [Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey](https://mlsanity.com/paper/2409.07626/) (2024)
- [On exploring the potential of quantum auto-encoder for learning quantum systems](https://mlsanity.com/paper/2106.15432/) (2021)
- [Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning](https://mlsanity.com/paper/2204.06904/) (2022)
- [Power of Quantum Generative Learning](https://mlsanity.com/paper/2205.04730/) (2022)
- [Transition Role of Entangled Data in Quantum Machine Learning](https://mlsanity.com/paper/2306.03481/) (2023)
- [Accelerating variational quantum algorithms with multiple quantum processors](https://mlsanity.com/paper/2106.12819/) (2021)
- [Coreset selection can accelerate quantum machine learning models with provable generalization](https://mlsanity.com/paper/2309.10441/) (2023)
- [Predictive Performance of Deep Quantum Data Re-uploading Models](https://mlsanity.com/paper/2505.20337/) (2025)
- [Shot-frugal and Robust quantum kernel classifiers](https://mlsanity.com/paper/2210.06971/) (2022)

## Abstract (arXiv)

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.