Towards understanding the power of quantum kernels in the NISQ era

Abstract

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.

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• Biology and medicine in the landscape of quantum advantages
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• Quantum Neural Network Classifiers: A Tutorial
• Quantum Machine Learning for Finance
• Quantum Phase Recognition via Quantum Kernel Methods
• Fock State-enhanced Expressivity of Quantum Machine Learning Models
• Quantum Gaussian Process Regression for Bayesian Optimization
• Quantum kernels to learn the phases of quantum matter
• Noisy Quantum Kernel Machines
• Transition Role of Entangled Data in Quantum Machine Learning
• Quantum Advantage Seeker with Kernels (QuASK): a software framework to speed up the research in quantum machine learning
• On exploring the potential of quantum auto-encoder for learning quantum systems
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• Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey
• The dilemma of quantum neural networks
• Enhanced feature encoding and classification on distributed quantum hardware
• The Inductive Bias of Quantum Kernels
• Quantum machine learning for multiclass classification beyond kernel methods
• Almost fault-tolerant quantum machine learning with drastic overhead reduction
• Accelerating variational quantum algorithms with multiple quantum processors
• Benchmarking of quantum fidelity kernels for Gaussian process regression
• Quantum fidelity kernel with a trapped-ion simulation platform