Training Quantum Embedding Kernels on Near-Term Quantum Computers

Abstract

Kernel methods are a cornerstone of classical machine learning. The idea of using quantum computers to compute kernels has recently attracted attention. Quantum embedding kernels (QEKs) constructed by embedding data into the Hilbert space of a quantum computer are a particular quantum kernel technique that allows to gather insights into learning problems and that are particularly suitable for noisy intermediate-scale quantum devices. In this work, we first provide an accessible introduction to quantum embedding kernels and then analyze the practical issues arising when realizing them on a noisy near-term quantum computer. We focus on quantum embedding kernels with variational parameters. These variational parameters are optimized for a given dataset by increasing the kernel-target alignment, a heuristic connected to the achievable classification accuracy. We further show under which conditions noise from device imperfections influences the predicted kernel and provide a strategy to mitigate these detrimental effects which is tailored to quantum embedding kernels. We also address the influence of finite sampling and derive bounds that put guarantees on the quality of the kernel matrix. We illustrate our findings by numerical experiments and tests on actual hardware.

19 pages, 13 figures

References in corpus (12)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Power of data in quantum machine learning
• A rigorous and robust quantum speed-up in supervised machine learning
• Direct Fidelity Estimation from Few Pauli Measurements
• Virtual Distillation for Quantum Error Mitigation
• Exponential Error Suppression for Near-Term Quantum Devices
• Quantum computing models for artificial neural networks
• On barren plateaus and cost function locality in variational quantum algorithms
• Towards understanding the power of quantum kernels in the NISQ era
• Unified approach to data-driven quantum error mitigation

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