Training Quantum Embedding Kernels on Near-Term Quantum Computers
This work addresses the problem of making quantum kernel methods feasible for machine learning practitioners on current quantum hardware, but it is incremental as it builds on existing quantum embedding kernel techniques.
The paper tackles the practical challenges of implementing quantum embedding kernels on noisy near-term quantum computers, focusing on optimizing variational parameters to improve classification accuracy and mitigating noise effects, with results demonstrated through numerical experiments and hardware tests.
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.