Effect of alternating layered ansatzes on trainability of projected quantum kernel

TL;DR

This paper investigates how alternating layered ansatzes affect the trainability of projected quantum kernels, revealing that shallow circuits and less entangled initial states mitigate the vanishing similarity issue, thus improving quantum kernel methods.

Contribution

It provides analytical and numerical insights into the conditions under which the vanishing similarity problem can be avoided in projected quantum kernels using alternating layered ansatzes.

Findings

Variance depends on circuit depth, local unitary block size, and initial state.

Shallow alternating layered ansatzes help avoid vanishing similarity.

Highly entangled initial states can cause trainability issues.

Abstract

Quantum kernel methods have been actively examined from both theoretical and practical perspectives due to the potential of quantum advantage in machine learning tasks. Despite a provable advantage of fine-tuned quantum kernels for specific problems, widespread practical usage of quantum kernel methods requires resolving the so-called vanishing similarity issue, where exponentially vanishing variance of the quantum kernels causes implementation infeasibility and trainability problems. In this work, we analytically and numerically investigate the vanishing similarity issue in projected quantum kernels with alternating layered ansatzes. We find that variance depends on circuit depth, size of local unitary blocks and initial state, indicating the issue is avoidable if shallow alternating layered ansatzes are used and initial state is not highly entangled. Our work provides some insights into design principles of projected quantum kernels and implies the need for caution when using highly entangled states as input to quantum kernel-based learning models.