In Search of Quantum Advantage: Estimating the Number of Shots in Quantum Kernel Methods

TL;DR

This paper investigates how to estimate the number of quantum circuit runs needed for accurate kernel value measurements in quantum machine learning, addressing inherent quantum measurement challenges.

Contribution

It introduces rules and heuristics for determining the required measurement precision and circuit runs, considering effects like spread and concentration in quantum kernels.

Findings

Validated estimation approach through numerical simulations

Identified key effects impacting measurement precision

Provided resource consumption insights for quantum kernel methods

Abstract

Quantum Machine Learning (QML) has gathered significant attention through approaches like Quantum Kernel Machines. While these methods hold considerable promise, their quantum nature presents inherent challenges. One major challenge is the limited resolution of estimated kernel values caused by the finite number of circuit runs performed on a quantum device. In this study, we propose a comprehensive system of rules and heuristics for estimating the required number of circuit runs in quantum kernel methods. We introduce two critical effects that necessitate an increased measurement precision through additional circuit runs: the spread effect and the concentration effect. The effects are analyzed in the context of fidelity and projected quantum kernels. To address these phenomena, we develop an approach for estimating desired precision of kernel values, which, in turn, is translated into the number of circuit runs. Our methodology is validated through extensive numerical simulations, focusing on the problem of exponential value concentration. We stress that quantum kernel methods should not only be considered from the machine learning performance perspective, but also from the context of the resource consumption. The results provide insights into the possible benefits of quantum kernel methods, offering a guidance for their application in quantum machine learning tasks.