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.

翻译：量子机器学习（QML）通过量子核方法等途径获得了广泛关注。尽管这些方法前景广阔，但其量子特性带来了固有的挑战。其中一个主要挑战是由于量子设备上执行的电路运行次数有限，导致估计的核值分辨率不足。本研究提出了一套完整的规则与启发式方法体系，用于估计量子核方法所需的电路运行次数。我们引入了两种关键效应，它们需要通过增加电路运行次数来提高测量精度：扩散效应与集中效应。这些效应在保真度核与投影量子核的背景下进行了分析。针对这些现象，我们开发了一种估计核值所需精度的方法，进而将其转化为电路运行次数。通过大量数值模拟，我们的方法在指数值集中问题上得到了验证。我们强调，量子核方法不仅应从机器学习性能的角度考量，还需结合资源消耗的背景进行评估。研究结果为理解量子核方法的潜在优势提供了见解，为其在量子机器学习任务中的应用提供了指导。