Quantum kernel methods are a candidate for quantum speed-ups in supervised machine learning. The number of quantum measurements N required for a reasonable kernel estimate is a critical resource, both from complexity considerations and because of the constraints of near-term quantum hardware. We emphasize that for classification tasks, the aim is reliable classification and not precise kernel evaluation, and demonstrate that the former is far more resource efficient. Furthermore, it is shown that the accuracy of classification is not a suitable performance metric in the presence of noise and we motivate a new metric that characterizes the reliability of classification. We then obtain a bound for N which ensures, with high probability, that classification errors over a dataset are bounded by the margin errors of an idealized quantum kernel classifier. Using chance constraint programming and the subgaussian bounds of quantum kernel distributions, we derive several Shot-frugal and Robust (ShofaR) programs starting from the primal formulation of the Support Vector Machine. This significantly reduces the number of quantum measurements needed and is robust to noise by construction. Our strategy is applicable to uncertainty in quantum kernels arising from any source of unbiased noise.

翻译：量子核方法是监督机器学习中实现量子加速的候选方案。从复杂性考量及近期量子硬件的限制出发，获得合理核估计所需的量子测量次数N是关键资源。我们强调，在分类任务中，目标是可靠分类而非精确核评估，并证明前者在资源利用上高效得多。此外，研究表明，在存在噪声的情况下，分类准确率并非合适的性能指标，我们提出了一种新的度量标准来表征分类可靠性。随后，我们推导出N的界限，该界限能以高概率确保，数据集上的分类误差受理想化量子核分类器边际误差的限制。利用机会约束规划和量子核分布的次高斯界限，我们从支持向量机的原始公式出发，推导出多个"节俭射击鲁棒"（ShofaR）方案。这显著降低了所需的量子测量次数，并且从构造上对噪声具有鲁棒性。我们的策略适用于由任何无偏噪声源引起的量子核不确定性。