Despite the mounting anticipation for the quantum revolution, the success of Quantum Machine Learning (QML) in the Noisy Intermediate-Scale Quantum (NISQ) era hinges on a largely unexplored factor: the generalization error bound, a cornerstone of robust and reliable machine learning models. Current QML research, while exploring novel algorithms and applications extensively, is predominantly situated in the context of noise-free, ideal quantum computers. However, Quantum Circuit (QC) operations in NISQ-era devices are susceptible to various noise sources and errors. In this article, we conduct a Systematic Mapping Study (SMS) to explore the state-of-the-art generalization bound for supervised QML in NISQ-era and analyze the latest practices in the field. Our study systematically summarizes the existing computational platforms with quantum hardware, datasets, optimization techniques, and the common properties of the bounds found in the literature. We further present the performance accuracy of various approaches in classical benchmark datasets like the MNIST and IRIS datasets. The SMS also highlights the limitations and challenges in QML in the NISQ era and discusses future research directions to advance the field. Using a detailed Boolean operators query in five reliable indexers, we collected 544 papers and filtered them to a small set of 37 relevant articles. This filtration was done following the best practice of SMS with well-defined research questions and inclusion and exclusion criteria.

翻译：尽管对量子革命的期待日益高涨，但量子机器学习在含噪声中等规模量子时代的成功，很大程度上取决于一个尚未充分探索的因素：泛化误差界——这是构建稳健可靠机器学习模型的基石。当前的量子机器学习研究在广泛探索新算法与应用的同时，主要基于无噪声的理想量子计算机背景展开。然而，NISQ时代设备中的量子电路操作易受各类噪声源与误差的影响。本文通过系统图谱研究，探索了NISQ时代监督式量子机器学习的前沿泛化误差界，并分析了该领域的最新实践。我们的研究系统总结了现有量子硬件计算平台、数据集、优化技术以及文献中发现的误差界共性特征。我们进一步展示了各类方法在经典基准数据集上的性能精度。该图谱研究同时揭示了NISQ时代量子机器学习存在的局限与挑战，并讨论了推动该领域发展的未来研究方向。通过在五个可靠索引数据库中使用精细的布尔运算符查询，我们收集了544篇文献，并筛选出37篇相关文章。此筛选过程遵循系统图谱研究的最佳实践，采用明确定义的研究问题及纳入排除标准。