Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Survey

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.