--We present a novel approach for detecting hallucinations in large language models (LLMs) by analyzing the probabilistic divergence between prompt and response hidden-state distributions. Counterintuitively, we find that hallucinated responses exhibit smaller deviations from their prompts compared to grounded responses, suggesting that hallucinations often arise from superficial rephrasing rather than substantive reasoning. T o enhance sensitivity, we employ deep learn-able kernels that automatically adapt to capture nuanced geometric differences between distributions. Our approach outperforms existing baselines, demonstrating state-of-the-art performance on several benchmarks. The method remains competitive even without kernel training, offering a robust, scalable solution for hallucination detection. In recent years, large language models (LLMs) have been widely adopted in many applications. However, they often generate hallucinations -- incorrect or fabricated content that does not match real-world facts or the provided context [1]. The latter case is of special interest, as it refers to incorrect generations in retrieval-augmented generation (RAG) settings, where LLMs rely on retrieved information to answer user queries.

Quantum-enhanced machine learning is a rapidly evolving field that aims to leverage the unique properties of quantum mechanics to enhance classical machine learning. However, the practical applicability of these methods remains an open question, particularly in the context of real-world datasets and the limitations of current quantum hardware. This work performs a benchmark study of Quantum Kernel Estimation (QKE) and Quantum Kernel Training (QKT) with a focus on classification tasks. Through a series of experiments, the versatility and generalization capabilities of two quantum feature mappings, namely ZZFeatureMap and CovariantFeatureMap, are analyzed in this context. Remarkably, these feature maps have been proposed in the literature under the conjecture of possible near-term quantum advantage and have shown promising performance in ad-hoc datasets. This study explores both artificial and established reference datasets and incorporates classical machine learning methods, specifically Support Vector Machines (SVMs) and logistic regression, as baseline comparisons. Experimental results indicate that quantum methods exhibit varying performance across different datasets. While they outperform classical methods in ad-hoc datasets, they frequently encounter difficulties in generalizing to unseen test data when dealing with reference classical datasets, even if achieving high classification accuracy on the training data. It is suggested that the choice of the feature mapping and the optimization of kernel parameters through QKT are critical for maximizing the effectiveness of quantum methods.