arXiv:2507.08255v1 Announce Type: cross Abstract: Missing data presents a critical challenge in real-world datasets, significantly degrading the performance of machine learning models. While Large Language Models (LLMs) have recently demonstrated remarkable capabilities in tabular data imputation, exemplified by frameworks like UnIMP, their reliance on classical embedding methods often limits their ability to capture complex, non-linear correlations, particularly in mixed-type data scenarios encompassing numerical, categorical, and textual features. This paper introduces Quantum-UnIMP, a novel framework that integrates shallow quantum circuits into an LLM-based imputation architecture. Our core innovation lies in replacing conventional classical input embeddings with quantum feature maps generated by an Instantaneous Quantum Polynomial (IQP) circuit. This approach enables the model to leverage quantum phenomena such as superposition and entanglement, thereby learning richer, more expressive representations of data and enhancing the recovery of intricate missingness patterns. Our experiments on benchmark mixed-type datasets demonstrate that Quantum-UnIMP reduces imputation error by up to 15.2% for numerical features (RMSE) and improves classification accuracy by 8.7% for categorical features (F1-Score) compared to state-of-the-art classical and LLM-based methods. These compelling results underscore the profound potential of quantum-enhanced representations for complex data imputation tasks, even with near-term quantum hardware.