Cardiac arrest remains one of the most lethal conditions encountered in intensive care units. Despite the growing availability of electronic health record data, existing mortality prediction studies in this population largely depend on static summaries derived from early admission. Such approaches ignore the temporal progression of physiological deterioration and recovery that unfolds throughout a patient's ICU stay. To address this limitation, we introduce QuanTiMedAI, a quantum-agentic framework developed for cardiac arrest mortality prediction using agentic AI guided quantum enhancement time series model. The proposed system combines an agentic large language model (LLM) for clinically informed feature discovery with a compact quantum recurrent network for temporality aware mortality prediction. Our findings demonstrate that agentic LLM-guided feature selection consistently outperforms conventional feature selection approaches, and the proposed quantum architecture achieves competitive predictive performance through nonlinear feature enhancement while keeping the number of parameters very low. Through extensive experimentation on a MIMIC-IV cohort of cardiac arrest patients, QuanTiMedAI's quantum-enhanced architecture attains an AUROC of 0.852 using only 605 parameters, an improvement of approximately 2.9\% over a current state-of-the-art baseline for this task. A structured ablation study systematically validates the contribution of each architectural design choice. These results show that quantum-enhanced sequential modeling can exceed classical recurrent networks while using substantially fewer parameters.

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