arXiv:2604.01455v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly explored for NP-hard combinatorial optimization problems, but most existing methods emphasize feasible-instance solution generation and do not explicitly address infeasibility detection. We propose an infeasibility-aware framework that combines certifiable dataset construction, supervised fine-tuning, and LLM-assisted downstream search. For the minor-embedding problem, we introduce a new mathematical programming formulation together with provable zero-phase infeasibility screening, which enables scalable construction of training instances labeled either as feasible with structured certificates or as certifiably infeasible. Using training data generated through this exact optimization pipeline, we show that an 8B-parameter LLM can be fine-tuned to jointly perform solution generation and infeasibility detection. We further utilize LLM outputs as warm starts for downstream local search, providing a practical way to accelerate optimization even when the LLM outputs are imperfect. Experiments show that our fine-tuned model improves overall accuracy by up to 30\% over GPT-5.2; meanwhile LLM-guided warm starts provide up to $2\times$ speedup compared with starting from scratch in downstream local search.

arXiv:2603.29944v2 Announce Type: replace-cross Abstract: Quantum sensing technologies offer transformative potential for ultra-sensitive biomedical sensing, yet their clinical translation remains constrained by classical noise limits and a reliance on macroscopic ensembles. We propose a unifying generational framework to organize the evolving landscape of quantum biosensors based on their utilization of quantum resources. First-generation devices utilize discrete energy levels for signal transduction but follow classical scaling laws. Second-generation sensors exploit quantum coherence to reach the standard quantum limit, while third-generation architectures leverage entanglement and spin squeezing to approach Heisenberg-limited precision. We further define an emerging fourth generation characterized by the end-to-end integration of quantum sensing with quantum learning and variational circuits, enabling adaptive inference directly within the quantum domain. By analyzing critical parameters such as bandwidth matching and sensor-tissue proximity, we identify key technological bottlenecks and propose a roadmap for transitioning from measuring physical observables to extracting structured biological information with quantum-enhanced intelligence.