Hybrid Quantum Selection of Learning Rates in Language-Model Training: Termination Criteria and the Cost Against Classical Selection

Learning-rate choices strongly affect language-model fine-tuning, and prior work shows that layer-wise learning rates can improve training; however, the best layer-group learning-rate profile is generally unknown. This paper studies quantum minimum finding as a layer-group learning-rate selector for a future coherent quantum training architecture. The search combines Dürr–Høyer minimum finding with BBHT search and considers two classes of stopping policies: fixed-budget and confidence-based termination. To simulate a coherent quantum search for the best learning-rate profile, measured profile scores at fixed training checkpoints are used to construct a lookup oracle that reproduces the required search behavior. The associated quantum-selection cost is evaluated under both a unit-cost model and IBM hardware-informed timing estimates. Experiments on a 1.5-billion-parameter language-model fine-tune evaluate when quantum selection can reduce the cost of exhaustive profile search, which becomes classically prohibitive as the learning-rate profile space grows.