Shuttling Compiler for Trapped-Ion Quantum Computers Based on Large Language Models

Trapped-ion quantum computers based on segmented traps rely on shuttling operations to establish long-range connectivity between sub-registers. Qubit routing dynamically reconfigures qubit positions so that all qubits involved in a gate operation are co-located within the same segment, a task whose complexity increases with system size. To address this challenge, we propose a layout-independent compilation strategy based on large language models (LLMs). Specifically, we fine-tune pretrained LLMs to generate the required shuttling operations. We evaluate this approach on linear and branched one-dimensional architectures using quantum circuits of up to 16 qubits. Our results show that the fine-tuned LLMs generate valid shuttling schedules and, in some cases, outperform previous shuttling compilers by requiring approximately 15 \% less shuttle overhead. However, results degrade as the algorithms increase in width and depth. In future, we plan to improve LLM-based shuttle compilation by enhancing our training pipeline using Direct Preference Optimization (DPO) and Gradient Regularized Policy Optimization (GRPO).