arXiv2026
Precision measurements of molecules offer an unparalleled paradigm to probe physics beyond the Standard Model. The rich internal structure within these molecules makes them exquisite sensors for detecting fundamental symmetry violations, local position invariance, and dark matter. While trapping and control of diatomic and a few very simple polyatomic molecules have been experimentally demonstrated, leveraging the complex rovibrational structure of more general polyatomics demands the development of robust and efficient quantum control schemes. In this study, we present reinforcement-learning quantum-logic spectroscopy (RL-QLS), a general, reinforcement-learning-designed, quantum logic approach to prepare molecular ions in single, pure quantum states. The reinforcement learning agent optimizes the pulse sequence, each followed by a projective measurement, and probabilistically manipulates the collapse of the quantum system to a single state. The performance of the RL-QLS control algorithm is numerically demonstrated for the polyatomic molecule H$_3$O$^+$ with 130 thermally populated eigenstates and degenerate transitions within inversion doublets, where quantum Markov decision process modeling and a physics-informed reward function play a key role, as well as for CaH$^+$ under the disturbance of environmental thermal radiation. The developed theoretical framework cohesively integrates techniques from quantum chemistry, AMO physics, and artificial intelligence, and we expect that the results can be readily implemented for quantum control of polyatomic molecular ions with densely populated structures, thereby enabling experimental tests of fundamental theories.