Complex control protocols and sensitivity to experimental imperfections have limited the practical implementation of quantum gate operations. Here, we present an analytical framework for universal single-qubit gates using rotational states of ultracold NaCs molecules. By encoding qubits in the lowest rotational energy levels, we employ a first-order Magnus expansion to derive closed-form unitary evolution from an optimized two-pulse sequence. This approach establishes precise amplitude and phase conditions for arbitrary single-qubit rotations, achieving gate fidelities above 0.9999 in numerical simulations. We further demonstrate that complex multi-gate sequences, including phase-locked operations, can be executed with minimal population leakage into auxiliary states. The time-dependent molecular orientation is shown to faithfully encode both the gate truth table and coherence dynamics, enabling practical gate tomography via weak-field polarization detection. Our analytical method is also applicable to other molecules and physical platforms, offering a potential path to high-fidelity, scalable molecular quantum processors.
@article{arxiv.2605.03461,
title = {Analytical two-pulse control of universal single-qubit gates in rotational ultracold NaCs molecules},
author = {Qi Chen and Hao-Xuan Luo and Jin-Kang Guo and Qian-Qian Hong and Li-Bao Fan and Chuan-Cun Shu},
journal= {arXiv preprint arXiv:2605.03461},
year = {2026}
}