ObjectiveQuantum logic gates serve as key components in realizing quantum computation, with high fidelity and robustness being directly linked to practical effectiveness. The geometric phase approach exhibits intrinsic resistance to local disturbances, offering unique advantages for efficient and stable quantum computing. Based on this, our study addresses error management in non-adiabatic geometric quantum gate operations, aiming to enhance gate fidelity through pulse design and parameter optimization, thereby achieving effective suppression of systematic errors.MethodsWe have established a theoretical framework for studying the robustness of non-adiabatic geometric quantum gates based on time-dependent perturbation theory. Using this framework, we analyzed the evolution of quantum gates and their responses to different types of errors. By deriving the expressions that quantify the impact of errors on fidelity, we proposed a new strategy for pulse design and parameter optimization based on an in-depth analysis of distinct error types.Results and discussionsOur results demonstrate that the proposed design significantly enhances the robustness and fidelity of quantum gates. Under the derived analytical conditions, our approach enables a simpler construction of quantum computing schemes and allows for rapid analysis of fidelity impacts from different errors. Additionally, we separated systematic errors based on the derived fidelity expressions, independently optimizing for detuning errors and Rabi errors. Through appropriate parameter selection and pulse design, we achieved second-order cancellation of Rabi errors in theory, maintaining high fidelity in complex environments. Numerical simulations further validated these results, demonstrating that this strategy yields clear fidelity advantages over conventional methods.ConclusionsThis study makes notable advances in pulse optimization for non-adiabatic geometric quantum gates, particularly in improving fidelity under Rabi error conditions. The proposed strategy, not dependent on strict pulse constraints, demonstrates broader applicability. This optimization approach not only provides an efficient solution for the current design of geometric quantum gates but also establishes a theoretical foundation for expanding their applicability and integration with other schemes in the future. Specifically, compared to some schemes in the literature, depending on the magnitude of the Rabi error, we can reduce the infidelity by 1 to 2 orders of magnitude. In conclusion, we developed a method to design pulses that are robust against systematic errors, particularly Rabi errors, while also being practical to implement experimentally.