Robustness enhancement of universal noncyclic geometric gates via evolution optimization

Noncyclic geometric gates aim to overcome the stringent constraints of conventional cyclic conditions and enhance the flexibility in evolution choice. Conceptually, they can also avoid the error problems arising from the violation of cyclicity, thus holding significance for improving the fault tolerance of quantum gates. However, current research on noncyclic geometric gates lacks a comprehensive exploration of their flexibility in evolution choice and validation of their effectiveness in resilience against multiple error sources present in practical quantum systems. In this paper, we systematically evaluate all noncyclic evolution conditions, elucidate their corresponding potential geometric trajectories, and identify optimal conditions for enhancing gate robustness by quantifying the resilience of constructed noncyclic geometric gates against universal systematic errors and residual crosstalk error. The optimized gates demonstrate significant robustness advantages over representative dynamical Rabi gates and conventional cyclic geometric gates. Furthermore, we validate the physical feasibility of high-fidelity noncyclic geometric gates in superconducting quantum circuits, with focused investigation into the impacts of intrinsic leakage errors and decoherence effects. Therefore, this work establishes a critical foundation for robust gate implementation toward practical fault-tolerant quantum processors.