Rydberg atoms have emerged as a promising platform for physical implementation of quantum computation. Nonadiabatic holonomic quantum computation (NHQC) provides a powerful route toward high-fidelity and intrinsically robust quantum control. Here we propose a universal framework for robust quantum control based on geometric-optimized NHQC, enabling ultrafast and error-resilient quantum gates on Rydberg atoms. By optimizing geometric phases, we realize gate operations that effectively suppress Rabi-frequency errors while maximizing gate speed, thereby resolving the long-standing trade-off between robustness and evolution time encountered in previous optimized gate schemes. Numerical simulations on a Rydberg-atom platform show that our scheme achieves fidelities exceeding $99.999\mathrm{\%}$ for single-qubit gates and $99.94\mathrm{\%}$ for two-qubit entangling gates, even in the presence of decoherence and Rabi-frequency errors of up to $20\mathrm{\%}$. Therefore, our protocol offers a powerful path toward high-fidelity, error-resistant NHQC on the neutral-atom platform, with broad potential applications in scalable quantum information processing.

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• Geometric & topological phases
• Quantum computation
• Quantum control
• Rydberg atoms & molecules