Systematic Rabi-amplitude and detuning errors remain important sources of infidelity in high-fidelity quantum gates. We develop a robust pulse-engineering scheme for nonadiabatic holonomic quantum computing in a three-level $\mathrm{\Lambda }$-type qutrit, combining inverse engineering with time-dependent perturbative analysis. Pulse shaping eliminates the leading second-order Rabi-amplitude contribution, while static detuning introduces a distinct population-mediated channel that cannot be removed within a single control loop. We therefore introduce a compensation loop that exactly cancels the dominant second-order $O_{13}^{\delta }$ contribution, with the residual $O_{12}^{\delta }$ channel further suppressed by pulse shaping. Using the logical average gate fidelity over the complete computational subspace, the optimized composite sequence reaches closed-system fidelities of 99.88%–99.99% for four representative single-qubit gates at $ϵ=0.2$ and $\delta /2\pi =2\mathrm{MHz}$. With phenomenological decoherence at $T_1=T_2=30\mathrm{\mu }\mathrm{s}$, the NOT and S gates retain fidelities of 99.72% and 99.79%, respectively, with a coherence-time crossover near $0.58\mathrm{\mu }\mathrm{s}$. These results identify the regime in which systematic-error suppression outweighs the decoherence cost of the additional control loop.

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• Adiabatic quantum optimization
• Geometric & topological phases
• Open quantum systems & decoherence
• Quantum computation
• Quantum control
• Quantum gates
• Quantum geometry
• Qudits