Robust Non-Adiabatic Holonomic Gating in Qutrits via Inverse-Engineered Pulse Shaping and Error Compensation

Systematic Rabi-amplitude and detuning errors remain important sources of infidelity in high-fidelity quantum gates. We develop a robust pulse-engineering scheme for non-adiabatic holonomic quantum computing in a three-level Λ-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 δ contribution, with the residual O 12 δ 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 δ/2π=2 MHz. With phenomenological decoherence at T 1=T 2=30 μ s, the NOT and S gates retain fidelities of 99.72% and 99.79%, respectively, with a coherence-time crossover near 0.58 μ s. These results identify the regime in which systematic-error suppression outweighs the decoherence cost of the additional control loop.