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

Systematic control errors, specifically Rabi frequency fluctuations and frequency detuning, constitute a primary bottleneck for high-fidelity quantum gates across leading platforms. In this work, we present a robust pulse engineering framework for non-adiabatic holonomic quantum computing (NHQC) in qutrit systems, combining inverse engineering with time-dependent perturbation theory. We derive analytical conditions for pulse shaping that intrinsically eliminate second-order Rabi errors. Furthermore, our analysis reveals that second-order detuning errors are fundamentally linked to the accumulated population in the auxiliary excited state, making them impossible to eliminate in a single loop. To overcome this, we introduce a compensation pulse strategy that rigorously cancels these residual errors. Although this composite scheme doubles the gate duration, we demonstrate that the suppression of systematic errors yields a significant net gain in fidelity, achieving values exceeding 99.9% under realistic experimental imperfections ($\epsilon=0.2$, $\delta=2~\text{MHz}$). This framework provides a rigorous and experimentally feasible pathway for high-fidelity quantum control in superconducting circuits, trapped ions, and neutral atom systems.