Fast and Robust Non-Adiabatic Holonomic Gates for Qutrit Systems

Abstract: Motivated by shortcuts to adiabaticity, we develop a framework that combines inverse engineering with time-dependent perturbation theory to implement non-adiabatic holonomic quantum computing (NHQC) in qutrit systems under realistic error sources. We derive analytical conditions that suppress second-order Rabi errors through tailored pulse parameters and eliminate detuning errors via a compensation pulse. Our analysis reveals the cancellation from the compensation pulse, which ensures robust gate operations. The proposed approach, broadly applicable to superconducting qubits, trapped ions, and atom-based platforms, provides a pathway to fast and error-resilient holonomic gates, potentially for scalable quantum computing.