Mitigation of systematic amplitude error in nonadiabatic holonomic operations

Nonadiabatic holonomic operations are based on nonadiabatic non-Abelian geometric phases, hence possessing the inherent geometric features for robustness against control errors. However, nonadiabatic holonomic operations are still sensitive to the systematic amplitude error induced by imperfect control of pulse timing or laser intensity. In this work, we present a scheme of nonadiabatic holonomic operations in order to mitigate the said systematic amplitude error. This is achieved by introducing a monitor qubit along with a conditional measurement on the monitor qubit that serves as an error correction device. We shall show how to filter out the undesired effect of the systematic amplitude error, thereby improving the performance of nonadiabatic holonomic operations.