  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.
