Exact analysis of gate noise effects on non-adiabatic transformations of spin-orbit qubits

We considered various types of potential noise in gates controlling non-adiabatic holonomic transformations of spin-qubits in one and two dimensional systems with the Rashba interaction. It is shown how exact results can be derived for deviations of spin rotation angle and fidelity of the qubit transformation after a completed transformation. Errors in initial values of gate potentials and time-dependent drivings are considered and exact results for white gate noise are derived and analysed in detail. It is demonstrated how the drivings can be tuned to optimise the final fidelity of the transformation and to minimise the variances of qubit transformations.