Robustness of non-adiabatic geometrical quantum gates from the viewpoint of composite pulses

Geometrical phases are expected to be robust against noise, but it is still an open question. In this presentation, we discuss two points. First, we show some of composite pulses widely employed in NMR are regarded as non-adiabatic geometrical quantum gates, in which the Aharanov-Anandan phase is used. Secondly, we study their robustness against fluctuation with a simple model. In our model, the fluctuation in control parameters are visualized as the fluctuation of the trajectory on the Bloch sphere. We show the composite pulses under consideration are still non-adiabatic geometrical quantum gates even in the presence of fluctuation; no dynamical phase appear. We also point out that the proper selection of noise model is important for evaluating the robustness in geometrical quantum gates; for example, the cyclic time evolution of a quantum system should be ensured. Although the composite pulses are usually employed in order to compensate imperfections in individual pulses such as resonance off-set and amplitude errors, we find that they can possess robustness against fluctuations in control parameters.