Composite pulses in NMR as non-adiabatic geometric quantum gates; Classification of fluctuations from robustness of geometric phases

Ota, Yukihiro; Kondo, Yasushi*

We show that some composite pulses widely employed in nuclear magnetic resonance experiments are regarded as non-adiabatic geometric quantum gates with Aharonov-Anandan phases. Thus, we obtain an alternative understanding of such techniques from fundamental viewpoints in quantum mechanics. To examine the robustness of such composite pulses against fluctuations, we propose a practical noise model in a two-level system. Then, we find that the composite pulses have purely geometrical nature even under a certain type of fluctuations. Furthermore, we classify fluctuations in terms of the robustness of geometric quantum gates.