Composite pulses in NMR as non-adiabatic geometric quantum gates

TL;DR

This paper demonstrates that certain composite pulses used in NMR are actually non-adiabatic geometric quantum gates with Aharonov-Anandan phases, revealing a fundamental quantum mechanical aspect and their robustness against specific fluctuations.

Contribution

It uncovers the geometric quantum nature of composite pulses in NMR and analyzes their robustness under a practical noise model.

Findings

Composite pulses are non-adiabatic geometric quantum gates.

They retain their geometric nature under certain fluctuations.

The study provides insights into the quantum mechanical foundations of NMR techniques.

Abstract

We show that some composite pulses widely employed in NMR experiments are regarded as non-adiabatic geometric quantum gates with Aharanov-Anandan phases. Thus, we reveal the presence of a fundamental issue on quantum mechanics behind the traditional technique of the composite pulses. To examine the robustness of such composite pulses against fluctuations, we present a practical noise model in a two-level system. Then, we find that the composite pulses possesses purely geometrical nature even under a specific type of fluctuations.