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Bulletin of the American Physical Society

Experimental realization of non-abelian geometric gates with a superconducting three-level system

A. A. Abdumalikov, J. M. Fink, Kristinn Júlíusson, Marek Pechal, S. B. Berger, Andreas J. Wallraff, Stefan Filipp

Published Mar 19, 2013• 0 citations
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The non-Abelian geometric phases appear only in a degenerate subspace and the most familiar model with such a subspace is the NNN-pod system. Here we propose an alternative system to realize a non-Abelian gauge structure. We demonstrate that a three-level system with a triangular form can have two degenerate eigenstates which can induce non-Abelian geometric phases, and notably they are the lowest eigenstates of the system. As an application of the degenerate subspace, we propose an experimentally feasible scheme to realize a universal set of quantum gates based on the adiabatic non-Abelian geometric phases. To shorten the evolution time constrained by the adiabatic condition, the shortcut to adiabaticity is adopted to speed up the adiabatic geometric quantum gates. The combination of the intrinsic geometric characteristic and shortcut to adiabaticity makes the quantum operations fast and robust against certain control errors.
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