Degenerate eigensubspace in a triangle-level system and its geometric quantum control

Degenerate eigensubspace in a triangle-level system and its geometric quantum control The non-Abelian geometric phases appear only in a degenerate subspace and the most familiar model with such a subspace is the N-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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Degenerate eigensubspace in a triangle-level system and its geometric quantum control

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Degenerate eigensubspace in a triangle-level system and its geometric quantum control

Abstract

The non-Abelian geometric phases appear only in a degenerate subspace and the most familiar model with such a subspace is the N-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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Publisher
The American Physical Society
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.012333
Publisher site
See Article on Publisher Site

Abstract

The non-Abelian geometric phases appear only in a degenerate subspace and the most familiar model with such a subspace is the N-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.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jul 27, 2017

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