Parallel transport in rotating frames and projective holonomic quantum computation

• URL: http://arxiv.org/abs/2405.20812v2
• Date: Fri, 18 Oct 2024 14:39:24 GMT
• Title: Parallel transport in rotating frames and projective holonomic quantum computation
• Authors: Ole Sönnerborn,
• Abstract summary: We develop a framework for nonadiabatic holonomic quantum computation with projective gates. We extend the isoholonomic inequality to projective gates, establishing a minimum execution time for projective holonomic quantum gates.
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• Abstract: Nonadiabatic holonomic quantum computation is a promising approach for implementing quantum gates, offering both efficiency and robustness against certain types of errors. A key element of this approach is a geometric constraint known as the parallel transport condition. In line with the principle of covariance, this condition must be appropriately modified when changing reference frames. In this paper, we detail how to adjust the parallel transport condition when transitioning from the laboratory frame to a rotating reference frame. Furthermore, building on gauge invariance considerations, we develop a framework for nonadiabatic holonomic quantum computation with projective gates. The parallel transport condition of this framework effectively addresses the issue of global dynamical phases inherent in conventional nonadiabatic holonomic quantum computation. Finally, we extend the isoholonomic inequality to projective gates, establishing a minimum execution time for projective holonomic quantum gates.

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