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arXiv · 2001.05182

Brachistochrone Non-Adiabatic Holonomic Quantum Control

Bao-Jie Liu·Zheng-Yuan Xue·Man-Hong Yung
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Abstract

In quantum control, geometrical operations could provide an extra layer of robustness against control errors. However, the conventional non-adiabatic holonomic quantum computation (NHQC) is limited by the fact that all of the operations require exactly the same amount of evolution time, even for a small-angle rotation. Furthermore, NHQC confines the driving part of the Hamiltonian to strictly cover a fixed pulse area, making it sensitive to control errors. Here we present an unconventional approach of NHQC, termed brachistochronic NHQC, for bypassing these limitations. Specifically, with B-NHQC, non-Abelian geometric gates can be time-optimized by following the brachistochrone curve, minimizing the impact from the environmental decoherence. Additionally, we demonstrate that B-NHQC is compatible with composed pulses, which can further enhance the robustness against pulse errors. For benchmarking, we provide a thorough analysis on the performance of B-NHQC under experimental conditions; we found that the gate error can be reduced by as much as 64% compared with NHQC.

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Bao-Jie Liu, Zheng-Yuan Xue, Man-Hong Yung. 2020-01-15. Brachistochrone Non-Adiabatic Holonomic Quantum Control. https://arxiv.org/abs/2001.05182

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