Mathematical analysis of quantum control landscapes, which aims to prove either absence or existence of traps for quantum control objective functionals, is an important topic in quantum control. In this work, we provide a rigorous analysis of quantum control landscapes for ultrafast generation of single-qubit quantum gates and show, combining analytical methods based on a sophisticated analysis of spectrum of the Hessian, and numerical optimization methods such as gradient ascent pulse engineering, differential evolution, and dual annealing, that control landscape for ultrafast generation of phase shift gates is free of traps.

中文翻译：

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用于超快生成单量子位相移量子门的量子控制格局

量子控制景观的数学分析旨在证明量子控制目标泛函是否存在陷阱，是量子控制的一个重要课题。在这项工作中，我们对超快生成单量子位量子门的量子控制环境进行了严格分析，并结合基于对 Hessian 光谱的复杂分析的分析方法和梯度上升脉冲工程等数值优化方法，微分演化和双重退火，控制超快生成相移门的环境没有陷阱。