We propose a novel method for constructing geometric quantum gates using three- or two-level systems, in which a controllable variable, the detuning between the driving frequency and the atomic energy spacing, is introduced to realize geometric transformations. In particular, we have two instantaneous eigenstates with opposite eigenvalues constituting a closed loop in the parameter space. The accumulated dynamical phase is then exactly cancelled when the loop is completed, which is beyond the traditional parallel-transport restriction. We apply the transitionless quantum driving method to enhance the speed and fidelity of geometric gates. Gate fidelity in the presence of decoherence is also estimated.

中文翻译：

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无过渡量子驱动辅助的基于Berry相的量子门

我们提出了一种使用三级或两级系统构造几何量子门的新方法，其中引入了一个可控变量，即驱动频率与原子能隙之间的失谐，以实现几何变换。特别是，我们有两个瞬时本征态，它们的本征值相反，构成了参数空间中的闭环。然后，当循环完成时，累积的动态相位将被完全取消，这超出了传统的并行传输限制。我们应用无过渡量子驱动方法来提高几何门的速度和保真度。还估计存在退相干时的门保真度。