Understanding how to tailor quantum dynamics to achieve the desired evolution is a crucial problem in almost all quantum technologies. Oftentimes an otherwise ideal quantum dynamics is corrupted by unavoidable interactions, and finding ways to mitigate the unwanted effects of such interactions on the dynamics is a very active field of research. Here, we present a very general method for designing high-efficiency control sequences that are fully compatible with experimental constraints on available interactions and their tunability. Our approach relies on the Magnus expansion to find order by order the necessary corrections that result in a high-fidelity operation. In the end finding, the control fields are reduced to solve a set of linear equations. We illustrate our method by applying it to a number of physically relevant problems: the strong-driving limit of a two-level system, fast squeezing in a parametrically driven cavity, the leakage problem in transmon qubit gates, and the acceleration of SNAP gates in a qubit-cavity system.

在几乎所有量子技术中，了解如何调整量子动力学以实现所需的进化都是一个关键问题。通常，原本理想的量子动力学通常会被不可避免的相互作用所破坏，寻找减轻此类相互作用对动力学的不良影响的方法是一个非常活跃的研究领域。在这里，我们提出了一种非常通用的方法来设计高效控制序列，该序列与对可用相互作用及其可调性的实验约束完全兼容。我们的方法依赖于Magnus扩展来按顺序查找顺序，以进行必要的校正，从而实现高保真操作。最后发现，控制场被缩小以求解一组线性方程。我们通过将其应用于许多与物理相关的问题来说明我们的方法：