We study the performance of approximate invariant-based inverse engineering, in which we design approximate dynamics so that it realizes a target process, determine its parameter schedule by using invariant-based inverse engineering, and control a true system according to it. We find that the worst-case performance of this control scheme can be evaluated by using the designed dynamics. By using a quantum speed limit formula, we derive a lower bound for overlap between the true dynamics and approximate dynamics. Notably, it can be calculated without knowledge of the true dynamics. We apply this bound to the above control scheme. We also find that the present result may be used for control scheduling.

• Received 8 December 2021
• Accepted 6 October 2022

DOI:https://doi.org/10.1103/PhysRevA.106.L040401