Estimation of optimal control for two-level and three-level quantum systems with bounded amplitude

TL;DR

This paper presents a numerical scheme to estimate the quantum speed limit and optimal control shapes in two- and three-level quantum systems with bounded amplitudes, outperforming existing methods like CRAB.

Contribution

A systematic numerical method for estimating quantum speed limits and optimal controls in multi-level systems, especially when analytical solutions are unavailable.

Findings

Accurate estimation of quantum speed limits for two- and three-level systems.

Optimal control fields are simple and experimentally feasible.

Our method outperforms the CRAB algorithm in efficiency and accuracy.

Abstract

A systematic scheme is proposed to numerically estimate the quantum speed limit and temporal shape of optimal control in two-level and three-level quantum systems with bounded amplitude. For the two-level system, two quantum state transitions are studied as illustration. Comparisons between numerical and analytical results are made, and deviations are significantly small. For the three-level system, two critical time points are determined with high accuracy, and optimal controls are obtained for different durations. The shape of optimized control field is simple and does not switch frequently, thus are easy to implement in experiment. In addition, we compare our method with the chopped random basis (CRAB), and the performance of our method is much better than that of CRAB. Our scheme is of importance in estimating the quantum speed limit and optimal control for cases in which analytical solution is absent.