# Robust optimal control of two-level quantum systems

## TL;DR

This paper develops optimal control strategies for two-level quantum systems that are robust against uncertainties, using Pontryagin's principle to derive minimal energy and time solutions and analyzing the control landscape complexity.

## Contribution

It introduces a method to find global optimal pulses for robustness in quantum control, providing insights into the control landscape's structure and complexity.

## Key findings

- Derived global optimal pulses for robustness against uncertainties.
- Established bounds on the control landscape dimension.
- Provided estimates of control complexity for robust quantum control.

## Abstract

We investigate the time and the energy minimum optimal solutions for the robust control of two-level quantum systems against offset or control field uncertainties. Using the Pontryagin Maximum Principle, we derive the global optimal pulses for the first robustness orders. We show that the dimension of the control landscape is lower or equal to 2N for a field robust to the N th order, which leads to an estimate of its complexity.