# Experimental verification of the inertial theorem control protocols

## TL;DR

This paper experimentally verifies the inertial theorem for quantum control in a trapped Ytterbium ion system, demonstrating stable analytical solutions for non-adiabatic driving that enhance rapid quantum manipulation.

## Contribution

It provides the first experimental validation of the inertial theorem for SU(2) systems, showing its effectiveness for fast and stable quantum control.

## Key findings

- Inertial solutions are stable to small deviations.
- The inertial theorem bridges sudden and adiabatic control regimes.
- Large deviations cause amplitude divergence, but phase remains accurate.

## Abstract

An experiment based on a trapped Ytterbium ion validates the inertial theorem for the SU(2) algebra. The qubit is encoded within the hyperfine states of the atom and controlled by RF fields. The inertial theorem generates analytical solutions for non-adiabatically driven systems that are `accelerated' slowly, bridging the gap between the sudden and adiabatic limits. These solutions are shown to be stable to small deviations, both experimentally and theoretically. As a result, the inertial solutions pave the way to rapid quantum control of closed, as well as open quantum systems. For large deviations from the inertial condition, the amplitude diverges while the phase remains accurate.