Experimental exploration over a quantum control landscape through nuclear magnetic resonance

TL;DR

This study experimentally investigates the control landscape of a quantum system using nuclear magnetic resonance, confirming theoretical predictions about the landscape's properties through various control experiments on a two-level proton system.

Contribution

It provides the first comprehensive experimental validation of quantum control landscape theory using NMR, demonstrating the practical applicability of theoretical predictions.

Findings

Experimental results match theoretical landscape predictions

Gradient and Hessian estimations successfully guide control optimization

NMR experiments confirm landscape topologies and features

Abstract

The growing successes in performing quantum control experiments motivated the development of control landscape analysis as a basis to explain these findings.When a quantum system is controlled by an electromagnetic field, the observable as a functional of the control field forms a landscape. Theoretical analyses have revealed many properties of control landscapes, especially regarding their slopes, curvatures, and topologies. A full experimental assessment of the landscape predictions is important for future consideration of controlling quantum phenomena. Nuclear magnetic resonance (NMR) is exploited here as an ideal laboratory setting for quantitative testing of the landscape principles. The experiments are performed on a simple two-level proton system in a H$_2$O-D$_2$O sample. We report a variety of NMR experiments roving over the control landscape based on estimation of the gradient and Hessian, including ascent or descent of the landscape, level set exploration, and an assessment of the theoretical predictions on the structure of the Hessian. The experimental results are fully consistent with the theoretical predictions. The procedures employed in this study provide the basis for future multispin control landscape exploration where additional features are predicted to exist.