# Robustness of Energy Landscape Controllers for Spin Rings under Coherent Excitation Transport

## TL;DR

This paper investigates the robustness of controllers for quantum spin rings in excitation transport, revealing differences in sensitivity depending on the optimization timing, which challenges classical control expectations.

## Contribution

It introduces a robustness analysis framework for quantum controllers based on logarithmic sensitivity, highlighting unique quantum-classical control differences.

## Key findings

- Quantum controllers show different error-sensitivity correlations based on timing optimization.
- Optimizing for exact time T versus a time window affects robustness characteristics.
- Classical control intuition does not fully apply to quantum excitation transport control.

## Abstract

The design and analysis of controllers to regulate excitation transport in quantum spin rings presents challenges in the application of classical feedback control techniques to synthesize effective control, and generates results in contradiction to the expectations of classical control theory. In this paper, we examine the robustness of controllers designed to optimize the fidelity of an excitation transfer to uncertainty in system and control parameters. We use the logarithmic sensitivity of the fidelity error as the measure of robustness, drawing on the classical control analog of the sensitivity of the tracking error. In our analysis we demonstrate that quantum systems optimized for coherent transport demonstrate significantly different correlation between error and the log-sensitivity depending on whether the controller is optimized for readout at an exact time T or over a time-window about T.