Optimal Control of Inhomogeneous Ensembles

TL;DR

This paper introduces a systematic computational approach using pseudospectral methods for optimal control of inhomogeneous ensembles, with applications in quantum systems and beyond, addressing hardware imperfections and environmental variations.

Contribution

It develops a pseudospectral-based computational method for optimal ensemble control, demonstrating convergence and broad applicability beyond quantum systems.

Findings

Successfully designed quantum pulses for standard and novel applications.

Proved convergence of the pseudospectral method for ensemble control.

Applicable to systems with parameter uncertainty across science and engineering.

Abstract

Inhomogeneity, in its many forms, appears frequently in practical physical systems. Readily apparent in quantum systems, inhomogeneity is caused by hardware imperfections, measurement inaccuracies, and environmental variations, and subsequently limits the performance and efficiency achievable in current experiments. In this paper, we provide a systematic methodology to mathematically characterize and optimally manipulate inhomogeneous ensembles with concepts taken from ensemble control. In particular, we develop a computational method to solve practical quantum pulse design problems cast as optimal ensemble control problems, based on multidimensional pseudospectral approximations. We motivate the utility of this method by designing pulses for both standard and novel applications. We also show the convergence of the pseudospectral method for optimal ensemble control. The concepts developed here are applicable beyond quantum control, such as to neuron systems, and furthermore to systems with by parameter uncertainty, which pervade all areas of science and engineering.