Exploiting Landscape Geometry to Enhance Quantum Optimal Control

TL;DR

This paper introduces a novel method to reshape irregular quantum optimal controls by exploiting the landscape geometry, specifically the null subspace of the Hessian, to produce smoother, experimentally feasible control protocols.

Contribution

It analytically proves the submanifold structure of QOC solutions in continuous systems and demonstrates a technique to smooth and compress controls for practical implementation.

Findings

Proven submanifold structure of QOC solutions in continuous variables.

Method to traverse the control landscape's null subspace.

Application to produce smoother, lab-ready control protocols.

Abstract

The successful application of Quantum Optimal Control (QOC) over the past decades unlocked the possibility of directing the dynamics of quantum systems. Nevertheless, solutions obtained from QOC algorithms are usually highly irregular, making them unsuitable for direct experimental implementation. In this paper, we propose a method to reshape those unattractive optimal controls. The approach is based on the fact that solutions to QOC problems are not isolated policies but constitute multidimensional submanifolds of control space. This was originally shown for finite-dimensional systems. Here, we analytically prove that this property is still valid in a continuous variable system. The degenerate subspace can be effectively traversed by moving in the null subspace of the hessian of the cost function, allowing for the pursuit of secondary objectives. To demonstrate the usefulness of this procedure, we apply the method to smooth and compress optimal protocols in order to meet laboratory demands.