Beyond bilinear controllability : applications to quantum control

TL;DR

This paper extends quantum control theory beyond traditional bilinear models by providing a new controllability criterion applicable to more complex, non-linear control scenarios involving sums of real functionals of controls.

Contribution

It introduces a novel controllability criterion for quantum systems with non-linear control dependencies, surpassing the limitations of bilinear models.

Findings

New controllability criterion for non-linear quantum control systems

Applicable to sums of real functionals of controls

Enhances understanding of quantum system controllability

Abstract

Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent works. Motivated by these applications, we give in this paper a criterion that applies to situations where the evolution operator is expressed as sum of possibly non-linear real functionals of the control that multiplies some time independent (coupling) operators.