Common Foundations of Optimal Control Across the Sciences: evidence of a free lunch

TL;DR

This paper reviews evidence across various sciences that many control landscapes are free of traps, facilitating easier optimization, and presents a unified mathematical framework highlighting commonalities in control behavior.

Contribution

It extends quantum control landscape analysis to other scientific domains, revealing shared features and proposing a unified mathematical framework.

Findings

Quantum control landscapes often have no traps.

Similar landscape features are observed in chemistry and biology.

A unified mathematical framework explains these commonalities.

Abstract

A common goal in the sciences is optimization of an objective function by selecting control variables such that a desired outcome is achieved. This scenario can be expressed in terms of a control landscape of an objective considered as a function of the control variables. At the most basic level, it is known that the vast majority of quantum control landscapes possess no traps, whose presence would hinder reaching the objective. This paper reviews and extends the quantum control landscape assessment, presenting evidence that the same highly favorable landscape features exist in many other domains of science. The implications of this broader evidence are discussed. Specifically, control landscape examples from quantum mechanics, chemistry, and evolutionary biology are presented. Despite the obvious differences, commonalities between these areas are highlighted within a unified mathematical framework. This mathematical framework is driven by the wide ranging experimental evidence on the ease of finding optimal controls (in terms of the required algorithmic search effort beyond laboratory set up overhead). The full scope and implications of this observed common control behavior pose an open question for assessment in further work.